River networks evolve as migrating drainage divides reshape river basins and change network topology by capture of river channels. We demonstrate that a characteristic metric of river network geometry gauges the horizontal motion of drainage divides. Assessing this metric throughout a landscape maps the dynamic states of entire river networks, revealing diverse conditions: Drainage divides in the Loess Plateau of China appear stationary; the young topography of Taiwan has migrating divides driving adjustment of major basins; and rivers draining the ancient landscape of the southeastern United States are reorganizing in response to escarpment retreat and coastal advance. The ability to measure the dynamic reorganization of river basins presents opportunities to examine landscape-scale interactions among tectonics, erosion, and ecology.

Dynamic reorganization of river basins.

: A system is described which: (a) replaces existing sets of diverse terrain indices with a group of statistics for point-characteristics; (b) calculates all of these statistics in a single computer run from a single data set; and (c) utilizes available altitude matrix data The procedures are applicable to Altitude matrix data at any grid mesh From altitudes in each 3 x 3 submatrix, a quadratic surface is fitted and solved for its first and second horizontal and vertical derivatives at the central point This yields the slope gradient, slope aspect, profile convexity, and plan convexity at every point in the original matrix, except for the peripheral rows and columns These 'point' descriptors are presented as: (1) line-printer shaded maps; (2) histograms; (3) scatter plots of each pair; (4) matrix of pair-wise correlations, plus circular regressions on aspect, and several multiple regressions, and (5) summary (moment-based) statistics In general, the five basic descriptors have little relation to each other, except that gradient is usually a quadratic function of altitude A comparison is made with other approaches, such as spectral analysis and fractal modelling The long-distance persistence properties of terrain mean that considerable extra variance at long wavelengths is usually incorporated when the study area is extended Hence the auto correlation function varies with the length of series or size of area Variance of derivatives are also affected, but means, skews, and kurtoses are not

Statistical Characterization of Altitude Matrices by Computer. Report 6. An Integrated System of Terrain Analysis and Slope Mapping.

The impact-induced deposition of Al13 clusters with icosahedral structure on Ni(0 0 1) surface was studied by molecular dynamics (MD) simulation using Finnis–Sinclair potentials. The incident kinetic energy (Ein) ranged from 0.01 to 30 eV per atom. The structural and dynamical properties of Al clusters on Ni surfaces were found to be strongly dependent on the impact energy. At much lower energy, the Al cluster deposited on the surface as a bulk molecule. However, the original icosahedral structure was transformed to the fcc-like one due to the interaction and the structure mismatch between the Al cluster and Ni surface. With increasing the impinging energy, the cluster was deformed severely when it contacted the substrate, and then broken up due to dense collision cascade. The cluster atoms spread on the surface at last. When the impact energy was higher than 11 eV, the defects, such as Al substitutions and Ni ejections, were observed. The simulation indicated that there exists an optimum energy range, which is suitable for Al epitaxial growth in layer by layer. In addition, at higher impinging energy, the atomic exchange between Al and Ni atoms will be favourable to surface alloying.

Nuclear instruments and methods in physics research section B : beam interactions with materials and atoms

Hillslope Form and Process

Tectonic activity generates topography, and the variability of tectonic forcing is responsible for topographic patterns and variability of relief in fluvial landscapes Despite this basic relation, the inverse problem, by which features of the topography are used for inferring tectonic uplift rates, has proven challenging Here we develop formal linear inversion schemes to infer a record of the rate of relative uplift as a function of space and time from the long profiles of rivers The relative uplift rate is the difference between the rates of rock uplift and of the base level change The inversion schemes are based on a closed-form analytic solution to the transient linear stream power model, and to increase model resolution they make use of the multiplicity of information made available by multiple rivers and their tributaries The distribution of the fluvial response time to tectonic perturbations is a key component of the inversion scheme, as this determines which tectonic events are preserved in the topography We develop two inversion parameterizations that differ in their assumptions about the tectonic forcing: space-invariant and time-space variability with an assumed spatial distribution The inversion schemes are applied to the Inyo Mountains, an uplifted block along the western boundary of the Basin and Range Province in California Inversion results indicate that the range has been experiencing an acceleration of the relative uplift in the past ∼2-3 Ma We use the inversion results to constrain the paleotopography and paleo-erosion rate along the range and to recover the throw rate history along the fault that bounds the Inyo range

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2014JF003079

Tectonics from fluvial topography using formal linear inversion: Theory and applications to the Inyo Mountains, California

[1] We present a statistical technique for analyzing longitudinal channel profiles. Our technique is based on the integral approach to channel analysis: Drainage area is integrated over flow distance to produce a transformed coordinate, χ, which has dimensions of length. Assuming that profile geometry is conditioned by the stream power law, defined as E = KAmSn where E is erosion rate, K is erodibility, A is drainage area, S is channel gradient, and m and n are constants, the slope of a transformed profile in χ-elevation space should reflect the ratio of erosion rate to channel erodibility raised to a power 1/n; this quantity is often referred to as the channel steepness and represents channel slope normalized for drainage area. Our technique tests all possible contiguous segments in the channel network to identify the most likely locations where channel steepness changes and also identifies the most likely m/n ratio. The technique identifies locations where either erodibility or erosion rates are most likely to be changing. Tests on a simulated landscape demonstrate that the technique can accurately retrieve both the m/n ratio and the correct number and location of segments eroding at different rates where model assumptions apply. Tests on natural landscapes illustrate how the method can distinguish between spurious channel convexities due to incorrect selection of the m/n ratio from those which are candidates for changing erodibility or erosion rates. We also show how, given erosion or uplift rate constraints, the method can be used to constrain the slope exponent, n.

/pdf/a-statistical-framework-to-quantify-spatial-variation-in-2xg7qg12kv.pdf

A statistical framework to quantify spatial variation in channel gradients using the integral method of channel profile analysis

It has long been suggested that climate shapes land surface topography through interactions between rainfall, runoff and erosion in drainage basins1,2,3,4. The longitudinal profile of a river (elevation versus distance downstream) is a key morphological attribute that reflects the history of drainage basin evolution, so its form should be diagnostic of the regional expression of climate and its interaction with the land surface5,6,7,8,9. However, both detecting climatic signatures in longitudinal profiles and deciphering the climatic mechanisms of their development have been challenging, owing to the lack of relevant global data and to the variable effects of tectonics, lithology, land surface properties and human activities10,11. Here we present a global dataset of 333,502 river longitudinal profiles, and use it to explore differences in overall profile shape (concavity) across climate zones. We show that river profiles are systematically straighter with increasing aridity. Through simple numerical modelling, we demonstrate that these global patterns in longitudinal profile shape can be explained by hydrological controls that reflect rainfall–runoff regimes in different climate zones. The most important of these is the downstream rate of change in streamflow, independent of the area of the drainage basin. Our results illustrate that river topography expresses a signature of aridity, suggesting that climate is a first-order control on the evolution of the drainage basin.

/pdf/aridity-is-expressed-in-river-topography-globally-14yl8b54ub.pdf

Aridity is expressed in river topography globally.

Hillslope length is a fundamental attribute of landscapes, intrinsically linked to drainage density, landslide hazard, biogeochemical cycling and hillslope sediment transport. Existing methods to estimate catchment average hillslope lengths include inversion of drainage density or identification of a break in slope–area scaling, where the hillslope domain transitions into the fluvial domain. Here we implement a technique which models flow from point sources on hilltops across pixels in a digital elevation model (DEM), based on flow directions calculated using pixel aspect, until reaching the channel network, defined using recently developed channel extraction algorithms. Through comparisons between these measurement techniques, we show that estimating hillslope length from plots of topographic slope versus drainage area, or by inverting measures of drainage density, systematically underestimates hillslope length. In addition, hillslope lengths estimated by slope–area scaling breaks show large variations between catchments of similar morphology and area. We then use hillslope length–relief structure of landscapes to explore nature of sediment flux operating on a landscape. Distinct topographic forms are predicted for end-member sediment flux laws which constrain sediment transport on hillslopes as being linearly or nonlinearly dependent on hillslope gradient. Because our method extracts hillslope profiles originating from every ridgetop pixel in a DEM, we show that the resulting population of hillslope length–relief measurements can be used to differentiate between linear and nonlinear sediment transport laws in soil mantled landscapes. We find that across a broad range of sites across the continental United States, topography is consistent with a sediment flux law in which transport is nonlinearly proportional to topographic gradient

https://onlinelibrary.wiley.com/doi/pdf/10.1002/esp.3884

How long is a hillslope

. In many locations, our ability to study the processes which shape the Earth are greatly enhanced through the use of high-resolution digital topographic data. However, although the availability of such datasets has markedly increased in recent years, many locations of significant geomorphic interest still do not have high-resolution topographic data available. Here, we aim to constrain how well we can understand surface processes through topographic analysis performed on lower-resolution data. We generate digital elevation models from point clouds at a range of grid resolutions from 1 to 30 m, which covers the range of widely used data resolutions available globally, at three locations in the United States. Using these data, the relationship between curvature and grid resolution is explored, alongside the estimation of the hillslope sediment transport coefficient (D, in m2 yr−1) for each landscape. Curvature, and consequently D, values are shown to be generally insensitive to grid resolution, particularly in landscapes with broad hilltops and valleys. Curvature distributions, however, become increasingly condensed around the mean, and theoretical considerations suggest caution should be used when extracting curvature from landscapes with sharp ridges. The sensitivity of curvature and topographic gradient to grid resolution are also explored through analysis of one-dimensional approximations of curvature and gradient, providing a theoretical basis for the results generated using two-dimensional topographic data. Two methods of extracting channels from topographic data are tested. A geometric method of channel extraction that finds channels by detecting threshold values of planform curvature is shown to perform well at resolutions up to 30 m in all three landscapes. The landscape parameters of hillslope length and relief are both successfully extracted at the same range of resolutions. These parameters can be used to detect landscape transience and our results suggest that such work need not be confined to high-resolution topographic data. A synthesis of the results presented in this work indicates that although high-resolution (e.g., 1 m) topographic data do yield exciting possibilities for geomorphic research, many key parameters can be understood in lower-resolution data, given careful consideration of how analyses are performed.

/pdf/how-does-grid-resolution-modulate-the-topographic-expression-4jp890ejbj.pdf

How does grid-resolution modulate the topographic expression of geomorphic processes?

. We report a new program for calculating catchment-averaged denudation rates from cosmogenic nuclide concentrations. The method (Catchment-Averaged denudatIon Rates from cosmogenic Nuclides: CAIRN) bundles previously reported production scaling and topographic shielding algorithms. In addition, it calculates production and shielding on a pixel-by-pixel basis. We explore the effect of sampling frequency across both azimuth (Δθ) and altitude (Δϕ) angles for topographic shielding and show that in high relief terrain a relatively high sampling frequency is required, with a good balance achieved between accuracy and computational expense at Δθ = 8° and Δϕ = 5°. CAIRN includes both internal and external uncertainty analysis, and is packaged in freely available software in order to facilitate easily reproducible denudation rate estimates. CAIRN calculates denudation rates but also automates catchment averaging of shielding and production, and thus can be used to provide reproducible input parameters for the CRONUS family of online calculators.

/pdf/the-cairn-method-automated-reproducible-calculation-of-uulktc4qrn.pdf

Stuart W. D. Grieve

Papers

A statistical framework to quantify spatial variation in channel gradients using the integral method of channel profile analysis

Aridity is expressed in river topography globally.

How long is a hillslope

How does grid-resolution modulate the topographic expression of geomorphic processes?

The CAIRN method: automated, reproducible calculation of catchment-averaged denudation rates from cosmogenic nuclide concentrations