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To allow for effective and sustainable coastal management and planning it is important to have the tools available to estimate extreme beach erosion levels. This paper, therefore, presents an evaluation of methods available for quantifying extreme beach erosion. Previous common practice is the use of a single benchmark (1 in \(N\) year) event to estimate the corresponding extreme erosion level. The limitations of this approach led to the development of more sophisticated temporal simulation frameworks providing robust statistical quantification of extreme beach erosion. These developments have resulted in a number of follow on studies to progress the methodology in line with a range of coastal morphodynamic modelling approaches. The discussion presented here, begins with basic empirical techniques and progresses up to those conducted using the most up-to-date morphodynamic models. Each methodology is applied to Narrabeen Beach, NSW, Australia, to compare and assess their suitability. The development of these methodologies is a relatively new topic, meaning that there is much scope for further progression. Although the use of state-of-the-art morphodynamic models is shown to give a good representation of erosion volumes, their impracticalities seem to outweigh the benefits. Incorporation of more realistic estimations of the storm and wave climate and the requirement for global evaluation are identified as central to further development.

Steep slopes significantly influence the propagation of both short period waves and accompanying long-period waves with the same time scale as the wave groups. Therefore, conventional wave models are not directly appropriate for the computation of the wave field on such a slope. A numerical model is proposed for the simulation of long-period water surface fluctuations forced by short-period wave groups. This model is based on the generalized conservation equations of mass and momentum. The conventional closure relationship used for radiation stresses in most previous long-period wave models is upgraded for steep slopes and an explicit relationship is found for the dynamic component of the mean bottom pressure. The model is verified through some wave flume data collected on a steep slope. The model is then used to investigate long-period water surface fluctuations on horizontal shelves with steep seaward faces. It is found through numerical investigations that the long-period water surface fluctuations on a steeply faced coastal shelf greatly depend on the transmission of short-period waves. For short-period waves propagating without breaking, steeply faced shelves provide large long-period waves while opposite is true for breaking short-period waves.

In this paper the smoothed particle hydrodynamics, (SPH), technique is used to investigate the pressure distribution on steps located in the non-aerated flow region of a stepped spillway for different discharges typical of skimming flow conditions. The open source code 2D SPHysics has been employed after being validated against the laboratory model studies of flow over broad crested weirs and flow over stepped spillways. The numerical results, in terms of the water surface and velocity profiles at different sections, are in good agreement with the corresponding experimental results. The code is then applied to determine the pressure distribution on the vertical and horizontal step faces. Also, the aspects of the pressure pattern are described and the positions/magnitudes of the maximum and minimum pressure values are presented.

UK coasts are subject to widespread erosion in part due to the cumulative effect of human intervention on soft coastlines, and further threatened due to more rapid change due to climate change, especially sea-level rise. At the same time, Shoreline Management now requires predictions of coastal evolution up to 100 years in the future. This leads to the challenge of predicting coastal geomorphic behaviour at the mesoscale (10 to 100 km and 10 to 100 years). Currently, this is often based on expert judgement. However, relevant components for mesoscale coastal simulation are emerging, including: (1) new methods for system-level analysis of coast, estuary and offshore landform behaviour, which include engineering and management interventions in a consistent manner to natural drivers; (2) well validated ‘bottom-up’ hydrodynamic and sediment transport models such as POLCOMS and TELEMAC; (3) operational ‘reduced complexity models’ of selected coastal landforms (e.g., cliffs (SCAPE), estuaries (ASMITA), saltmarsh (SLAMM)); and (4) growing observational datasets that allow data-driven approaches to coastal analysis and prediction. The iCOASST Project will use these components to develop and apply an integrated systems modelling framework for mesoscale coastal simulation as explained in this paper.

In this paper, beach profile surveys acquired over more than a decade at a sandy beach (Narrabeen Beach, New South Wales, Australia) and a composite sand–gravel beach (Milford-on-Sea, Christchurch Bay, UK) are analysed to compare and contrast cross-shore morphodynamics of the two beach types. The different behavioural characteristics of the two beach types at decadal, inter-annual and intra-annual time scales are investigated. Comparisons of beach profiles with Dean's equilibrium profile and Vellinga's erosion profile show that the Dean's profile satisfactorily represents the time mean profiles of both beach types. Statistical and Empirical Orthogonal Function (EOF) analyses confirm the generally accepted model that the inter-tidal zone is the most morphodynamically active region on a sandy beach whereas the swash zone is the most dynamic region on a mixed sand–gravel beach. The results also imply that during storms composite sand–gravel beaches may become unstable due to cutback of the upper beach while sandy beaches are more likely to be unstable as a result of beach lowering due to sediment transport from the inter-tidal zone to the sub-tidal zone during storms. EOF results also show that Milford-on-Sea beach is in a state of steady recession while the Narrabeen Beach shows a cyclic erosion–accretion variability. A multivariate technique (Canonical Correlation Analysis, CCA) shows that on the composite beach a strong correlation exists between incident wave steepness and profile response, which could be attributed to the unsaturated surf zone, whereas on the sandy beach any correlation is much less evident.

A medium term morphodynamic prediction model for beach profiles, based on a 1-D diffusion formulation, is demonstrated here. The model combines an inverse methodology with a data-driven approach to derive unknown key parameters in the model governing equation. The field site used to demonstrate the model is Milford-on-Sea beach located within the Christchurch Bay beach system on the south coast of the UK, where historic measurements of cross-shore beach profile surveys and incident waves have been recorded over two decades. Despite the simplicity of the modelling approach, the model gives encouraging predictions of cross-shore beach profile changes at Milford-on-Sea. The predictive ability of the model is tested by forecasting measured beach changes on the basis of parameter calibrations performed on an independent set of measurements. Comparisons are also made against the results of a purely data-driven technique. In both cases the new method shows measureable improvements.

The long-term morphodynamic response of the Clyde Estuary to any possible change in environmental forcing associated with global climate change and human interference is examined here using a model based on a systems approach. The model, which uses Boolean Algebra as its formal mathematical language, provides a qualitative insight into the long term morphodynamic behaviour of the estuarine system, at this level without the need for detailed and quantitative hydrodynamic and morphodynamic process knowledge or extensive data resources. The model predictions suggest that the long-term morphological changes in the Clyde Estuary largely depend on the fluvial flow of the River Clyde. Salt marshes in the upper reaches of the estuary were found to be the most vulnerable morphological feature of the estuary. In the event of increased river flow in the future, a likely situation according to climate change scenarios, saltmarshes will deplete or disappear altogether, irrespective of the sediment influx into the estuary. Changes to waves and tides will also contribute to the evolution by taking the estuary through significantly different intermediate morphological states whilst evolving towards a stable end state.

The long-term morphodynamic response of estuarine systems to sea level rise and human interference has been studied using a Boolean network approach. The method uses Boolean variables to represent the different elements of the estuarine system, their inter-relationships and the external forcing. The response of a variable to a given change can be deduced from the corresponding Boolean function, which describes the feedbacks between that particular variable and the others in the network. This approach provides qualitative insights into the behaviour of estuary systems without the need for a detailed and quantitative specification of linkages between the various components of the system. Three types of estuaries: glacial valley, drowned river valley and drowned coastal plain are analysed and the results are compared. These estuary types are different in their origin and also have different characteristics due to the geomorphological elements present in each. Human interference, in the form of construction and dredging, has also been considered. An analysis of estuary systems shows that the nature of long-term morphodynamical response to sea level rise depends on the type of estuary and the availability of external sediment to meet the increasing sediment demand within the system. If the estuary has an abundant influx of external sediment on a continuous basis, then the estuary is able to maintain its geomorphology and reach a stable state. In the absence of adequate supply of external sediment, some of the prominent features such as salt marshes and spits are likely to recede or disappear altogether during the process of morphological evolution against sea level rise. Our analysis also suggests that the moderate human interference in the form of dredging and structural construction does not have a significant impact on the overall geomorphology of estuaries in the long-term. However, changes in intermediate evolutionary states can occur in response to such intervention, thereby showing short-to-medium term impacts on estuary systems.

A systems method based on a Boolean approach is used to predict medium- to long-term behaviour of estuary morphology. Boolean networks are formed for various types of generic estuaries by taking into account the feedback involved between various estuary elements and external forcing which drive morphological evolution. A logical framework is then developed, and the Boolean matrix is derived. Various different potential morphological evolutionary pathways are then selected from the Boolean matrix, analysed, and discussed. The Boolean method provides a complementary approach for qualitative modelling of complex estuary systems. The method was applied to the Ribble Estuary in northwest England, and the predictions from the Boolean approach were in very good qualitative agreement with the observed morphological evolution of the Ribble Estuary during the last 150 years.

A new technique for predicting long-term variations in estuary morphology is developed using a morphological evolution equation that isolates diffusive and non-diffusive processes in estuaries. The contribution from non-diffusive processes to the morphological changes of the estuary is incorporated in the governing equation by a source function. The source function is derived by solving an inverse problem using historic survey data of the Humber estuary, UK covering a period of 150 years. Source functions derived for the consecutive pairs of bathymetry surveys show a significant structure persistent throughout the entire data set. Large scale features such as tidal channels, tidal flats and linear banks in the outer estuary are persistently visible in the source function. Empirical Orthogonal Function (EOF) analysis is used to analyse the spatial and temporal variation in the source function. The first spatial eigenfunction which corresponds to the time-mean value of the source function captures over 92% of the mean square of the data. Over 65% of the data variance is captured by the first six eigenfunctions. The first temporal eigenfunction which corresponds to the mean value of the source function is almost constant as expected.

Low-frequency waves in the surf and swash zones on various beach slopes are discussed using numerical simulations. Simulated surface elevations of both primary waves and low-frequency waves across the surf zone were first compared with experimental data and good agreement found. Low-frequency wave characteristics are then discussed in terms of their physical nature and their relationship to the primary wave field on a series of sea bottom slopes. Unlike primary waves, low-frequency wave energy increases towards the shoreline. Low-frequency waves in the surf and swash are a function of incident waves and the sea bottom slope and hence the saturation level of the surf zone. Wave energy on a gently sloping beach is dominated by low-frequency waves while primary waves play a significant role on a steep beach. Low-frequency wave radiation from the surf zone on a given beach depends on primary wave frequency and beach slope. However, a very poor correlation was found between surf similarity parameter and low-frequency wave radiation.

A weakly non-linear Boussinesq model with a slot-type shoreline boundary is used to simulate swash oscillations on beaches. Numerical simulations of swash were compared with laboratory measurements and in general good agreement found (less than 15% root-mean-square error of surface elevation except in regular waves). A series of numerical experiments on shoreline movement were then performed for a range of beach slopes and incident wave conditions. The resulting swash characteristics are then discussed in terms of their physical nature and spectral properties. On steep slopes, both individual bores and infragravity waves are equally significant in driving the swash while infragravity waves alone drive them on mild slopes. Swash excursions on any given slope are found to be highest when individual bores from a partially saturated surf zone ride on top of low-frequency waves. This is confirmed by the relationship found between swash excursion and wave groupiness in the surf zone. Swash excursions increase with increasing incident wave energy, even in fully saturated surf zones. However, a poor correlation is found between swash excursion and the surf similarity parameter due to the involvement of infragravity wave energy in the swash.

A laboratory study of the flow over a bar with a single rip channel has been performed. First, the well-known pattern of a bar circulation cell with a strong offshore-directed current out through the rip channel and a weaker onshore-directed return flow over the bar is documented. Then measurements of the three-dimensional structure of the flow in the area where the rip channel, the bar and the trough meet and well inside the rip channel are presented. These measurements reveal that 3D effects play an important role, and that a depth-integrated viewpoint may not always be sufficient for predicting the flow in the near bed region. Particle-tracking experiments illustrate the near bed flow pattern over the entire area. These demonstrate how the overall trajectory pattern changes as a function of the distance of wave breaking from the bar crest: For some conditions, the rip current is fed from the trough and for other conditions it is fed directly from the bar. Both the 3D measurements and the trajectory tests show the existence of a weaker onshore-directed near-bed drift in the area where the rip current ceases. Finally, in a series of sensitivity tests, measurements of the rip current intensity for different wave climate and water level conditions reveal a strong correlation between the rip current intensity and the wave height (both normalized).

Accurate prediction of medium- and long-term morphological changes in estuaries remains very challenging. Approaches to predicting the morphological evolution of estuaries generally follow one of two types: Process based modelling and system behaviour modelling. Even though with the latter models, the underlying physical processes may not be fully explained, they provide good qualitative results. This has encouraged the development of hybrid models with simplified dynamics that are designed to predict estuary morphodynamic change by including only predominant processes. Here, we apply a new hybrid model to the Deben Estuary in the UK, which is a hybrid between process-based and behaviour-oriented approaches. The success of the analysis depends on the availability and precision of the historic data. Yearly scale changes of the Deben source terms are well predicted. Further analysis of source function is necessary for longer term predictions.

In this paper, the application of a 3D numerical model covering the area of Pentland Firth channel (Scotland, UK) to investigate the hydrodynamics related to tidal energy extraction is presented in detail. A full validation analysis is carried out so that the fully operational 3D hydrodynamic model could be applied with confidence in order to explore possible impacts of tidal devices on the ambient marine environment. Following that, a higher resolution hydrodynamic and morphodynamic model covering the area of Inner Sound channel, between the Island of Stroma and Scottish Mainland, favoured for tidal energy extraction inside Pentland Firth, is set up. Preliminary results indicate that the existing morphodynamics of the observed sandbank areas inside Inner Sound Channel are very dynamic. In such a dynamic environment, results imply that possible alterations in tidal currents due to energy extraction may have some implications on the existing morphodynamic regime.

Dune erosion at sandy coastal systems poses significant threat to the hinterland areas due to flooding and subsequent damage to life and property. The Sefton Coast (Fig.1), bounded by Mersey (South) and Ribble (North) estuaries in the Liverpool Bay, represents about 20% of the UK’s dune system, has a high recreational value, form an effective coastal flood defense and consists of a significant number of conservation areas of national and international interest. This area is however susceptible to erosion during storm events where landward retreat occurs leading to dune breach and coastal flooding. Present study focused on an area around the Formby Point of the Sefton Coast (dashed-line polygon in Fig.1), which is a highly dynamic sedimentary system. The dune system at Formby Point beach showed continuous accretion (max ~4.7 m/year) during the last century but has become an eroding beach since early twentieth century (max. ~6.2 m/year). However, beach accretion can still be seen in far south and north of Fomby Point. The Sefton Coast experiences a semi-diurnal macrotidal regime with a mean spring tidal range reaching 8.22 m (Esteves et al., 2012). Mean annual significant wave height (Hs) is about 0.53 m while extremes exceed 5 m (Brown et al., 2010). The aim of this study is to investigate the response of the Formby Point dune system to extreme storm conditions based on the March 2010 storm event (max. Hs>3.5 m, see Brown, 2010). We use the 2DH process-based morphological model XBeach, which has been developed to investigate dune erosion under extreme conditions (Roelvink et al., 2009), in combination with the SWAN spectral wave model (Booij et al., 1999). The model set-up consists of a coarse-grid model (Sefton) and a fine-grid model (Formby Point) which encloses the area of interest. The Sefton model is driven by the Liverpool Bay WaveNet buoy wave data (Esteves et al., 2012). The outputs of the Sefton model provide wave and water level boundary conditions to the Formby Point morphodynamic model to investigate the beach response to the selected storm event. The model setup described above is then used to simulate nearshore hydrodynamics and morphodynamics. Fig. 1shows a snapshot of simulated Hs corresponding to the storm event occurred in the Liverpool Bay during 30 March and 02 April 2010, at the mean tidal level. Offshore waves are significantly attenuated when travelled from offshore to nearshore. Fig. 2 shows the model simulated exposure of the dune system and the beach during Low Water (LW) (a) and High Water (HW) (b). At LW, the beach exposes up to about 3 km while at HW, the entire beach drowns, exposing the dune system to incoming waves. Therefore, a storm event combined with HW may lead to damage the dune system and hence flooding of the hinterland of the River Alte area, due to the low dune height in this area. Relatively high morphological changes are observed around the Crosby channel area (see location in Fig. 1). The storm driven dune erosion occurred during the HW. Large storm waves propagate along the Crosby channel towards the River Alte area. The River Alte area is susceptible to coastal flooding during storms, as a result of the low dune crest in this area. Work is currently in progress to predict the dune evolution and flooding under the future climate change and sea level rise scenarios.

This paper presents a new combined statistical-process based approach for modeling storm driven, cross-shore beach profile response. The approach discussed here involves combining detailed statistical modeling of offshore storm data and a process based morphodynamic model (XBeach), to assess the medium to long-term morphodynamic response of cross-shore beach profiles. Up until now the use of process-based models has been curtailed at the storm event timescale. This approach allows inclusion of the post-storm recovery, in addition to individual event impacts, thus allowing longer-term predictions. The calibration of XBeach for modeling, both, storm induced erosion and post- storm recovery, taking Narrabeen Beach, NSW, Australia as a case study; and the approach used to combine XBeach with the statistical framework to develop the approach are discussed.

In this paper, cross-shore morphodynamic evolution of a sand and sand-gravel composite beach, are compared and contrasted used historic surveys of beach profiles. The differential behavior of cross-shore morphodynamics at a range of time scales covering event-scale dynamics up to intra-annual scale variability are investigated and discussed. The application of equilibrium concept to both beach types is explored through Dean’s equilibrium profile and Vellinga’s beach erosion profile. Variability of cross-shore profile dynamics are quantified and discussed through bulk statistical analysis. Multi-scale morphodynamic trends are determined using Empirical Orthogonal Eigenfunction (EOF) analysis. The above analysis enables to recognise failure mechanism of each beach type during a storm.

The paper describes the development of a hybrid behaviour-oriented/data-driven shoreline evolution model. The model is based on a form of advection–diffusion formulation widely known to describe shoreline change. The approach breaks down the model governing equation into two parts, one describing the contribution from time-averaged wave-driven processes through a spatially varying diffusion coefficient and the other describing time-varying wave contributions and all other processes that contribute to shoreline change, through a source function. Both the diffusion coefficient and the source function are site-specific and unknown. Historic incident wave measurements are used to determine the diffusion coefficient at a given site. The source function is derived by the inverse solution of the model governing equation using historic shoreline surveys. The method is demonstrated for Colwyn Bay beach at Conwy Bay in North Wales, UK. For drift-dominated shorelines, the technique can isolate the contributions of cross-shore and long-shore transport to shoreline change over a range of timescales, which is critical in implementing coastal defence measures.

The need for reliable modelling techniques for the prediction of morphological change in coastal settings has become increasingly important to coastal planners and policy makers in recent years due to the effects of accelerated sea level rise and a shift in approach from coastal defence to coastal management. In this research a new cellular automata based model is developed in order to bridge the gap between current bottom-up, process based models and top-down behaviour oriented models of estuarine morphodynamic evolution, and make predictions of morphological change over medium time-scales (one year to several decades). The key processes of tidal flows, waves, sediment transport and salt marsh ecology are represented in simplified form in order to capture the complex interactions and feedbacks that occur between them and which ultimately determine how the morphology will develop in response to environmental change. The initial bathymetry of the estuary is represented by a cluster of rectangular cells in a CA domain. Tidal flows are estimated using a new routing model, which shows good agreement with a conventional 2D hydrodynamic model but is much more computationally efficient.

The Severn Estuary (west coast of UK) is a highly dynamic environment and thus understanding of sediment transport under both natural and man-made changes is vital to the sustainable use of the coastal area in this region. The area is likely to be the site of the world’s first tidal energy lagoon. The construction and operation of the lagoon will result in some localised changes to hydrodynamic processes, leading to some potential changes in sediment transport and depositional processes at identified receptors within Swansea Bay (Fairley et al., 2014, Fairley et al., 2016, TLSB, 2016). There are some concerns about the possible impacts on the Site of Special Scientific Interest – SSSI (Blackpill and Crymlyn Burrows) and Kenfig Special Area of Conservation – SAC (not shown on figure), located Southeast of the tidal lagoon. A three dimensional hydrodynamics model (DELFT3D) of the Swansea bay area has been set up to investigate the sediment transport dynamics within Swansea Bay and longer term hydrodynamics of bedform features in the area. This project will underpin improved environmental understanding and coastal management in the Swansea Bay region because the models produced will also provide input data for other projects reliant on tide, wave and sediment transport information in the area.

Flooding and coastal erosion is a frequent and widespread natural hazard in the UK. With increasing urban development pressures on flood systems and changing global climate, frequency and severity of flooding is rapidly increasing. Temporal clustering of flood events in time has a critical effect in reducing the ability of systems to recover to the pre-flood ‘norm’, leading to amplified flood damages in the second flood event. This can be considered as system memory, the timeframes of which will be highly variable and range from days to years according to system components. The current assumptions of flood risk are based on single-event simulations and fail to consider the spatio-temporal dynamics of morphological memory due to coastal erosion. The floodMEMORY project attempts to address this issue through a continuous flood simulation framework based on temporal clustering of flood drivers.