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  • Journal article
    Craske J, van Reeuwijk M, 2016,

    Generalised unsteady plume theory

    , Journal of Fluid Mechanics, Vol: 792, Pages: 1013-1052, ISSN: 1469-7645

    We develop a generalised unsteady plume theory and compare it with a new direct numerical simulation (DNS) dataset for an ensemble of statistically unsteady turbulent plumes. The theoretical framework described in this paper generalises previous models and exposes several fundamental aspects of the physics of unsteady plumes. The framework allows one to understand how the structure of the governing integral equations depends on the assumptions one makes about the radial dependence of the longitudinal velocity, turbulence and pressure. Consequently, the ill-posed models identified by Scase & Hewitt (J. Fluid Mech., vol. 697, 2012, p. 455) are shown to be the result of anon-physical assumption regarding the velocity profile. The framework reveals that these ill-posed unsteady plume models are degenerate cases amongst a comparatively large set of well-posed models that can be derived from the generalised unsteady plume equations that we obtain. Drawing on the results of DNS of a plume subjected to an instantaneous step change in its source buoyancy flux, we use the framework in a diagnostic capacityto investigate the properties of the resulting travelling wave. In general, the governing integral equations are hyperbolic, becoming parabolic in the limiting case of a `top-hat' model, and the travelling wave can be classified as lazy, pure or forced according to the particular assumptions that are invoked to close the integral equations. Guided by observations from the DNS data, we use the framework in a prognostic capacity to develop a relatively simple, accurate and well-posed model of unsteady plumes that is based on the assumption of a Gaussian velocity profile. An analytical solution is presented for a pure straight-sided plume that is consistent with the key features observed from the DNS.

  • Journal article
    Pelecanos L, Kontoe S, Zdravkovic L, 2016,

    Dam–reservoir interaction effects on the elastic dynamic response of concrete and earth dams

    , Soil Dynamics and Earthquake Engineering, Vol: 82, Pages: 138-141, ISSN: 0267-7261

    The relative effects of dam–reservoir interaction on the dynamic response of concrete and earth dams are studied. The amplification of accelerations at the dam crest is explored under harmonic acceleration load. For certain cases of concrete dams the accelerations can be significantly affected by the upstream reservoir, whereas this influence is smaller for earth dams.

  • Journal article
    Quattrocchi G, Gorman GJ, Piggott MD, Cucco Aet al., 2016,

    M2, overtides and compound tides generation in the Strait of Messina: the response of a non-hydrostatic, finite-element ocean model

    , JOURNAL OF COASTAL RESEARCH, Pages: 657-661, ISSN: 0749-0208
  • Journal article
    Smith R, Hill J, Collins GS, Piggott MD, Kramer S, Parkinson S, Wilson Cet al., 2016,

    Comparing approaches for numerical modelling of tsunami generation by deformable submarine slides

    , Ocean Modelling, Vol: 100, Pages: 125-140, ISSN: 1463-5003

    Tsunami generated by submarine slides are arguably an under-consideredrisk in comparison to earthquake-generated tsunami. Numerical simulationsof submarine slide-generated waves can be used to identify the important factorsin determining wave characteristics. Here we use Fluidity, an open sourcefinite element code, to simulate waves generated by deformable submarineslides. Fluidity uses flexible unstructured meshes combined with adaptivitywhich alters the mesh topology and resolution based on the simulationstate, focussing or reducing resolution, when and where it is required. Fluidityalso allows a number of different numerical approaches to be taken tosimulate submarine slide deformation, free-surface representation, and wavegeneration within the same numerical framework. In this work we use amulti-material approach, considering either two materials (slide and waterwith a free surface) or three materials (slide, water and air), as well as asediment model (sediment, water and free surface) approach. In all casesthe slide is treated as a viscous fluid. Our results are shown to be consistentwith laboratory experiments using a deformable submarine slide, anddemonstrate good agreement when compared with other numerical models.The three different approaches for simulating submarine slide dynamics andtsunami wave generation produce similar waveforms and slide deformationgeometries. However, each has its own merits depending on the application.Mesh adaptivity is shown to be able to reduce the computational cost withoutcompromising the accuracy of results.

  • Journal article
    Kramer SC, Piggott MD, 2016,

    A correction to the enhanced bottom drag parameterisation of tidal turbines

    , Renewable Energy, Vol: 92, Pages: 385-396, ISSN: 1879-0682

    Hydrodynamic modelling is an important tool for the development of tidalstream energy projects. Many hydrodynamic models incorporate the effect oftidal turbines through an enhanced bottom drag. In this paper we show thatalthough for coarse grid resolutions (kilometre scale) the resulting force exertedon the flow agrees well with the theoretical value, the force starts decreasingwith decreasing grid sizes when these become smaller than the length scale ofthe wake recovery. This is because the assumption that the upstream velocitycan be approximated by the local model velocity, is no longer valid. Using linearmomentum actuator disc theory however, we derive a relationship between thesetwo velocities and formulate a correction to the enhanced bottom drag formulationthat consistently applies a force that remains close to the theoretical value,for all grid sizes down to the turbine scale. In addition, a better understandingof the relation between the model, upstream, and actual turbine velocity, aspredicted by actuator disc theory, leads to an improved estimate of the usefullyextractable energy. We show how the corrections can be applied (demonstratedhere for the models MIKE 21 and Fluidity) by a simple modification of the dragcoefficient.

  • Journal article
    Johnson BC, Collins GS, Minton DA, Bowling TJ, Simonson BM, Zuber MTet al., 2016,

    Spherule layers, crater scaling laws, and the population of ancient terrestrial craters

    , Icarus, Vol: 271, Pages: 350-359, ISSN: 1090-2643

    Ancient layers of impact spherules provide a record of Earth's early bombardment history. Here, we compare different bombardment histories to the spherule layer record and show that 3.2-3.5 Ga the flux of large impactors (10-100 km in diameter) was likely 20-40 times higher than today. The E-belt model of early Solar System dynamics suggests that an increased impactor flux during the Archean is the result of the destabilization of an inward extension of the main asteroid belt (Bottke, W.F., Vokrouhlický, D., Minton, D., Nesvorný, D., Morbidelli, A., Brasser, R., Simonson, B., Levison, H.F., 2012. Nature 485, 78–81). Here, we find that the nominal flux predicted by the E-belt model is 7-19 times too low to explain the spherule layer record. Moreover, rather than making most lunar basins younger than 4.1 Gyr old, the nominal E-belt model, coupled with a corrected crater diameter scaling law, only produces two lunar basins larger than 300 km in diameter. We also show that the spherule layer record when coupled with the lunar cratering record and careful consideration of crater scaling laws can constrain the size distribution of ancient terrestrial impactors. The preferred population is main-belt-like up to ∼50 km in diameter transitioning to a steep distribution going to larger sizes.

  • Journal article
    Corbett LB, Bierman PR, Rood DH, 2016,

    Constraining multi-stage exposure-burial scenarios for boulders preserved beneath cold-based glacial ice in Thule, northwest Greenland

    , Earth and Planetary Science Letters, Vol: 440, Pages: 147-157, ISSN: 0012-821X

    Boulders and landscapes preserved beneath cold-based, nonerosiveglacial ice violate assumptions associated with simple cosmogenicexposure dating. In such a setting, simple single isotope exposure agesover estimate the latest period of surface exposure; hence, alternateapproaches are required to constrain the multi-stage exposure/burialhistories of such samples. Here, we report 28 paired analyses of 10Be and26Al in boulder samples from Thule, northwest Greenland. We use numericalmodels of exposure and burial as well as Monte Carlo simulations toconstrain glacial chronology and infer process in this Arctic regiondominated by cold-based ice. We investigate three specific cases that canarise with paired nuclide data: (1) exposure ages that are coeval withdeglaciation and 26Al/10Be ratios consistent with constant exposure; (2)exposure ages that pre-date deglaciation and 26Al/10Be ratios consistentwith burial following initial exposure; and (3) exposure ages that predatedeglaciation and 26Al/10Be ratios consistent with constant exposure.Most glacially-transported boulders in Thule have complex histories; somewere exposed for tens of thousands of years and buried for at leasthundreds of thousands of years, while others underwent only limitedburial. These boulders were recycled through different generations oftill over multiple glacial/interglacial cycles, likely experiencingpartial or complete shielding during interglacial periods due to rotationor shallow burial by sediments. Our work demonstrates that the landscapein Thule, like many high-latitude landscapes, was shaped over long timedurations and multiple glacial and interglacial periods throughout theQuaternary.

  • Software
    Piggott MD, 2016,

    Thetis

    Finite element flow solver for simulating coastal and estuarine flows.

  • Journal article
    Quan X, Zhang B, Liu JG, Wu Yet al., 2016,

    An Efficient General Algorithm for SAR Imaging: Complex Approximate Message Passing Combined With Backprojection

    , IEEE Geoscience and Remote Sensing Letters, Vol: 13, Pages: 535-539, ISSN: 1558-0571
  • Journal article
    Han B, Zdravkovic L, Kontoe S, 2016,

    Numerical and analytical investigation of compressional wave propagation in saturated soils

    , Computers and Geotechnics, Vol: 75, Pages: 93-102, ISSN: 1873-7633

    In geotechnical earthquake engineering, wave propagation plays afundamental role in engineering applications related to the dynamic response ofgeotechnical structures and to site response analysis. However, current engineeringpractice is primarily concentrated on the investigation of shear wave propagation andthe corresponding site response only to the horizontal components of the ground motion.Due to the repeated recent observations of strong vertical ground motions andcompressional damage of engineering structures, there is an increasing need to carry outa comprehensive investigation of vertical site response and the associated compressionalwave propagation, particularly when performing the seismic design for criticalstructures (e.g. nuclear power plants and high dams). Therefore, in this paper, thecompressional wave propagation mechanism in saturated soils is investigated byemploying hydro-mechanically (HM) coupled analytical and numerical methods. A HManalytical solution for compressional wave propagation is first studied based on Biot’stheory, which shows the existence of two types of compressional waves (fast and slowwaves) and indicates that their characteristics (i.e. wave dispersion and attenuation) arehighly dependent on some key geotechnical and seismic parameters (i.e. thepermeability, soil stiffness and loading frequency). The subsequent HM Finite Element(FE) study reproduces the duality of compressional waves and identifies the dominantpermeability ranges for the existence of the two waves. In particular the existence of theslow compression wave is observed for a range of permeability and loading frequencythat is relevant for geotechnical earthquake engineering applications. In order to accountfor the effects of soil permeability on compressional dynamic soil behaviour and soilproperties (i.e. P-wave velocities and damping ratios), the coupled consolidationanalysis is therefore recommended as the only tool capable of accurately simulating thedyna

  • Journal article
    Massart BYG, Jackson MD, Hampson GJ, Johnson HDet al., 2016,

    Effective flow properties of heterolithic, cross-bedded tidal sandstones: Part 2. Flow simulation

    , AAPG Bulletin, Vol: 100, Pages: 723-742, ISSN: 0149-1423

    Tidal heterolithic sandstone reservoirs are heterogeneous at the sub-meter scale, due to the ubiquitous presence of intercalated sandstone and mudstone laminae. Core-plug permeability measurements fail to sample a representative volume of this heterogeneity. Here we investigate the impact of mudstone drape distribution on the effective permeability of heterolithic, cross-bedded tidal sandstones using three-dimensional (3D) surface-based “mini-models” that capture the geometry of cross-beds at an appropriate scale. The impact of seven geometric parameters has been determined: (1) mudstone fraction, (2) sandstone laminae thickness, (3) mudstone drape continuity, (4) toeset dip, (5) climb angle of foreset-toeset surfaces, (6) proportion of foresets to toesets, and (7) trough or tabular geometry of the cross-beds.We begin by identifying a representative elementary volume (REV) of 1 m3, confirming that the model volume of 9 m3 yields representative permeability values. Effective permeability decreases as the mudstone fraction increases, and is highly anisotropic: vertical permeability falls to c. 0.5% of the sandstone permeability at a mudstone fraction of 25%, while the horizontal permeability falls to c. 5% and c. 50% of the sandstone value in the dip (across mudstone drapes) and strike (parallel to mudstone drapes) directions, respectively. There is considerable spread around these values, because each parameter investigated can significantly impact effective permeability, with the impact depending upon the flow direction and mudstone fraction. The results yield improved estimates of effective permeability in heterolithic, cross-bedded sandstones, which can be used to populate reservoir-scale model grid blocks using estimates of mudstone fraction and geometrical parameters obtained from core and outcrop-analog data.

  • Journal article
    Corbett LB, Bierman PR, Rood DH, 2016,

    An approach for optimizing in SITU cosmogenic 10BE sample preparation

    , Quaternary Geochronology, Vol: 33, Pages: 24-34, ISSN: 1871-1014

    Optimizing sample preparation for the isotopic measurement of 10Be extracted from quartz mineral separates has a direct positive effect on the accuracy and precision of isotopic analysis. Here, we demonstrate the value of tracing Be throughout the extraction process (both after dissolution and after processing), producing pure Be (by optimizing ion exchange chromatography methods and quantifying quartz mineral separate and final Be fraction purity), and minimizing backgrounds (through reducing both laboratory process blanks and 10B isobaric interference). These optimization strategies increase the amount of 10Be available for analysis during accelerator mass spectrometry (AMS), while simultaneously decreasing interference and contamination, and ensuring that sample performance matches standard performance during analysis. After optimization of our laboratory's extraction methodology, 9Be3+ ion beam currents measured during AMS analysis, a metric for sample purity and Be yield through the extraction process, matched the 9Be3+ beam currents of AMS standards analyzed at the same time considering nearly 800 samples. Optimization of laboratory procedures leads to purer samples that perform better, more consistently, and more similarly to standards during AMS analysis, allowing for improved precision and accuracy of measurements used for dating and quantification of Earth surface processes.

  • Journal article
    Van Dijk W, Densmore A, Singh A, Sinha R, Mason P, Joshi S, Nayak N, Kumar M, Shekhar S, Kumar D, Rai Set al., 2016,

    Linking the morphology of fluvial fan systems to aquifer stratigraphy in the Sutlej-Yamuna plain of northwest India

    , Journal of Geophysical Research, Vol: 121, Pages: 201-222, ISSN: 0148-0227

    The Indo-Gangetic foreland basin has some of the highest rates of groundwater extractionin the world, focused in the states of Punjab and Haryana in northwest India. Any assessment of theeffects of extraction on groundwater variation requires understanding of the geometry and sedimentaryarchitecture of the alluvial aquifers, which in turn are set by their geomorphic and depositional setting. Toassess the overall architecture of the aquifer system, we used satellite imagery and digital elevation modelsto map the geomorphology of the Sutlej and Yamuna fan systems, while aquifer geometry was assessedusing 243 wells that extend to ∼200 m depth. Aquifers formed by sandy channel bodies in the subsurfaceof the Sutlej and Yamuna fans have a median thickness of 7 and 6 m, respectively, and follow heavy-tailedthickness distributions. These distributions, along with evidence of persistence in aquifer fractions asdetermined from compensation analysis, indicate persistent reoccupation of channel positions and suggestthat the major aquifers consist of stacked, multistoried channel bodies. The percentage of aquifer material inindividual boreholes decreases down fan, although the exponent on the aquifer body thickness distributionremains similar, indicating that the total number of aquifer bodies decreases down fan but that individualbodies do not thin appreciably, particularly on the Yamuna fan. The interfan area and the fan marginal zonehave thinner aquifers and a lower proportion of aquifer material, even in proximal locations. We concludethat geomorphic setting provides a first-order control on the thickness, geometry, and stacking pattern ofaquifer bodies across this critical region.

  • Journal article
    Bao Q, Han K, Lin Y, Zhang B, Liu J, Hong Wet al., 2016,

    Imaging method for downward-looking sparse linear array three-dimensional synthetic aperture radar based on reweighted atomic norm

    , JOURNAL OF APPLIED REMOTE SENSING, Vol: 10, ISSN: 1931-3195
  • Journal article
    Bender AM, Amos CB, Bierman P, Rood DH, Staisch L, Kelsey H, Sherrod Bet al., 2016,

    Differential uplift and incision of the Yakima River terraces, central Washington State

    , Journal of Geophysical Research: Solid Earth, Vol: 121, Pages: 365-384, ISSN: 2169-9356

    The fault-related Yakima folds deform Miocene basalts and younger deposits of the Columbia Plateau in central Washington State. Geodesy implies ~2 mm/yr of NNE directed shortening across the folds, but until now the distribution and rates of Quaternary deformation among individual structures has been unclear. South of Ellensburg, Washington, the Yakima River cuts a ~600 m deep canyon across several Yakima folds, preserving gravel-mantled strath terraces that record progressive bedrock incision and related rock uplift. Here we integrate cosmogenic isochron burial dating of the strath terrace gravels with lidar analysis and field mapping to quantify rates of Quaternary differential incision and rock uplift across two folds transected by the Yakima River: Manastash and Umtanum Ridge. Isochron burial ages from in situ produced 26Al and 10Be at seven sites across the folds date episodes of strath terrace formation over the past ~2.9 Ma. Average bedrock incision rates across the Manastash (~88 m/Myr) and Umtanum Ridge (~46 m/Myr) anticlines are roughly 4 to 8 times higher than rates in the intervening syncline (~14 m/Myr) and outside the canyon (~10 m/Myr). These contrasting rates demonstrate differential bedrock incision driven by ongoing Quaternary rock uplift across the folds at rates corresponding to ~0.13 and ~0.06 mm/yr shortening across postulated master faults dipping 30 ± 10°S beneath the Manastash and Umtanum Ridge anticlines, respectively. The reported Quaternary shortening across the anticlines accounts for ~10% of the ~2 mm/yr geodetic budget, suggesting that other Yakima structures actively accommodate the remaining contemporary deformation.

  • Journal article
    Vire A, Spinneken J, Piggott MD, Pain CC, Kramer SCet al., 2016,

    Application of the immersed-body method to simulatewave–structure interactions

    , European Journal of Mechanics B: Fluids, Vol: 55, Pages: 330-339, ISSN: 1873-7390

    This study aims at demonstrating the capability of the immersed-body method to simulate wave–structure interactions using a non-linear finite-element model. In this approach, the Navier–Stokes equations are solved on an extended mesh covering the whole computational domain (i.e. fluids and structure). The structure is identified on the extended mesh through a nonzero solid-concentration field, which is obtained by conservatively mapping the mesh discretising the structure onto the extended mesh. A penalty term relaxes the fluid and structural velocities to one another in the regions covered by the structure. The paper is novel in that it combines the immersed-body method with wave modelling and mesh adaptivity. The focus of the paper is therefore on demonstrating the capability of this new methodology in reproducing well-established test cases, rather than investigating new physical phenomena in wave–structure interactions. Two cases are considered for a bottom-mounted pile. First, the pile is placed in a numerical wave tank, where propagating waves are modelled through a free-surface boundary condition. For regular and irregular waves, it is shown that the wave dynamics are accurately modelled by the computational fluid dynamics model and only small discrepancies are observed in the close vicinity of the structure. Second, the structure is subjected to a dam-break wave impact obtained by removing a barrier between air and water. In that case, an additional advection equation is solved for a fluid-concentration field that tracks the evolution of the air–water interface. It is shown that the load associated with the wave impact on the structure compares well with existing numerical and experimental data.

  • Journal article
    Davies DR, LeVoci G, Goes S, Kramer SC, Wilson CRet al., 2016,

    The Mantle Wedge's Transient 3-D Flow Regime and Thermal Structure

    , Geochemistry Geophysics Geosystems, Vol: 17, Pages: 78-100, ISSN: 1525-2027

    Arc volcanism, volatile cycling, mineralization, and continental crust formation are likely regulated by the mantle wedge's flow regime and thermal structure. Wedge flow is often assumed to follow a regular corner-flow pattern. However, studies that incorporate a hydrated rheology and thermal buoyancy predict internal small-scale-convection (SSC). Here, we systematically explore mantle-wedge dynamics in 3-D simulations. We find that longitudinal “Richter-rolls” of SSC (with trench-perpendicular axes) commonly occur if wedge hydration reduces viscosities to inline image Pa s, although transient transverse rolls (with trench-parallel axes) can dominate at viscosities of inline image Pa s. Rolls below the arc and back arc differ. Subarc rolls have similar trench-parallel and trench-perpendicular dimensions of 100–150 km and evolve on a 1–5 Myr time-scale. Subback-arc instabilities, on the other hand, coalesce into elongated sheets, usually with a preferential trench-perpendicular alignment, display a wavelength of 150–400 km and vary on a 5–10 Myr time scale. The modulating influence of subback-arc ridges on the subarc system increases with stronger wedge hydration, higher subduction velocity, and thicker upper plates. We find that trench-parallel averages of wedge velocities and temperature are consistent with those predicted in 2-D models. However, lithospheric thinning through SSC is somewhat enhanced in 3-D, thus expanding hydrous melting regions and shifting dehydration boundaries. Subarc Richter-rolls generate time-dependent trench-parallel temperature variations of up to inline image K, which exceed the transient 50–100 K variations predicted in 2-D and may contribute to arc-volcano spacing and the variable seismic velocity structures imaged beneath some arcs.

  • Journal article
    Portenga EW, Rood DH, Bishop P, Bierman PRet al., 2016,

    A late Holocene onset of Aboriginal burning in southeastern Australia

    , Geology, ISSN: 1943-2682

    The extent to which Aboriginal Australians used fire to modify their environment has been debated for decades and is generally based on charcoal and pollen records rather than landscape responses to land-use change. Here we investigate the sensitivity of in-situ–produced 10Be, an isotope commonly used in geomorphological contexts, to anthropogenic perturbations in the southeastern Australian Tablelands. Comparing 10Be-derived erosion rates from fluvial sediment (8.7 ± 0.9 mm k.y.–1; 1 standard error, SE; n = 11) and rock outcrops (5.3 ± 1.4 mm k.y.–1; 1 SE; n = 6) confirms that landscape lowering rates integrating over 104–105 yr are consistent with rates previously derived from studies integrating over 104 to >107 yr. We then model an expected 10Be inventory in fluvial sediment if background erosion rates were perturbed by a low-intensity, high-frequency Aboriginal burning regime. When we run the model using the average erosion rate derived from 10Be in fluvial sediment (8.7 mm k.y.–1), measured and modeled 10Be concentrations overlap between ca. 3 ka and 1 ka. Our modeling is consistent with intensified Aboriginal use of fire in the late Holocene, a time when Aboriginal population growth is widely recognized.

  • Journal article
    McPhillips D, Hoke GD, Liu-Zeng J, Bierman PR, Rood DH, Niedermann Set al., 2016,

    Dating the incision of the Yangtze River gorge at the First Bend using three-nuclide burial ages

    , Geophysical Research Letters, Vol: 43, Pages: 101-110, ISSN: 1944-8007

    Incision of the Yangtze River gorge is widely interpreted as evidence for lower crustal flow beneath the southeast margin of the Tibetan Plateau. Previous work focused on the onset of incision, but the duration of incision remains unknown. Here we present cosmogenic nuclide burial ages of sediments collected from caves on the walls of the gorge that show the gorge was incised ~1 km sometime between 18 and 9 Ma. Thereafter, incision slowed substantially. We resolve middle Miocene burial ages by using three nuclides and accounting for in situ muogenic production. This approach explains the absolute concentrations of 10Be, 26Al, and 21Ne, as well as 26Al/10Be and 21Ne/10Be ratios. A declining incision rate challenges existing geodynamic interpretations by suggesting that either (1) surface uplift has ceased immediately south of the plateau margin or (2) gorge incision is not a useful proxy for the timing of surface uplift.

  • Journal article
    Allen PA, Michael NA, D'Arcy M, Roda-Boluda DC, Whittaker AC, Duller RA, Armitage JJet al., 2016,

    Fractionation of grain size in terrestrial sediment routing systems

    , BASIN RESEARCH, Vol: 29, Pages: 180-202, ISSN: 0950-091X

    Sediment is fractionated by size during its cascade from source to sink in sediment routing systems. It is anticipated, therefore, that the grain size distribution of sediment will undergo down-system changes as a result of fluvial sorting processes and selective deposition. We assess this hypothesis by comparing grain size statistical properties of samples from within the erosional source region with those that have undergone different amounts of transport. A truncated Pareto distribution describes well the coarser half of the clast size distribution of regolith, coarse channel bed sediment and proximal debris flows (particularly their levees), as well as the coarser half of the clast size distribution of gravels that have undergone considerable amounts of transport in rivers. The Pareto shape parameter a evolves in response to mobilization, sediment transport and, importantly, the selective extraction of particles from the surface flow to build underlying stratigraphy. A goodness of fit statistic, the Kolmogorov–Smirnov vertical difference, illustrates the closeness of the observed clast size distributions to the Pareto, Weibull and log-normal models as a function of distance from the depositional apex. The goodness of fit of the particle size distribution of regolith varies with bedrock geology. Bedload sediment at catchment outlets is fitted well by the log-normal and truncated Pareto models, whereas the exponential Weibull model provides a less good fit. In the Eocene Escanilla palaeo-sediment routing system of the south-central Pyrenees, the log-normal and truncated Pareto models provide excellent fits for distances of up to 80 km from the depositional apex, whereas the Weibull fit progressively worsens with increasing transport distance. A similar trend is found in the Miocene–Pliocene gravels of the Nebraskan Great Plains over a distance of >300 km. Despite the large fractionation in mean grain size and gravel percentage from source region to

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