A linear inverse method to reconstruct paleo-topography

Fox, Matthew

doi:10.1016/j.geomorph.2019.03.034

Cited by 19 publications

(11 citation statements)

References 109 publications

(148 reference statements)

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“…The magnitude of fluvial incision, associated with changes in rock uplift, can be estimated from the relict topography upstream of major non‐lithological knickpoints (Berlin & Anderson, 2007; Gallen et al., 2013; Miller et al., 2013; Schildgen et al., 2012). In particular, the reconstructed river projection from the relict landscape allows permits determination of the supposed elevation of the paleo‐base level and hence the magnitude of minimum incision/surface uplift and the paleo‐relief before the development of the knickpoints (i.e., predating uplift; Fox, 2019; Heidarzadeh et al., 2017; Olivetti et al., 2016). These estimates, however, represent the incision into a specific surface which may be undergoing continued erosion itself.…”

Section: Methodsmentioning

confidence: 99%

Surface Uplift and Topographic Rejuvenation of a Tectonically Inactive Range: Insights From the Anti‐Atlas and the Siroua Massif (Morocco)

et al. 2023

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Section: Methodsmentioning

confidence: 99%

Surface Uplift and Topographic Rejuvenation of a Tectonically Inactive Range: Insights From the Anti‐Atlas and the Siroua Massif (Morocco)

et al. 2023

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“…such that lithologic variability in setting hillslope morphology should be limited. In addition, while common elsewhere in the OCR (Franczyk et al, 2019;LaHusen et al, 2020;Roering et al, 2005), the sites we have selected for analysis do not exhibit pronounced evidence of deep-seated landslides, which may bias C HT values, complicating comparison to known erosion rates from CRN analysis. As such, Hadsall Creek, the NFSR, and Bear Creek provide an ideal spectrum of hillslopes that allows for assessment of C HT measurement techniques (Fig.…”

Section: Study Site: Oregon Coast Rangementioning

confidence: 99%

Hilltop curvature as a proxy for erosion rate: wavelets enable rapid computation and reveal systematic underestimation

Struble

Roering

2021

Earth Surf. Dynam.

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Abstract. Estimation of erosion rate is an important component of landscape evolution studies, particularly in settings where transience or spatial variability in uplift or erosion generates diverse landform morphologies. While bedrock rivers are often used to constrain the timing and magnitude of changes in baselevel lowering, hilltop curvature (or convexity), CHT, provides an additional opportunity to map variations in erosion rate given that average slope angle becomes insensitive to erosion rate owing to threshold slope processes. CHT measurement techniques applied in prior studies (e.g., polynomial functions), however, tend to be computationally expensive when they rely on high-resolution topographic data such as lidar, limiting the spatial extent of hillslope geomorphic studies to small study regions. Alternative techniques such as spectral tools like continuous wavelet transforms present an opportunity to rapidly document trends in hilltop convexity across expansive areas. Here, we demonstrate how continuous wavelet transforms (CWTs) can be used to calculate the Laplacian of elevation, which we utilize to estimate erosion rate in three catchments of the Oregon Coast Range that exhibit varying slope angle, slope length, and hilltop convexity, implying differential erosion. We observe that CHT values calculated with the CWT are similar to those obtained from 2D polynomial functions. Consistent with recent studies, we find that erosion rates estimated with CHT from both CWTs and 2D polynomial functions are consistent with erosion rates constrained with cosmogenic radionuclides from stream sediments. Importantly, our CWT approach calculates curvature at least 103 times more quickly than 2D polynomials. This efficiency advantage of the CWT increases with domain size. As such, continuous wavelet transforms provide a compelling approach to rapidly quantify regional variations in erosion rate as well as lithology, structure, and hillslope sediment transport processes, which are encoded in hillslope morphology. Finally, we test the accuracy of CWT and 2D polynomial techniques by constructing a series of synthetic hillslopes generated by a theoretical nonlinear transport model that exhibit a range of erosion rates and topographic noise characteristics. Notably, we find that neither CWTs nor 2D polynomials reproduce the theoretically prescribed CHT value for hillslopes experiencing moderate to fast erosion rates, even when no topographic noise is added. Rather, CHT is systematically underestimated, producing a power law relationship between erosion rate and CHT that can be attributed to the increasing prominence of planar hillslopes that narrow the zone of hilltop convexity as erosion rate increases. As such, we recommend careful consideration of measurement length scale when applying CHT to estimate erosion rate in moderate to fast-eroding landscapes, where curvature measurement techniques may be prone to systematic underestimation.

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“…To reconstruct the paleo‐topography, we follow the simplification as in Fox (2019), which assumes that topography was in steady state prior to an uplift rate change. By discretizing the river profile into a limited number ( N ) of pixels, the present‐day ( t * = 0) elevation of pixel i can be expressed in a discrete form (Fox, 2019; Goren et al., 2014) as

z_{i} = {falsefalse}_{\sum}^{j = 1} (χ_{j} - χ_{j - 1}) u_{j}^{*},

in which the pixels are ordered upstream from the outlet such that χ 0 = 0.…”

Section: Methodsmentioning

confidence: 99%

z_{i} = {falsefalse}_{\sum}^{j = 1} (χ_{j} - χ_{j - 1}) u_{j}^{*},

in which the pixels are ordered upstream from the outlet such that χ 0 = 0. Then by dividing the uplift history into a small number ( q ) of intervals ( q ≪ N ), solving u * becomes an overdetermined inverse problem (Goren et al., 2014), for which we optimize using a linear least‐squares method (with the lsqnonneg function in the MATLAB software).…”

Section: Inverting the River Profile For Incision History And Paleotopographymentioning

confidence: 99%

Incision History of the Three Gorges, Yangtze River Constrained From Inversion of River Profiles and Low‐Temperature Thermochronological Data

2021

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As the longest river in Asia, development of the Yangtze River (Figure 1) was a major reorganization of the river networks in East Asia, and has played an important role in the evolution of the region's topography and landscape. During the Cenozoic, the collision between the Indian and Eurasian Plates led to the rise of the Tibetan Plateau (Rowley & Currie, 2006; Wang et al., 2008), which created the current east-tilting topography of East Asia. Previous studies suggest that this marked reshaping of the topography rearranged the drainage networks of the large rivers originating on the Tibetan Plateau, including the Upper Yangtze River (Clark et al., 2004; Clift et al., 2006; Zheng , 2015). These studies hypothesized that the Upper Yangtze River used to flow southwards and drain into the South China Sea through a path parallel to the Mekong River, for example, the paleo-Red River (Clift et al., 2006). In line with this hypothesis, some studies (e.g., Clark et al., 2004; Richardson et al., 2010) further suggest a reversal of the river flow direction in the Sichuan Basin (Figure 1b): prior to the connection between the Upper and Middle Yangtze River, rivers in the Sichuan Basin used to drain westwards, joining the western part of the Upper Yangtze River before flowing toward the South China Sea. This hypothesis predicts a paleo-drainage divide on the eastern margin of the Sichuan Basin, which separated the west-and east-flowing drainage systems. Therefore, to test the above hypothesis about the evolution of the Yangtze River, constraining the incision history of the potential paleo-drainage divide between the Upper and Middle Yangtze is crucial. On the eastern margin of the Sichuan Basin, several mountain ranges from high topography, including the Daba Shan, Wu Shan, and Xuefeng Shan (Figure 1b), which present as the most likely barriers between large drainage systems. These mountains formed as products of the collision between the North China and Yangtze Cratons during the Mesozoic (Li et al., 2017; Wang et al., 2003), and no evidence indicates a significant orogenic process in the area during the Cenozoic (Hu et al., 2006). Across the mountains, the

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A linear inverse method to reconstruct paleo-topography

Cited by 19 publications

References 109 publications

Surface Uplift and Topographic Rejuvenation of a Tectonically Inactive Range: Insights From the Anti‐Atlas and the Siroua Massif (Morocco)

Surface Uplift and Topographic Rejuvenation of a Tectonically Inactive Range: Insights From the Anti‐Atlas and the Siroua Massif (Morocco)

Hilltop curvature as a proxy for erosion rate: wavelets enable rapid computation and reveal systematic underestimation

Incision History of the Three Gorges, Yangtze River Constrained From Inversion of River Profiles and Low‐Temperature Thermochronological Data

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