A comprehensive system of definitions of land surface (topographic) curvatures, with implications for their application in geoscience modelling and prediction

Minár, Jozef; Evans, Ian S.; Jenčo, Marián

doi:10.1016/j.earscirev.2020.103414

Cited by 70 publications

(46 citation statements)

References 111 publications

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“…Similarly, hillslope geomorphic transport laws formulated for soil-mantled landscapes allow for estimation of uplift and erosion rates as well as prediction of the migration of hillcrests in response to landscape transience (Forte and Whipple, 2018;Mohren et al, 2020;Mudd, 2017;Mudd andFurbish, 2007, 2005;Roering, 2008;Roering et al, 2007Roering et al, , 2001Roering et al, , 1999. Over 100 years ago, it was proposed that hillslope form, specifically slope and curvature, may be an effective predictor of erosion rate, as hillslopes steepen and lengthen to accommodate increases in baselevel lowering (Gilbert, 1909(Gilbert, , 1877.…”

Section: Introductionmentioning

confidence: 99%

“…Despite the insensitivity of hillslope gradient in rapidly eroding landscapes, soil-mantled hillslopes remain an effective record of landscape transience and uplift. Specifically, hilltop curvature continues to respond to baselevel lowering when uplift and erosion rates are high, even as slope becomes insensitive to ever-increasing erosion rate (Hurst et al, 2012;Mohren et al, 2020;Roering et al, 2007). For a one-dimensional hillslope at steady state, erosion rate, E [L T −1 ], can be estimated as…”

Section: Introductionmentioning

confidence: 99%

“…As elaborated in the methodology proposed by Hurst et al (2012), the PFT is not required to pass through any digital elevation model (DEM) nodes; hence, λ can be understood as a smoothing scale, thus measuring the background C HT and removing topographic noise. While the application of PFTs has proven useful for calculating curvature to estimate erosion rate and predict spatial and temporal variations in uplift (e.g., Clubb et al, 2020;Godard et al, 2020;Hurst et al, 2019Hurst et al, , 2013Hurst et al, , 2012Mohren et al, 2020;Roering et al, 2007), PFTs are computationally cumbersome, hindering large-scale exploitation of highresolution topographic datasets that have become increasingly available. Here, we demonstrate that 2D continuous wavelet transforms (CWTs) provide an alternative and computationally efficient approach to calculating hilltop curvature, operating at least 10 2 to > 10 3 times faster than PFTs, with the relative efficiency advantage of CWTs increasing with the size of digital elevation models.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…The first derivative provides slope and aspect, two components of a 3D vector. The second derivative of elevation leads to a number of curvature values, which have confusing and inconsistent terminology and computations in GIS software (Minár, Evans, & Jenčo, 2020).…”

mentioning

confidence: 99%

LiDAR point cloud and ICESat‐2 evaluation of 1 second global digital elevation models: Copernicus wins

Guth

Geoffroy

2021

Transactions in GIS

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“…While a variety of polynomial forms and curvature definitions have been utilized (e.g. Minár et al, 2020;Moore et al, 1991), Hurst et al (2012) found that 6 term functions were sufficient for measuring curvature to estimate erosion rate. Specifically, Hurst et al (2012) used least squared regression to fit a surface, z, to topography, such that,…”

Section: Introductionmentioning

confidence: 99%

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

Struble¹,

Roering²

2021

Preprint

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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 102–103 times more quickly than 2D polynomials. 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 artifacts from 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.

show abstract

A comprehensive system of definitions of land surface (topographic) curvatures, with implications for their application in geoscience modelling and prediction

Cited by 70 publications

References 111 publications

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

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

LiDAR point cloud and ICESat‐2 evaluation of 1 second global digital elevation models: Copernicus wins

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

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