Beach profile evolution as an inverse problem

Beach evolution models are normally applied in a prognostic fashion, with parameters and boundary conditions estimated from previous experience or other forecasts. Here, we use observations of beach profiles to solve a beach profile evolution equation in an inverse manner to determine model parameters and source function. The data used to demonstrate the method are from Christchurch Bay in Dorset, UK. It was found that there is a significant contribution from diffusive processes to the morphodynamic evolution of the beach profiles and that the development and disappearance of near-shore coastal features such as upper beach berms and inter- and sub-tidal bars are well captured by the source function in the governing equation.     

A gradient plasticity model for lüders band propagation

At the onset of plastic deformation some materials exhibit non-monotonic behaviour in that after initially yielding the flow stress decreases with continuing strain, passing through a minimum. Strain softening destabilizes homogeneous configurations and results in the formation of bands of localized deformation. Within these bands the macro and microscales of the deformation overlap and accordingly terms have to be included in the evolution equation for the plastic strain to provide the necessary information on the material's behaviour at the next smaller scale. In the model chosen here the evolution equation has the form of a reaction diffusion equation, whereby physically the diffusion term accounts for the nonlocal interaction between dislocations on neighbouring slip planes. The model predicts the band propagation velocity, the width of the propagation front and the strain profile.     

Field measurements of intertidal bar evolution on a high‐energy beach system

Nearshore bars play a pivotal role in coastal behaviour, helping to protect and restore beach systems particularly in post‐storm conditions. Examination of bar behaviour under various forcing conditions is important to help understand the short‐ to medium‐term evolution of sandy beach systems. This study carried out over a nine‐week period examines, the behaviour of three intertidal bars along a high energy sandy beach system in northwest Ireland using high‐frequency topographic surveys and detailed nearshore hydrodynamic modelling. Results show that, in general, there was onshore migration for all the bars during the study period, despite the variability observed between bars, which was driven mostly by wave dominated processes. Under the prevailing conditions migration rates of up to 1.83 m day^?1 and as low as 0.07 m day^?1 were observed. During higher wave energy events the migration rates of the bars decelerated in their onshore route, however, under lower wave energy conditions, they quickly accelerated maintaining their shoreward migration direction. Tidal influence appears to be subordinate in these conditions, being restricted to moderating the localized wave energy at low tides and in maintaining runnel configurations providing accommodation space for advancing slip faces. The study highlights the intricate behavioural patterns of intertidal bar behaviour along a high energy sandy coastline and provides new insights into the relative importance of wave and tidal forcing on bar behaviour over a relatively short time period. Copyright © 2016 John Wiley & Sons, Ltd.     

A Markov model for beach changes on the holderness coast of England

Markov models offer an objective and quantitative method of assessing beach changes. For a stretch of the Holderness coast a beach classification scheme was devised and a probabilistic first order matrix model based on surveyed profile data was produced. This could describe and predict transitions between beach types and between different time periods. Different profile types dominated different coastal locations and seasonal variations were seen. In order to improve the accuracy of prediction throughout the year a second, ‘winter’, model was added to the original ‘summer’ one. Although the models had been prepared independently of wave conditions, a comparison of the wave record and beach transitions revealed that waves under 0·3–0·5 m high produced fairly static beaches; when waves were between 0·5 and 1·0 m the beach was more dynamic and variable, while waves over 1·0 m led to the depletion of the upper beach. This was broadly in accordance with published theory. Markov models have the advantage that they can be adjusted periodically if conditions change, and are thus useful for prediction on coasts for which no wave records exist.     

Lithological controls on soft cliff planshape evolution under high and low sediment availability

This paper addresses a series of geomorphic questions relating to large‐scale (> 1 km), long‐term (100 – 1,000 years) coastal planshape evolution. Previous research on soft‐cliff coasts has recognised the role of protective fronting beach volumes on reducing rates of cliff toe retreat. However, it is the maintenance of this critical threshold that ultimately determines two contrasting modes of shoreline behaviour: Mode A, in which there is little beach sediment and shoreline evolution is controlled by material strength; and, Mode B, when ample beach sediment means that shoreline evolution is controlled by longshore sediment transport. Here we use a numerical model (SCAPE) to investigate temporal and spatial changes in beach volume on a broader range of feedbacks than considered in previous models. The transition between Mode A and Mode B coasts is defined by relative sediment inputs to outputs and used to explore how these contrasting modes control the evolution of an initial linear frontage exhibiting longshore changes in cliff lithology (material resistance and the proportion of beach grade material in the eroded bedrock). Under Mode A, relative changes in material resistance result in long term heterogeneous rates of retreat, which result in the development of persistent headland and embayment features. However, under Mode B, feedbacks between coastal planshape, longshore sediment transport, beach volume and wave energy result in steady state retreat rates regardless of longshore variations in resistance. Results are compared and contrasted to previous simulations and site specific examples and a conceptual model of Mode A and Mode B interactions presented. Copyright © 2015 John Wiley & Sons, Ltd.     

Application of a stochastic differential equation to the prediction of shoreline evolution

Shoreline evolution due to longshore sediment transport is one of the most important problems in coastal engineering and management. This paper describes a method to predict the probability distributions of long-term shoreline positions in which the evolution process is based on the standard one-line model recast into a stochastic differential equation. The time-dependent and spatially varying probability density function of the shoreline position leads to a Fokker–Planck equation model. The behaviour of the model is evaluated by applying it to two simple shoreline configurations: a single long jetty perpendicular to a straight shoreline and a rectangular beach nourishment case. The sensitivity of the model predictions to variations in the wave climate parameters is shown. The results indicate that the proposed model is robust and computationally efficient compared with the conventional Monte Carlo simulations.     

Daily morphological changes determined by high‐energy events on an embayed beach: a qualitative model

This paper examines the daily morphological responses of Sununga Beach, an embayed beach located on the south‐eastern Brazilian coast, to storms in the South Atlantic Ocean. The main mechanisms and timing of beach erosion and accretion, the relationship between wave height and direction, and beach volume changes are considered, to establish a qualitative model for short‐term embayed beach morphological changes. The methodology consisted of daily topographic surveys during the month of May in 2001, 2002, and 2003, using an RTK‐GPS (real‐time kinematics – global positioning system). Weather and wave model results were used to correlate hydrodynamics and beach morphology. The results indicate that the morphodynamics of Sununga Beach are characterized by a process of beach rotation, which occurred more or less clearly during all three surveys. Unlike what has been commonly described in the literature for longer time intervals and alternations of fair and stormy weather, the beach rotation processes on Sununga Beach occurred under conditions of moderate‐to‐high wave energy change (wave heights greater than 2 m). An integrated evaluation of the behaviour of the meteorological aspects, together with beach morphology, enabled us to recognize that extra‐tropical cyclones were the most important agent in remobilizing the beach planform, whether in beach rotation or in cross‐shore erosion. Copyright © 2010 John Wiley & Sons, Ltd.     

Equilibrium modeling of the beach profile on a macrotidal embayed low tide terrace beach

Eleven-year long time series of monthly beach profile surveys and hourly incident wave conditions are analyzed for a macrotidal Low Tide Terrace beach. The lower intertidal zone of the beach has a pluriannual cycle, whereas the upper beach profile has a predominantly seasonal cycle. An equilibrium model is applied to study the variation of the contour elevation positions in the intertidal zone as a function of the wave energy, wave power, and water level. When forcing the model with wave energy, the predictive ability of the equilibrium model is around 60% in the upper intertidal zone but decreases to 40% in the lower intertidal zone. Using wave power increases the predictive ability up to 70% in both the upper and lower intertidal zones. However, changes around the inflection point are not well predicted. The equilibrium model is then extended to take into account the effects of the tide level. The initial results do not show an increase in the predictive capacity of the model, but do allow the model free parameters to represent more accurately the values expected in a macrotidal environment. This allows comparing the empirical model calibration in different tidal environment. The interpretation of the model free parameter variation across the intertidal zone highlights the behavior of the different zones along the intertidal beach profile. This contributes to a global interpretation of the four model parameters for beaches with different tidal ranges, and therefore to a global model applicable at a wide variety sites.     

Methodology of seasonal morphological modelisation for nourishment strategies on a Mediterranean beach

A modified 2DH morphodynamical model was employed to simulate the evolution of large-scale features with major implications for beach nourishment. The study was focused on modelling the evolution of material artificially placed in different parts of the profile, extracting or adding material to the natural bars, and quantifying how the profile responds to different wave climates and nourishment placements. The simulated results were compared with field data from a Mediterranean beach.     

Computer simulation of nearshore bar formation

A computer simulation model, developed from a conceptual model of sediment transport patterns associated with nearshore bars, is presented. The model simulates wave shoaling, breaking and reformation along a profile normal to the shore from deep water to the beach and determines rates and directions of sediment transport under wave orbital currents and rip cell circulation. The model successfully generates a barred profile from an initial planar profile and under most conditions achieves a state of dynamic equilibrium with sediment circulating across the bars. Input values for wave height, wave period, offshore slope and tidal range were varied in turn in order to determine their individual effect on the shape of the equilibrium profile formed. Breaker type—spilling or plunging—is incorporated in the model and also appears to be a significant factor in determining the shape of the equilibrium profile.     

Theoretical analysis of wave-induced gravel movements

One of the primary objectives of coastal research is the erection and testing of mechanically sound, predictive models for the two- and three-dimensional form of beach and nearshore bathymetries in order to account for and to predict coastal response to changing wave, tidal and sea-level conditions. The relationship between flow parameters and the mass transport of non-cohesive sedimentary particles has long been of importance in fluvial, aeolian and marine environments, but despite the existence of many numerical beach models, any of which might be developed to account for longer-term evolution, it is apparent that fundamental problems remain, not only in the representation of hydrodynamic and sediment dynamic processes but also in the choice of appropriate forcing functions for long-term simulations in real-time or quasi-real-time. An alternative is developed here in which frequency domain representations of a simplified set of process and response algorithms are presented, so that hydrodynamic, sediment dynamic and geomorphological parameters are related by a simple series of spectral gain functions. In particular, we concentrate on the relationship between the nearbed orthogonal flow spectrum and the resulting sediment mass transport rate. Numerical solutions, using both non-linear and linearized forms of the momentum equation, are presented.     

Solution of the linear diffusion equation for modelling erosion processes with a time varying diffusion coefficient

In the present paper the differential equation of the temporal development of a landform (mountain) with a time dependent diffusion coefficient is solved. It is shown that the shape and dimensions of the landform at time t are independent of the specific variation of the diffusion coefficient with time; they only depend on the mean value of the diffusion coefficient in the time interval where the erosion process takes place. Studying the behaviour of the solution of the differential equation in the wave number domain, it is concluded that Fourier analysis may help in estimating, in quantitative terms, the initial dimensions, the age or, alternatively, the value of the diffusion coefficient of the landform. The theoretical predictions are tested on a hill of the southern part of the Ural mountainous region, in order to show how the results of the mathematical analysis can be used in describing, in quantitative terms, the morphological development of landforms due to erosion processes. Copyright © 2007 John Wiley & Sons, Ltd.     

Modelling the time-varying extent of groundwater seepage on tidal beaches

The outcrop of groundwater on tidal beaches distinguishes an upper unsaturated region from a lower saturated region of the intertidal profile. Since the 1940s, it has been recognized that the extent of groundwater seepage at the beach face is one factor determining the tendency for erosive or accretionary conditions to prevail. As a primary step towards incorporating bed saturation characteristics within cross-shore sediment transport models, this paper (and accompanying program disk) details a simple model to simulate the time-varying extent of seepage face development across tidal beaches. From a comparison with field results obtained on the macrotidal Central Queensland (Australia) coast, the model appears to provide an encouraging degree of predictive capability. The model also assists in highlighting the sensitivity of seepage face development to varying beach face, tide and wave characteristics.     

Links between wave forcing,offshore islands and a macro‐tidal headland‐bound bay beach

Profiles were analysed in conjunction with wave climate to assess offshore island influences on an embayed beach at Tenby, Wales. Time series analyses showed medium and short‐term beach oscillation, with volume exchanges between zones lagging by up to six months. Dominant southerly and southwesterly waves caused sub and low tidal longshore drift from south towards north, while less frequent southeasterly waves generated counter drift. Modelled inshore breaking waves had less energy than offshore ones and the former behaved differently between the low and high tidal zones (spring tidal range of 7 · 5 m). Variations in wave direction from directly behind the islands resulted in reduced wave heights and statistical analyses agreed with wave model results. These were correlated to morphological change and it was concluded that offshore islands change wave dynamics and modify the morphology of embayed beaches in their lee. Consequently, this work provides significant new insights into offshore island influences, shoreline behaviour and especially tidal setting Copyright © 2013 John Wiley & Sons, Ltd.     

The role of beach morphology on coastal cliff erosion under extreme waves

Erosion of hard‐rock coastal cliffs is understood to be caused by a combination of both marine and sub‐aerial processes. Beach morphology, tidal elevation and significant wave heights, especially under extreme storm conditions, can lead to variability in wave energy flux to the cliff‐toe. Wave and water level measurements in the nearshore under energetic conditions are difficult to obtain and in situ observations are rare. Here we use monthly cliff‐face volume changes detected using terrestrial laser scanning alongside beach morphological changes and modelled nearshore hydrodynamics to examine how exposed cliffs respond to changes in extreme wave conditions and beach morphology. The measurements cover the North Atlantic storms of 2013 to 2014 and consider two exposed stretches of coastline (Porthleven and Godrevy, UK) with contrasting beach morphology fronting the cliffs; a flat dissipative sandy beach at Godrevy and a steep reflective gravel beach at Porthleven. Beach slope and the elevation of the beach–cliff junction were found to influence the frequency of cliff inundation and the power of wave–cliff impacts. Numerical modelling (XBeach‐G) showed that under highly energetic wave conditions, i.e. those that occurred in the North Atlantic during winter 2013–2014, with H_s = 5.5 m (dissipative site) and 8 m (reflective site), the combination of greater wave height and steeper beach at the reflective site led to amplified wave run‐up, subjecting these cliffs to waves over four times as powerful as those impacting the cliffs at the dissipative site (39 kWm^‐1 compared with 9 kWm^‐1). This study highlighted the sensitivity of cliff erosion to extreme wave conditions, where the majority (over 90% of the annual value) of cliff‐face erosion ensued during the winter. The significance of these short‐term erosion rates in the context of long‐term retreat illustrates the importance of incorporating short‐term beach and wave dynamics into geomorphological studies of coastal cliff change. © 2017 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.     

Observations on sandbar behaviour along a man‐made curved coast

Sandbars, submerged ridges of sand parallel to the shoreline, affect surfzone circulation, beach topography and beach width. Under time‐varying wave forcing, sandbars may migrate onshore and offshore, referred to as two‐dimensional (2D) behaviour, and vary in planshape from alongshore uniform ridges to alongshore non‐uniform ridges through the growth and decay of three‐dimensional (3D) patterns, referred to as 3D behaviour. Although 2D and 3D sandbar behaviour is reasonably well understood along straight coasts, this is not the case for curved coasts, where the curvature can invoke spatial variability in wave forcing. Here, we analyse sandbar behaviour along the ～3000 m man‐made curved coastline of the Sand Engine, Netherlands, and determine the wave conditions governing this behaviour. 2D and 3D behaviour was quantified within a box north and west of the Sand Engine's tip, respectively, using a 2.4‐year dataset of daily low‐tide video images and a sparser bathymetric dataset. The northern and western sides behaved similarly in terms of 2D behaviour, with seasonal onshore and offshore migration, resulting in a stable position on inter‐annual timescales. However, both sandbar geometry and 3D behaviour differed substantially between both sides. The geometric differences (bar shape, bar crest depth and wavelength of 3D patterns) are consistent with computed alongshore differences in breaker height due to refraction. The differences in the timing in growth, decay and morphological coupling of 3D patterns in the sandbar and shoreline are likely related to differences in the local wave angle, imposed by the curved coast. Similar dependency of bar behaviour on local wave height and angle may be expected elsewhere along curved coasts, e.g. shoreline sandwaves, cuspate forelands or embayed beaches. Copyright © 2017 John Wiley & Sons, Ltd.     

新疆北天山地区中强震前单台地震波参数异常特征研究

强地震的孕育过程也是孕震介质的形成过程,在强震前震源附近小地震的地震波运动学,动力学特征的变化过程,则反映了孕震介质的变化过程,为研究地震的孕育,发展和发生的过程,采用单台地震波振幅比,尾波持续时间比,尾波衰减系数这３项地震波参数作为地震学短期前兆指标,分析其震兆特征,从而达到监测孕震介质变化的目的,研究结果表明,单台地震波参数能够有效地发现地震的前兆,但地震波参数的前兆图像复杂多变,不具有统一的     

Beach erosion and recovery during consecutive storms at a steep‐sloping,meso‐tidal beach

This study analyses beach morphological change during six consecutive storms acting on the meso‐tidal Faro Beach (south Portugal) between 15 December 2009 and 7 January 2010. Morphological change of the sub‐aerial beach profile was monitored through frequent topographic surveys across 11 transects. Measurements of the surf/swash zone dimensions, nearshore bar dynamics, and wave run‐up were extracted from time averaged and timestack coastal images, and wave and tidal data were obtained from offshore stations. All the information combined suggests that during consecutive storm events, the antecedent morphological state can initially be the dominant controlling factor of beach response; while the hydrodynamic forcing, and especially the tide and surge levels, become more important during the later stages of a storm period. The dataset also reveals the dynamic nature of steep‐sloping beaches, since sub‐aerial beach volume reductions up to 30 m³/m were followed by intertidal area recovery (–2 < z < 3 m) with rates reaching ~10 m³/m. However, the observed cumulative dune erosion and profile pivoting imply that storms, even of regular intensity, can have a dramatic impact when they occur in groups. Nearshore bars seemed to respond to temporal scales more related to storm sequences than to individual events. The formation of a prominent crescentic offshore bar at ~200 m from the shoreline appeared to reverse the previous offshore migration trend of the inner bar, which was gradually shifted close to the seaward swash zone boundary. The partially understood nearshore bar processes appeared to be critical for storm wave attenuation in the surf zone; and were considered mainly responsible for the poor interpretation of the observed beach behaviour on the grounds of standard, non‐dimensional, morphological parameters. Copyright © 2011 John Wiley & Sons, Ltd.     

Measurements and modelling of beach groundwater flow in the swash-zone: a review

This paper reviews research on beach groundwater dynamics and identifies research questions which will need to be answered before swash zone sediment transport and beach profile evolution can be successfully modelled. Beach groundwater hydrodynamics are a result of combined forcing from the tide and waves at a range of frequencies, and a large number of observations exist which describe the shape and elevation of the beach watertable in response to tidal forcing at diurnal, semi-diurnal and spring-neap tidal frequencies. Models of beach watertable response to tidal forcing have been successfully validated; however, models of watertable response to wave forcing are less well developed and require verification. Improved predictions of swash zone sediment transport and beach profile evolution cannot be achieved unless the complex fluid and sediment interactions between the surface flow and the beach groundwater are better understood, particularly the sensitivity of sediment transport processes to flow perpendicular to the permeable bed.The presence of a capillary fringe, particularly when it lies just below the sand surface, has influences on beach groundwater dynamics. The presence of a capillary fringe can have a significant effect on the exchange of water between the ocean and the coastal aquifer, particularly in terms of the storage capacity of the aquifer. Field and laboratory observations have also shown that natural groundwater waves usually propagate faster and decay more slowly in aquifers with a capillary fringe, and observations which suggest that horizontal flows may also occur in the capillary zone have been reported. The effects of infiltration and exfiltration are generally invoked to explain why beaches with a low watertable tend to accrete and beaches with a high watertable tend to erode. However, the relative importance of processes such as infiltration losses in the swash, changes in the effective weight of the sediment, and modified shear stress due to boundary layer thinning, are not yet clear. Experimental work on the influence of seepage flows within sediment beds provides conflicting results concerning the effect on bed stability. Both modelling and experimental work indicates that the hydraulic conductivity of the beach is a critical parameter. However, hydraulic conductivity varies both spatially and temporally on beaches, particularly on gravel and mixed sand and gravel beaches. Another important, but poorly understood, consideration in beach groundwater studies is the role of air encapsulation during the wetting of beach sand.     

Sediment budget controls on foredune height: Comparing simulation model results with field data

The form, height and volume of coastal foredunes reflects the long‐term interaction of a suite of nearshore and aeolian processes that control the amount of sand delivered to the foredune from the beach versus the amount removed or carried inland. In this paper, the morphological evolution of more than six decades is used to inform the development of a simple computer model that simulates foredune growth. The suggestion by others that increased steepness of the seaward slope will retard sediment supply from the beach to the foredune due to development of a flow stagnation zone in front of the foredune, hence limiting foredune growth, was examined. Our long‐term data demonstrate that sediment can be transferred from the beach to the foredune, even with a steep foredune stoss slope, primarily because much of the sediment transfer takes place under oblique rather than onshore winds. During such conditions, the apparent aspect ratio of the dune to the oncoming flow is less steep and conditions are not as favourable for the formation of a stagnation zone. The model shows that the rate of growth in foredune height varies as a function of sediment input from the beach and erosion due to storm events, as expected, but it also demonstrates that the rate of growth in foredune height per unit volume increase will decrease over time, which gives the perception of an equilibrium height having been reached asymptotically. As the foredune grows in size, an increasing volume of sediment is needed to yield a unit increase in height, therefore the apparent growth rate appears to slow. Copyright © 2018 John Wiley & Sons, Ltd.