Wave transformation across a macrotidal shore platform under low to moderate energy conditions

We investigate how waves are transformed across a shore platform as this is a central question in rock coast geomorphology. We present results from deployment of three pressure transducers over four days, across a sloping, wide (~200 m) cliff‐backed shore platform in a macrotidal setting, in South Wales, United Kingdom. Cross‐shore variations in wave heights were evident under the predominantly low to moderate (significant wave height < 1.4 m) energy conditions measured. At the outer transducer 50 m from the seaward edge of the platform (163 m from the cliff) high tide water depths were 8+ m meaning that waves crossed the shore platform without breaking. At the mid‐platform position water depth was 5 m. Water depth at the inner transducer (6 m from the cliff platform junction) at high tide was 1.4 m. This shallow water depth forced wave breaking, thereby limiting wave heights on the inner platform. Maximum wave height at the middle and inner transducers were 2.41 and 2.39 m, respectively, and significant wave height 1.35 m and 1.34 m, respectively. Inner platform high tide wave heights were generally larger where energy was up to 335% greater than near the seaward edge where waves were smaller. Infragravity energy was less than 13% of the total energy spectra with energy in the swell, wind and capillary frequencies accounting for 87% of the total energy. Wave transformation is thus spatially variable and is strongly modulated by platform elevation and the tidal range. While shore platforms in microtidal environments have been shown to be highly dissipative, in this macro‐tidal setting up to 90% of the offshore wave energy reached the landward cliff at high tide, so that the shore platform cliff is much more reflective. Copyright © 2017 John Wiley & Sons, Ltd.     

Defining shore platform boundaries using airborne laser scan data: a preliminary investigation

As an initial evaluation of the potential of digital elevation models (DEMs) and geographic information systems (GISs) for geomorphic characterization of rocky shorelines, airborne laser scan (ALS) data have been used to characterize shore platforms around Shag Point, southeastern New Zealand. The platforms have been characterized using field‐based techniques in previously published research, and therefore offer an ideal site for evaluation purposes. The main challenge involved the delineation of the shore platform area in terms of landward and seaward extents. The cliff top and landward edge of the shore platform was readily mapped, whereas the seaward edge of platforms was mapped with lesser precision due to difficulties associated with tidal inundation and the interference of wave action and surface water. In the central region of the study area (～0·1 km²) higher platform elevations and dense point cloud data enabled the generation of a high‐resolution (1 m) DEM. In analysing the DEM, ALS offered an advantage over the previous field survey in respect of the ability to assess continuous topography in plan‐view. The extent and form of two distinctive erosional surfaces is clearly apparent and was revealed through classifications based on slope and elevation. The spatial continuity of the upper surface implies that, in addition to the role of rock structure described in previous work, sea level and wave exposure may have been important factors in the generation and preservation of platform morphology at Shag Point. Copyright © 2007 John Wiley & Sons, Ltd.     

Hydrodynamic constraints and storm wave characteristics on a sub‐horizontal shore platform

Few studies of wave processes on shore platforms have addressed the hydrodynamic thresholds that control wave transformation and energy dissipation, especially under storm conditions. We present results of a field experiment conducted during a storm on a sub‐horizontal shore platform on the east coast of Auckland, New Zealand. Small (<0.5 m) locally generated waves typically occur at the field site, whereas during the experiment the offshore wave height reached 2.3 m. Our results illustrate the important control that platform morphology has on wave characteristics. At the seaward edge of the platform a scarp abruptly descends beneath low tide level. Wave height immediately seaward of the platform was controlled by the incident conditions, but near the cliff toe wave height on the platform was independent of incident conditions. Results show that a depth threshold at the seaward platform edge > 2.5 times the gravity wave height (0.05–0.33 Hz) is necessary for waves to propagate onto the platform without breaking. On the platform surface the wave height is a direct function of water depth, with limiting maximum wave height to water depth ratios of 0.55 and 0.78 at the centre of the platform and cliff toe, respectively. A relative ‘platform edge submergence’ (water depth/water height ratio) threshold of 1.1 is identified, below which infragravity (<0.05 Hz) wave energy dominates the platform energy spectra, and above which gravity waves are dominant. Infragravity wave height transformation across the platform is governed by the relative platform edge submergence. Finally, the paper describes the first observations of wave setup on a shore platform. During the peak of the storm, wave setup on the platform at low tide (0.21 m) is consistent with measurements from planar sandy beaches, but at higher tidal stages the ratio between incident wave height and maximum setup was lower than expected. Copyright © 2014 John Wiley & Sons, Ltd.     

Lateral variability of flow over a sill in a channel of southern Chile

Measurements of velocity and density profiles were used to describe the tidal and mean flow structure across and along a sill in Refugio Channel, a fjord-like inlet in Southern Chile (43.9°S). These are the first oceanographic measurements of any kind effected in Refugio Channel. Current profiles were obtained with a 307.2-kHz acoustic Doppler current profiler during two semidiurnal cycles along a repeated triangular circuit. Two along-channel transects formed the sides of the triangle that crossed the sill and were identified as the western and eastern transects. One cross-channel transect, the base of the triangle, was located on the seaward side of the sill. Density profiles were obtained at the corners of the triangle. The longitudinal mean flow in the western transect showed a two-layer exchange structure over the landward side of the sill. The structure of net seaward flow at the surface and landward flow at depth was disrupted by the sill in such a way that over the seaward side of the sill, only seaward flow was observed throughout the water column. This likely resulted from the blocking of landward net flow by the sill. In the eastern transect, two-layer exchange dominated over most of the transect and was consistent with the observed density profiles. Over the seaward side of the sill, a surface layer, ∼10m deep, flowed landward as a third layer. This feature should have been caused by river input further seaward (to the north) and produced a surface convergence region over the sill. In terms of tidal flows, the greatest tidal current amplitudes were 40cm s⁻¹ over the sill as the flow accelerated through the reduced cross-sectional area of the channel. Near-surface flow convergences were identified over both along-channel transects.     

Modelling the effect of waves,weathering and beach development on shore platform development

A mathematical model was used to study shore platform development. Mechanical wave erosion was dependent on such variables as tidal range, wave height and period, breaker height and depth, breaker type, surf zone width and bottom roughness, submarine gradient, rock resistance and the elevational frequency of wave action within the intertidal zone. Also included were the effects of sand and pebble accumulation, cliff height and debris mobility, and downwearing associated with tidal wetting and drying. The occurrence, location and thickness of beaches often depended on initially quite minor variations in platform morphology, but owing to their abrasive or protective effect on underlying rock surfaces, they were able to produce marked differences in platform morphology. Generalizations are difficult, but the model suggests that platform gradient increases with tidal range. Platform width also increases with tidal range with slow downwearing but it decreases with fast downwearing. Platform gradient decreases and width increases with wave energy, and decreasing rock resistance and platform roughness. With low tidal range, platform gradient is generally lower and platform width greater with beaches of fine sand than with gravel, but the relationship is more variable with a high tidal range. Platform width increases and platform gradient decreases with the rate of downwearing on bare surfaces, particularly in low tidal range environments, but the pattern is less clear on beach‐covered platforms. Platforms with large amounts of beach sediment tend to be narrower and steeper than bare platform surfaces. Platform gradient increases and platform width decreases with increasing cliff height and with decreasing cliff debris mobility. Copyright © 2005 John Wiley & Sons, Ltd.     

Flow convergence over a broad,flat continental shelf

The broad (～500 km) southeastern Bering Sea continental shelf contains three fronts; outer (shelf break, ～170-m depth), middle (～100-m depth), and inner (～50-m depth). The shelf break and inner fronts appear to be analogous to similar fronts reported from other mid-latitude continental shelves; extensively studied examples are from the mid-Atlantic bight, off Nova Scotia, and around the British Isles. The middle front may have counterparts on the broad North Sea and East China Sea shelves.One-month current and temperature records from either side of the middle front, ～150 km landward from the shelf break, showed convergence in the layers deeper than 30 m in both the cross-shelf flow field and heat flux. The convergence was ～3 cm s^?1, so an average upwelling at ～1 × 10^?3cm s^?1 and divergence in the surface layer were required to maintain continuity. Variations in the degree of convergence arose primarily from 1 to 5-day fluctuations in sub-tidal flow across the outer shelf domain seaward of the front.Diffusive landward heat flux was dominated by tidal scales. Horizontal eddy conductivities describing the flux were ～1 ? 10⁶ on the landward side and ～5 × 10⁶cm² s^?1 on the seaward side, and were less in the layers above the bottom layer. Advective flux by the mean flow was the same order as diffusive flux, but landward in the bottom layer and seaward in the mid-water column layers, in agreement with deductions from water mass analyses. Frontal effects reduced the net cross-shelf heat flux beneath ～30 m by about 50%. The observation of a flow convergence in the middle of a broad, flat continental shelf poses an important question of dynamics.     

Identifying mechanisms of shore platform erosion using Structure-from-Motion (SfM) photogrammetry

Shore platforms control wave energy transformation which, in turn, controls energy delivery to the cliff toe and nearshore sediment transport. Insight into shore platform erosion rates has conventionally been constrained at millimetre-scales using micro-erosion metres, and at metre-scales using cartographic data. On apparently slowly eroding coasts, such approaches are fundamentally reliant upon long-term observation to capture emergent erosion patterns. Where in practise timescales are short, and where change is either below the resolution or saturates the mode of measurement, the collection of data that enables the identification of the actual mechanisms of erosion is hindered. We developed a method to monitor shore platform erosion at millimetre resolution within metre-scale monitoring plots using Structure-from-Motion photogrammetry. We conducted monthly surveys at 15 0.25 m² sites distributed across the Hartle Loup platform in North Yorkshire, UK, over one year. We derived topographic data at 0.001 m resolution, retaining a vertical precision of change detection of 0.001 m. We captured a mean erosion rate of 0.528 mm yr^-1, but this varied considerably both across the platform and through the year. We characterized the volume and shape of eroded material. The detachment volume–frequency and shape distributions suggest that erosion happens primarily via removal of shale platelets. We identify that the at-a-point erosion rate can be predicted by the distance from the cliff and the tidal level, whereby erosion rates are higher closer to the cliff and at locations of higher tidal duration. The size of individual detachments is controlled by local micro-topography and rock structure, whereby larger detachments are observed on more rough sections of the platform. Faster erosion rates and larger detachments occur in summer months, rather than in more energetic winter conditions. These results have the potential to form the basis of improved models of how platforms erode over both short- and long-timescales. © 2019 John Wiley & Sons, Ltd.     

Cyclic channel-shoal dynamics at the Ameland inlet: the impact on waves,tides, and sediment transport

Ocean Dynamics - Ebb-tidal deltas are shallow features seaward of tidal inlets, acting as a wave filter for the nearby barrier island and a source of sediment for the landward tidal basin. On many...     

Critical notch depths for failure of coastal limestone cliffs: case study at Kuro‐shima Island,Okinawa, Japan

Development of a notch at the base of a cliff reduces cliff stability and often induces a collapse. Pleistocene limestone coastal cliffs of elevation 5?m in Kuro‐shima, Ryukyu Islands, have a prominent notch with a depth of 3–4?m at their bases. Around these coastal cliffs, collapses different from previous studies of cliff collapses in the Ryukyu Islands were found; collapses in Kuro‐shima have a horizontal failure surface. The horizontal failure surface, situated at the height of the failure surface corresponding to the retreat point of the notch, is bounded by vertical joints cutting the whole cliff and the reef flat in front of the cliff. Two types of horizontal failure surface were found, triangular and quadrangular; the distinction appears to depend on the angle between the vertical joints and the front face of the cliff. Prior to collapse, these cliffs appear to have been separated from the adjacent cliffs by the development of vertical joints. Consequently, a cliff that will collapse can be identified in advance; cliff instability is strongly dependent on the development of a notch. To study the effect of notch development on cliff collapse, the notch depth at which collapse occurs was calculated using stability analysis. Instability of a cliff increases with notch depth; collapse occurs at the horizontal failure surface when the ratio of the notch depth to the seaward length of the cliff is approximately 0·5–0·7 for a triangular failure surface, and 0·7–0·9 for a quadrangular failure surface. Copyright © 2010 John Wiley & Sons, Ltd.     

Sea stack formation and the role of abrasion on beach‐mantled headlands

Sea stacks are common and striking coastal landforms, but few details are known about how, how quickly, and under what conditions they form. We present numerical and analytical models of sea stack formation due to preferential erosion along a pre‐existing headland to address these basic questions. On sediment‐rich rocky coasts, as sea cliffs erode and retreat, they produce beach sediment that is distributed by alongshore sediment transport and controls future sea cliff retreat rates. Depending on their width, beaches can encourage or discourage sea cliff erosion by acting either as an abrasive tool or a protective cover that dissipates wave energy seaward of the cliff. Along the flanks of rocky headlands where pocket beaches are often curved and narrow due to wave field variability, abrasion can accelerate alongshore‐directed sea cliff erosion. Eventually, abrasion‐induced preferential erosion can cut a channel through a headland, separating it from the mainland to become a sea stack. Under a symmetrical wave climate (i.e. equal influence of waves approaching the coastline from the right and from the left), numerical and analytical model results suggest that sea stack formation time and plan‐view size are proportional to preferential erosion intensity (caused by, for example, abrasion and/or local rock weakness from joints, faults, or fractures) and initial headland aspect ratio, and that sea stack formation is discouraged when the sediment input from sea cliff retreat is too high (i.e. sea cliffs retreat quickly or are sand‐rich). When initial headland aspect ratio is too small, and the headland is ‘rounded’ (much wider in the alongshore direction at its base than at its seaward apex), the headland is less conducive to sea stack formation. On top of these geomorphic and morphologic controls, a highly asymmetrical wave climate decreases sea stack size and discourages stack formation through rock–sediment interactions. Copyright © 2014 John Wiley & Sons, Ltd.     

Sea‐cliff retreat and shore platform widening: steady‐state equilibrium?

We challenge the notion of steady‐state equilibrium in the context of progressive cliff retreat on micro‐tidal coasts. Ocean waves break at or close to the abrupt seaward edge of near‐horizontal shore platforms and then rapidly lose height due to turbulence and friction. Conceptual models assume that wave height decays exponentially with distance from the platform edge, and that the platform edge does not erode under stable sea‐level. These assumptions combine to a steady‐state view of Holocene cliff retreat. We argue that this model is not generally applicable. Recent data show that: (1) exponential decay in wave height is not the most appropriate conceptual model of wave decay; (2) by solely considering wave energy at gravity wave frequencies the steady‐state model neglects a possible formative role for infragravity waves. Here we draw attention to possible mechanisms through which infragravity waves may drive cliff retreat over much greater distances (and longer timescales) than imaginable under the established conceptual model. Copyright © 2013 John Wiley & Sons, Ltd.     

Towards an improved understanding of erosion rates and tidal notch development on limestone coasts in the Tropics: 10 years of micro‐erosion meter measurements,Phang Nga Bay,Thailand

Knowledge and understanding of shore platform erosion and tidal notch development in the tropics and subtropics relies mainly on short‐term studies conducted on recently deposited carbonate rocks, predominantly Holocene and Quaternary reef limestones and aeolianites. This paper presents erosion rates, measured over a 10 year period on notches and platforms developed on the Permian, Ratburi limestone at Phang Nga Bay, Thailand. In so doing it contributes to informing a particular knowledge gap in our understanding of the erosion dynamics of shore platform and tidal notch development in the tropics and subtropics – notch erosion rates on relatively hard, ancient limestones measured directly on the rock surface using a micro‐erosion meter (MEM) over time periods of a decade or more. The average intertidal erosion rate of 0.231 mm/yr is lower than erosion rates measured over 2–3 years on recent, weaker carbonate rocks. Average erosion rates at Phang Nga vary according to location and site and are, in rank order from highest to lowest: Mid‐platform (0.324 mm/yr) > Notch floor (0.289 mm/yr) > Rear notch wall (0.228 mm/yr) > Lower platform (0.140 mm/yr) > Notch roof (0.107 mm/yr) and Supratidal (0.095 mm/yr). The micro‐relief of the eroding rock surfaces in each of these positions exhibits marked differences that are seemingly associated with differences in dominant physical and bio‐erosion processes. The results begin to help inform knowledge of longer term shore platform erosion dynamics, models of marine notch development and have implications for the use of marine notches as indicators of changes in sea level and the duration of past sea levels. Copyright © 2014 John Wiley & Sons, Ltd.     

Erosion of a cyclic saltmarsh in Morecambe Bay,North-West England

This paper presents results of investigations (1983–1992) into rates of change, morphology and processes occurring during the current erosional phase in a Morecambe Bay cyclic saltmarsh, in which it has narrowed from c. 1000 m (1975) to c. 150 m (1992). Monthly monitoring of marsh edge erosion and creek knickpoint retreat has revealed temporal and spatial variations. Highest frequency changes of low magnitude coincided with non-storm conditions and overmarsh tides above 5·80 m OD, which submerged the whole marsh. Less frequent changes of greater magnitude were associated with both overmarsh tides and strong onshore winds over 15 ms^?1, which generated high energy waves. The lowest frequency change of greatest magnitude occurred during an extreme onshore storm event and surge. Morphologically, during the erosional phase, a low angled landward slope was generated as erosion of the c. 0·5 m high active seaward cliff coincided with vertical accretion of 0·07 ma^?1 of relatively coarse sediment on the marsh surface immediately landward. Tidal hydrodynamics strongly influence the saltmarsh, which is confined to the upper 2·5 m of the macrotidal range (maximum c. 10·5 m). During overmarsh spring tides (maximum creek flood flow rate 0·13 ms^?1, up to bankfull level), flooding begins over lower landward creek banks before submerging the higher marsh edge. During ebb tides, water trapped by this higher edge can escape seaward only via the creeks (maximum ebb velocities 2·07 ms^?1 below bankfull level). Wave erosion also is limited to spring tides. Monthly mapping of the Kent Estuary channel pattern seaward of the saltmarsh showed that medium term higher erosion rates were related to the presence of a large channel, which lowered the adjacent creek base level and allowed larger waves to attack the marsh edge than when a sandbank flanked the marsh. Major River Kent channel shifts appear to initiate accretional or erosional phases of cyclic saltmarsh development.     

Lithological control on the elevation of shore platforms in a microtidal setting

The shore platforms on Shag Point, southern New Zealand, are quasi‐horizontal surfaces and are developed between supratidal and low water spring levels. A range of morphologies occur, with more exposed platforms having a distinct low‐tide cliff, in contrast to low‐tide surfaces where the seaward edge is buried beneath rubble and macro‐algal growth. The platforms range in width from 20 to 80 m and are eroded into Late Cretaceous/Early Tertiary fine marine sandstones and mudstones. Shore platforms have formed in two principal lithological units: a homogeneous unit that is characterized by few discontinuities, and a fractured unit with joints spaced about 0·5 m apart. Rock hardness is low in both units (L‐type Schmidt hammer rebound values of 31 ± 4), and there is little systematic variation in values between the two units in which platforms have developed. Case‐hardened concretions within the sandstone are significantly harder than surrounding rock and cause local relief of metre scale as the spherical diagenetic features are eroded from the bedrock. They do not, however, appear to affect broad‐scale platform geometry. Joints within the bedrock are a primary control on platform elevation. Platforms formed in jointed rock occur at the lower portion of the intertidal zone, in contrast to platforms formed in unjointed bedrock, in which horizontal surfaces occur at or above mean high water spring tide level. Rock structure, therefore, appears to be the primary determinant factor of platform geometry at Shag Point. Copyright © 2006 John Wiley & Sons, Ltd.     

Modelling the relative dominance of wave erosion and weathering processes in shore platform development in micro‐ to mega‐tidal settings

In this paper we use a numerical model to explore the relative dominance of two main processes in shore platform development: wave erosion; weathering due to wetting and drying. The modelling approach differs from previous work in several aspects, including: the way that it accounts for weathering arising from gradual surficial intertidal rock degradation; subtidal profile shape development; and the consideration of a broad erosion parameter space in which, at either end of the erosion spectrum, shore platform profiles are produced by waves or weathering alone. Results show that in micro‐tidal settings, wave erosion dominates the evolution of (i) shore platforms that become largely subtidal and (ii) sub‐horizontal shore platforms that have a receding seaward edge. Weathering processes dominate the evolution of sub‐horizontal shore platforms with a stable seaward edge. In contrast, sloping shore platforms in mega‐tidal settings are produced across the full range of the process‐dominance spectrum depending on the how the erosional efficacy of wave erosion and weathering are parameterized. Morphological feedbacks control the process‐dominance. In small tidal environments wave processes are strongly controlled by the presence/absence of an abrupt seaward edge, but this influence is much smaller in large tidal environments due to larger water depths particularly at high tides. In large tidal environments, similar shore platform profile geometries can be produced by either wave‐dominant or weathering‐dominant process regimes. Equifinality in shore platform development has been noted in other studies, but mainly in the context of smaller‐scale (centimetre to metre) erosion features. Here we draw attention to geomorphic equifinality at the scale of the shore platform itself. Progress requires a greater understanding of the actual mechanics of the process regimes operating on shore platforms. However, this paper makes a substantial contribution to the debate by identifying the physical conditions that allow clear statements about process dominance. © 2018 John Wiley & Sons, Ltd.     

Instability of coral limestone cliffs due to extreme waves

Many boulders are located around the coastal cliffs with height of below 5 m made of coral limestone at Kuro‐shima, Okinawa, Japan. The origin of the boulders appears to be coral limestone cliffs which show developed notches. We undertook stability analysis, involving the wave pressure due to tsunamis, of wave‐induced collapse of the cliffs. We find that extreme waves are capable of inducing cliff collapse, as observed in circumstances where gravity is insufficient. Copyright © 2010 John Wiley and Sons, Ltd.     

Rock coast inheritance: an example from Galicia,northwestern Spain

A shore platform on the western coast of Galicia in northwestern Spain has been inherited from interglacial stages when sea level was similar to today. The wide, gently sloping intertidal platform is backed in places by supratidal rock ledges, and in other places by a steeper and narrower supratidal ramp. The gradient of the intertidal platform is consistent with the relationship between platform gradient and tidal range, but the slope of the ramp is much too high. The abandoned and degraded sea cliff is grass-covered along most of this coast, and the ledges and the ramp, which extend up to several metres above the highest tides, are covered by lichen and, in places, by salt-tolerant plants. Radiocarbon-dated sediments in the cliff, which range up to 36 000 years in age, lie on top of an ancient beach deposit. The former beach, remnants of which are found in situ on the ramp and rock ledges, as well as two caves that are filled with the dated sediments, are probably last interglacial in age. The morphological and sedimentary evidence suggests that the supratidal ramp and ledges were also formed during the last interglacial stage, whereas the wider intertidal platform is probably the product of several older interglacials, when sea level was generally similar to today. A general model is proposed for the inheritance of shore platforms in macro- and microtidal environments. Copyright © 1999 John Wiley & Sons, Ltd.     

Transport over a narrow shelf: Exuma Cays, Bahamas

Current meter and temperature data were collected over a 402-day period from an outer shelf and a tidal channel study site in the Exuma Cays, Bahamas. The shelf width is less than 2 km, and floods and ebbs through a nearby tidal channel extend across the entire shelf and reduce coherence of wind forcing and along-shelf flow. The data are used in perturbation analyses to investigate the across-shelf turbulent transport of heat and momentum over seasonal time scales. Data show a net landward transport of both heat and momentum over the course of the study, but the perturbation products contain distinct seasonal cycles. In fall and winter months, across-shelf heat and momentum fluxes are landward, while during spring and summer months fluxes are seaward. Comparison of shelf-water temperature with the temperature of bank water leaving on the ebb suggests that seasonal cycles of across-shelf heat and momentum in shelf waters are influenced by the seasonal export of relatively warm and cool water from Great Bahama Bank.Responsible Editor: Iris Grabemann     

Lateral dynamics and associated transport of sediment in the upper reaches of a partially mixed estuary,Chesapeake Bay,USA

Data from time series of transects made over a tidal period across a section of the upper Chesapeake Bay, USA, reveal the influence of lateral dynamics on sediment transport in an area with a deep channel and broad extents of shallower flanks. Contributions to lateral momentum by rotation (Coriolis plus channel curvature), cross channel density gradients and cross channel surface slope were estimated, and the friction and acceleration terms needed to complete the balance were compared to patterns of observed lateral circulation. During ebb, net rotation effects were larger because of river velocity and reinforcement of Coriolis by curvature. During flood, stratification was greater because of landward advection of strong vertical density gradients. Together, the ebb intensified lateral circulation and flood intensified stratification focused sediment and sediment transport along the left side of the estuary (looking seaward). The tendency for greater stratification on flood and net sediment flux toward the left-hand shoal are contrary to more common models which, in the northern hemisphere, predict greater resuspension on flood and move sediment toward the right-hand shoal. These tidal asymmetries interact with the lateral circulation to focus net sediment flux on the left side of the estuary, and to produce net ebb directed sediment transport at the surface of the same order of magnitude as net flood directed sediment transport at the bottom.