Data-based forecasting of beach volumes on monthly to yearly timescales

Data-based methods for forecasting beach volumes are tested using ground-measured bathymetry from Duck, North Carolina, comprising 26 profiles, 20 year duration and one-month resolution. Derived beach volume time series show weak seasonal and strong event signals. The forecasting methods used are: Holt–Winters (standard and modified), three types of linear regression, and a default forecast in which the latest measurement persists unchanged into the future. Improved forecast accuracies are obtained by two modifications to Holt–Winters, involving an autocorrelation correction and long-term trend-damping, and by smoothing the fitting data using running medians or wavelet approximations. Beach volume forecasts are tested mainly at monthly intervals up to 12 months ahead, with further tests at up to 36 months ahead. Overall, modified Holt–Winters performs best and the default forecast second-best. With an added artificial seasonal signal, modified Holt–Winters outperforms the other methods more substantially.     

A relationship to describe the cumulative impact of storm clusters on beach erosion

Estimation of erosion volumes for adequate dry beach buffer zones is commonly estimated on the basis of a single extreme event, such as the 1 in 100 year storm. However, the cumulative impact of several smaller, closely spaced storms can lead to equal, if not more, dry beach loss, but this is often not quantified. Here we use a calibrated model for dune erosion, XBeach, to hindcast the cumulative erosion impact of a series of historical storms that impacted the Gold Coast, Queensland region in 1967. Over a 6-month period, four named cyclones (Dinah, Barbara, Elaine, and Glenda) and three East Coast Lows caused a cumulative erosion volume greater than the predicted 1 in 100 year event. Results presented here show that XBeach was capable of reproducing the measured dry beach erosion volume to within 21% and shoreline retreat to within 10%. The storms were then run in 17 different sequences to determine if sequencing influenced final modeled erosion volumes. It is shown that storm sequencing did not significantly affect the total eroded volumes. However, individual storm volumes were influenced by the antecedent state of the beach (i.e. prior cumulative erosion). Power-law relationships between cumulative energy density (∑ E) and eroded volume (∆V) as well as cumulative wave power ((∑ P)) and eroded volume (∆V) both explained more than 94% of the modeled dry beach erosion for the 1967 storm sequences. When the relationship was compared with observed and modeled erosion volumes for similar beaches but different storm forcing, the inclusion of pre-storm beach swash slope (β_swash) in the parameterization was found to increase the applicability of the power-law relationship over a broader range of conditions.     

Coastal defence through wave farms

The possibility of using wave farms for coastal defence warrants investigation because wave energy is poised to become a major renewable in many countries over the next decades. The fundamental question in this regard is whether a wave farm can be used to reduce beach erosion under storm conditions. If the answer to this question is positive, then a wave farm can have coastal defence as a subsidiary function, in addition to its primary role of producing carbon-free energy. The objective of this work is to address this question by comparing the response of a beach in the face of a storm in two scenarios: with and without the wave farm. For this comparison a set of ad hoc impact indicators is developed: the bed level impact (BLI), beach face eroded area (FEA), non-dimensional erosion reduction (NER), and mean cumulative eroded area (CEA); and their values are determined by means of two coupled models: a high-resolution wave propagation model (SWAN) and a coastal processes model (XBeach). The study is conducted through a case study: Perranporth Beach (UK). Backed by a well-developed dune system, Perranporth has a bar between − 5 m and − 10 m. The results show that the wave farm reduces the eroded volume by as much as 50% and thus contributes effectively to coastal protection. This synergy between marine renewable energy and coastal defence may well contribute to improving the viability of wave farms through savings in conventional coastal protection.     

Data-based yearly forecasting of beach volumes along the Dutch North Sea coast

Beach and nearshore levels have been measured yearly along the entire Dutch North Sea coast since the mid 1960s (the ‘Jarkus’ data set). This data set has been processed to create separate time series of beach volumes at longshore intervals of about 250 m, giving over 2000 time series in total. These time series typically show a high annual variability with weak long-term trends. The present Dutch national coastal management strategy involves making year-ahead forecasts of beach volumes by extrapolating a linear least squares trend through the previous ten years' data separately for each longshore location. In this paper, these forecasts are shown to be worse than the trivial forecast in which the most recently measured beach volume persists unchanged into the future, with a mean square error (MSE) about 13.5% worse (equivalent to a root mean square error (RMSE) 6.5% worse). Improvements to these forecasts are sought by testing six different univariate forecasting methods. The two best methods improve on the persistence of the most recently measured beach volume by about 15% MSE (8% RMSE), and on the presently used linear least squares trend method by about 25% MSE (13.5% RMSE). Further comparisons are made between the forecasting methods to investigate several factors. These include varying the amount of fitting data for the forecasting methods, smoothing of the fitting data, different methods for interpolating gaps in the data, the longshore aggregation of data, making forecasts for coastal profiles with and without nourishments, and making forecasts up to five years ahead. These forecasting methods are designed as a coastal management tool to provide yearly forecasts quickly and routinely for the whole Dutch North Sea coast.     

Runup estimations on a macrotidal sandy beach

This paper presents a methodological approach to calculate runup from the analysis of morphodynamic conditions on a macrotidal sandy beach. The method is based on measurements of the elevation of high-tide deposits and on the analysis of morphological and hydrodynamic changes. A series of measurements has been carried out on the beach of Vougot (Brittany, France) under different wave conditions. This allowed to assess runup formula effectiveness on a macrotidal sandy beach and to determine the best slope parameters to estimate runup. The results suggest that on that macrotidal sandy beach the slope of the active section of the upper beach should be used instead of the entire slope of the foreshore, the latter resulting in an underestimation of runup elevations when used in predictive equations from the literature. Results obtained with widely used equations are relatively well correlated with observed values (r² = 0.63). An analysis of the relationship between observed runup elevations and various variables has enabled the establishment of a runup estimation formula with a relatively good fit to the study site (r² = 0.86).     

Tsunami-like solitary waves impinging and overtopping an impermeable seawall: Experiment and RANS modeling

This study investigates tsunami-like solitary waves impinging and overtopping an impermeable trapezoidal seawall on a 1:20 sloping beach. New laboratory experiments are performed for describing three typical cases: a turbulent bore rushes inland and subsequently impacts and overtops the seawall (Type 1); a wave directly collapses on the seawall and then generates overtopping flow (Type 2); and, a wave straightforwardly overtops the seawall crown and collapses behind the seawall (Type 3). A two-dimensional volume of fluid (VOF) type model called the COBRAS (COrnell BReaking And Structure) model, which is based on the Reynolds-Averaged Navier–Stokes (RANS) equations and the k–ε turbulence closure solver, is validated by experimental data and then applied to investigate wave dynamics for which laboratory data are unavailable. Additionally, a set of numerical experiments is conducted to examine the dynamic wave acting force due to waves impacting the seawall. Effects of wave nonlinearity and freeboard are elucidated. Special attention is given to a distinct vortex evolutionary behavior behind the seawall, in which the dynamic properties of entrapped air-bubbles are briefly addressed experimentally and numerically.     

Numerical modelling of erosion and accretion of plane sloping beaches at different scales

The paper focuses on the numerical simulation of erosion of plane sloping beaches by irregular wave attack in three wave flumes of different scales. One of the prime objectives of the tests was to provide a consistent data set for the improvement of numerical beach profile models. A practical application of this research with wave attack on plane sloping beaches is the erosion of the plane beaches after nourishment. Three models (CROSMOR, UNIBEST-TC and DELFT3D) have been used to simulate the flume experimental results focusing on the wave height distribution and the morphological development (erosion and deposition) along the beach profiles. Overall, the model predictions for wave heights show consistent results. Generally, the computed wave heights (H_rms and H_1/3) are within 10% to 15% of the measured values for all tests (under-prediction of the largest wave heights close to the shore). The three models can simulate the beach erosion of the wave flume tests (erosive tests) reasonably well using default values of the sand transport parameters. The model performance for the accretive tests is less good than that for the erosive tests. A practical field application of this research is the erosion of nourished beaches, as these beaches generally have rather plane beach slopes immediately after nourishment. Various graphs are given to estimate the beach erosion of nourished beaches.     

On the evolution and run-up of breaking solitary waves on a mild sloping beach

This paper presents new laboratory experiments carried out in a supertank (300 m × 5 m × 5.2 m) of breaking solitary waves evolution on a 1:60 plane beach. The measured data are employed to re-examine existing formulae that include breaking criterion, amplitude evolution and run-up height. The properties of shoreline motion, underwater particle velocity and scale effect on run-up height are briefly discussed. Based on our analyses, it is evidently found that there exist five zones during a wave amplitude evolution course on the present mild slope. A simple formula which is capable of predicting maximum run-up height for a breaking solitary wave on a uniform beach with a wide range of beach slope (1:15–1:60) is also proposed. The calculated results from the present model agree favorably with available laboratory data, indicating that our method is compatible with other predictive models.     

Seasonal persistence of a small southern California beach fill

Torrey Pines State Beach, a site with large seasonal fluctuations in sand level, received a small shoreface beach fill (about 160,000 m³) in April 2001. The 600 m-long, flat-topped nourishment pad extended from a highway riprap revetment seaward about 60 m, terminating in a 2 m-tall vertical scarp. A 2.7 km alongshore span, centered on the nourishment region, was monitored prior to the nourishment and biweekly to monthly for the following 2 years. For the first 7 months after the nourishment, through fall 2001, significant wave heights were small, and the elevated beach fill remained in place, with little change near and above Mean Sea Level (MSL). In contrast, the shoreline accreted on nearby control beaches following a seasonal pattern common in southern California, reducing the elevation difference between the nourished and adjacent beaches. During the first winter storm (3 m significant wave height), the shoreline retreated rapidly over the entire 2.7 km survey reach, forming an alongshore-oriented sandbar in 3 to 4 m water depth [Seymour, R.J., Guza, R.T., O'Reilly, W., Elgar, S., 2004. Rapid erosion of a Southern California beach fill. Coastal Engineering 52 (2), 151–158.]. We show that the winter sandbar, most pronounced offshore of the nourishment, moved back onto the beach face during summer 2002 (following the usual seasonal pattern) and formed a wider beach above MSL at the site of the original nourishment than on the control beaches. Thus, the April 2001 shoreline nourishment was detectable until late fall 2002, persisting locally over a full seasonal cycle. In an extended 7-year time series, total sand volumes (summed between the back beach and 8 m water depth, over the entire 2.7 km reach) exhibit multi-year fluctuations of unknown origin that are twice as large as the nourishment volume.     

Beach nourishments at Coolangatta Bay over the period 1987–2005: Impacts and lessons

Erosion of the southern Gold Coast beaches (SE Queensland, Australia) was exacerbated after the extension of the Tweed River training walls in the early 1960s. To achieve the objective of restoring and maintaining beach amenity, significant nourishment works have been undertaken in Coolangatta Bay over the past 30 years. Particularly, under the Tweed River Entrance Sand Bypassing Project (TRESBP) since 1995, a number of nourishment campaigns and the implementation of a permanent sand bypass system in 2001 have resulted in significant changes of Coolangatta Bay morphology. The present case study investigates the influence of both wave climate and nourishment works on the area extending from the updrift Snapper Rocks area to downdrift Kirra Beach. SWAN spectral wave model is implemented at Coolangatta Bay area and forced by the global wave model WW3 to estimate wave forcing and the potential natural longshore drift entering in Coolangatta. Specific transects extracted from accurate bathymetric surveys are used to investigate and quantify Coolangatta Bay sedimentation for the period 1987–2005. A network of Argus video stations provides high sample rate information on the shoreline evolution. Results show that, over the past 10 years, Coolangatta Bay has infilled rapidly. Sedimentation reached up to 6 m in some areas between 1995 and 2005, with beach width increasing by 200 m at Kirra Beach. Rapid seaward shoreline migration is consistent with the intense over-pumping of sand relative to the natural potential to move sand alongshore. The nourishment strategy used during this project has successfully delivered large amounts of sand to the southern Gold Coast embayment, although it has been up to now controversial from many community perspectives. The artificial sand bypassing process proved to be much more efficient than depositing the dredged sand in the nearshore area which requires a significant period of low energy condition in order for the deposited sediment to migrate shoreward and weld to the shore. This case study confirms that, when carefully undertaken, sand bypassing is a sustainable and flexible soft engineering approach which can work in concert with natural processes.     

How much data is enough? The importance of morphological sampling interval and duration for calibration of empirical shoreline models

The ability to robustly predict future shoreline position under the influence of changing waves and sea-level rise is a key challenge to scientists and engineers alike. While extrapolating a linear trend out in time is a common baseline approach, the recent development of a number of empirical shoreline models allows the prediction of storm and annual-scale variability as well. The largest constraint in applying these models is the availability of high quality, adequate duration data sets in order to calibrate model free parameters. This contribution outlines several such models and discusses the monitoring programs required to calibrate and hindcast shoreline change from 1 to 10 years at two distinct beach types: a storm-dominated site and the second exhibiting a large seasonal variability. The seasonally-dominated site required longer data sets but was less sensitive to sampling interval, while the storm-dominated site converged on shorter, more frequently sampled data sets. In general, calibration based on a single year of observed shorelines resulted in a large range of model skill and was not considered robust. Monitoring programs of at least two years, with shorelines sampled at dt ≤ 30 days were sufficient to determine initial estimates of calibration coefficients and hindcast short-term (1–5 years) shoreline variability. In the presence of unresolved model processes and noise, hindcasting longer (5 + years) data sets required longer (5 + years) calibration data sets, particularly when sampling intervals exceeded 60 days.     

Modelling gravel beach dynamics with XBeach

Numerical cross-shore profile evolution models have been good at predicting beach erosion during storm conditions, but have difficulty in predicting the accretion of the beach during calm periods. This paper describes the progress made in modifying and applying the public domain XBeach code to the prediction and explanation of the observed behaviour of coarse-grained beaches in the laboratory and the field under accretive conditions. The paper outlines in details the changes made to the original code (version 12), including the introduction of a new morphological module based upon Soulsby's sediment transport equation for waves and currents, and the incorporation of Packwood's infiltration approach in the unsaturated area of the swash region. The competence of this modified model during calm conditions for describing the steepening of the profile, and the growth of the beach berm is demonstrated. Preliminary results on the behaviour of the beach subject to both waves and tides are presented. Good agreement is found between the model simulations and large-scale laboratory measurements, as well as field observations from a composite beach in the UK. The reasons for the model's capabilities are discussed.     

Beach response to a fixed sand bypassing system

Indian River Inlet is located at roughly the mid-point of the Atlantic coast of Delaware and connects the ocean to two Delaware inland bays. Jetties constructed in 1940 have maintained the inlet for navigation purposes but have also acted as a barrier to net northerly alongshore sediment transport causing downdrift erosion. A mobile, land-based bypassing system was initiated in 1990 in an effort to counteract this erosion. Beach profile data from 1985 (pre-bypassing) until 2008 are used to investigate the effect of the sand bypassing system on beaches adjacent to the inlet. The downdrift beach experienced horizontal shoreline erosion between 10 and 60 m during the pre-bypassing period but accreted 10–20 m during the bypassing period. The mean shoreline location on the updrift beach during bypassing is 10–20 m landward (erosion) of its position during the pre-bypassing period. Empirical orthogonal function (EOF) amplitudes from analyses performed on mean-removed elevation surfaces during the periods of highest bypassed volume (average of 83% of design rate) showed that the influence of the bypassing system on the downdrift beach extends to about 1500 m of the inlet. An EOF analysis showed that different morphologic responses were evident following the initiation of bypass operations. Temporal variations of shoreline and beach morphology were correlated to the temporal variations in bypassing rates on the downdrift beach only. The downdrift beach response was greatest near the inlet for larger bypassing volumes. Correlation in these instances occurred with a roughly 1-year time lag suggesting that the beach quickly redistributes the bypassed sand. EOF amplitude and shoreline response are weakly correlated to bypassed volumes when the system bypassed smaller volumes (average of 56% of design rate) of sand suggesting that there is a minimum bypassing rate, regardless of yearly variability, below which the effect on the downdrift beach is obscured.     

Using stochastic population process models to predict the impact of climate change

More than ten years ago a paper was published in which stochastic population process models were fitted to time series of two marine polychaete species in the western Wadden Sea, The Netherlands (Van der Meer et al., 2000). For the predator species, model fits pointed to a strong effect of average sea surface winter temperature on the population dynamics, and one-year ahead model forecasts correlated well with true observations (r = 0.90). During the last decade a pronounced warming of the area occurred. Average winter temperature increased with 0.9 °C. Here we show that despite the high goodness-of-fit whilst using the original dataset, predictive capability of the models for the recent warm period was poor.     

An investigation of the multi-scale temporal variability of beach profiles at Duck using wavelet packet transforms

In an earlier paper a particular discrete wavelet transform (DWT) was used to study the complex variation of beach profile changes. However, use of the DWT requires that the sequence of spatial and temporal resolution is fixed as a dyadic sequence, which means that the variability over longer intervals is not characterised well. Here we introduce the discrete wavelet packet transform (DWPT) that uses an adaptive scaling to partition the data variance, according to an entropy cost function. The advantages of this approach are demonstrated by its application to the study of temporal variability of a 22 year record of beach profile data from the Field Research Facility (FRF) at Duck, North Carolina, USA. Time series of beach elevations at three locations across a particular profile are investigated in detail. We conclude that the DWPT provides a superior analysis of non-stationary time series to that of the DWT, with improved resolution of the scale intervals of the variability. The beach elevation around the shoreline is shown to respond at both sub-annual and interannual scales, but variability at an annual scale is weak. Moving seaward into deeper water, the variance is partitioned into fewer and longer scales. It is confirmed that elevation changes around the inner bar at Duck exhibit a strong interannual variation consistent with Plant et al. (Plant, N.G., Holman, R.A. and Freilich, M.H., 1999. A simple model for interannual sandbar behaviour. Journal of Geophysical Research 104(C7), 15755–15776). Around 23% of the variance around the inner bar is explained at the temporal scale of 64–128 months, which is consistent with the bar behaviour of 6 years found by Ruessink et al. (Ruessink, B. G., Wijnberg, K. M., Holman, R. A., Kuriyama, Y. and Van Enckevort, I. M. J., 2003. Intersite comparison of interannual nearshore bar behaviour. Journal of Geophysical Research, 108 (C8): 1–12). A significant new finding is, however, that about 26% of the variance is attributable to temporal scales of 16–21.3 months. Reconstruction of the wavelet packet components for individual temporal scales is shown to provide a means for identifying the impact and scale of non-stationary events, such as storms, on the beach response. This provides further information that can be used to interpret the morphological changes in terms of the forcing processes and also serves to inform morphodynamic modelling.     

Implementation and modification of a three-dimensional radiation stress formulation for surf zone and rip-current applications

Regional Ocean Modeling System (ROMS v 3.0), a three-dimensional numerical ocean model, was previously enhanced for shallow water applications by including wave-induced radiation stress forcing provided through coupling to wave propagation models (SWAN, REF/DIF). This enhancement made it suitable for surf zone applications as demonstrated using examples of obliquely incident waves on a planar beach and rip current formation in longshore bar trough morphology (Haas and Warner, 2009). In this contribution, we present an update to the coupled model which implements a wave roller model and also a modified method of the radiation stress term based on Mellor (2008, 2011a,b,in press) that includes a vertical distribution which better simulates non-conservative (i.e., wave breaking) processes and appears to be more appropriate for sigma coordinates in very shallow waters where wave breaking conditions dominate. The improvements of the modified model are shown through simulations of several cases that include: (a) obliquely incident spectral waves on a planar beach; (b) obliquely incident spectral waves on a natural barred beach (DUCK'94 experiment); (c) alongshore variable offshore wave forcing on a planar beach; (d) alongshore varying bathymetry with constant offshore wave forcing; and (e) nearshore barred morphology with rip-channels. Quantitative and qualitative comparisons to previous analytical, numerical, laboratory studies and field measurements show that the modified model replicates surf zone recirculation patterns (onshore drift at the surface and undertow at the bottom) more accurately than previous formulations based on radiation stress (Haas and Warner, 2009). The results of the model and test cases are further explored for identifying the forces operating in rip current development and the potential implication for sediment transport and rip channel development. Also, model analysis showed that rip current strength is higher when waves approach at angles of 5° to 10° in comparison to normally incident waves.     

Modelling Thermohaline Properties in an Estuarine Upwelling Ecosystem (R?́a de Vigo: NW Spain) Using Box-Jenkins Transfer Function Models

Since 1987, twice weekly, hydrological variables have been monitored at a fixed station in the R?́a de Vigo (NW Spain), aiming to examine the time scales of variability and the relationships to meteorological conditions. The present paper analyses: (1) the advantage of Box-Jenkins transfer function (TF) models (single output–multiple input), a type of linear stochastic model, to describe the dynamic behaviour of the system; and (2) the coupling between the R?́a and meteorological events at the time scale of autonomy of this coastal inlet affected by the Iberian coastal upwelling, approximately a fortnightly period. In order to achieve these objectives, thermohaline properties have been used to characterize the estuarine ecosystem (output variables), while wind regime, runoff in the drainage basin and incoming solar radiation have been considered as the main forcing variables (input variables). The use of the amplitude time series, derived from principal component analysis (PCA) applied to the deseasonalized meteorological variables, is also explored as a different set of input variables.When compared with standard regression models, all TF models built to describe thermohaline behaviour had reduced residual variance. Similar TF models, as well as percentage of explained variance, were also obtained when meteorological variables or the amplitude time series were used as input variables. The fitted TF models provided an insight into the ‘ inertial ’ behaviour of the system and the time scales of coupling of the system with the forcing variables. The plausible physical mechanisms which link the response of the system with the observed meteorological variability are also discussed. As could be expected, bottom thermohaline properties show a stronger inertial behaviour than the surface ones, which is particularly marked for bottom temperature. Besides, the shelf domain, by means of upwelling-downwelling events, strongly influences surface and bottom temperature, as well as bottom salinity; by contrast, surface salinity is mainly influenced by the effect of wind along the main axis of the R?́a and runoff. In relation to the time scales of coupling between the system and the forcing variables, thermohaline properties show a dependance with the meteorological conditions in, at least, the immediately preceding fortnight period. It was concluded that: (1) TF models that incorporate meteorological information described the dynamic behaviour of the system adequately; and (2) this type of model can be useful as a first approximation to develop more sophisticated (deterministic) models, since, with the purpose of modelling any state variable of the system, both the coupling between different domains and the time scales of the interactions must be taken into account.     

Swash zone sediment fluxes: Field observations

This paper describes newly obtained, high-frequency observations of beach face morphological change over numerous tidal cycles on a macrotidal sandy beach made using a large array of ultrasonic altimeters. These measurements enable the net cross-shore sediment fluxes associated with many thousands of individual swash events to be quantified. It is revealed that regardless of the direction of net morphological change on a tidal time scale, measured net fluxes per event are essentially normally distributed, with nearly equal numbers of onshore and offshore-directed events. The majority of swash events cause net cross-shore sediment fluxes smaller than ± 50 kg m^− 1 and the mean sediment flux per swash event is only O(± 1 kg m^− 1) leading to limited overall morphological change. However, much larger events which deposit or remove hundreds of kilograms of sand per meter width of beach occur at irregular intervals throughout the course of a tide. It was found that swash–swash interactions tend to increase the transport potential of a swash event and the majority of the swash events that cause these larger values of sediment flux include one or more interactions. The majority of the larger sediment fluxes were therefore measured in the lower swash zone, close to the surf/swash boundary where swash–swash interactions are most common. Despite the existence of individual swash events that can cause fluxes of sediment that are comparable to those observed on a tidal time scale, frequent reversals in transport direction act to limit net transport such that the beach face volume remains in a state of dynamic equilibrium and does not rapidly erode or accrete.     

Finite volume scheme for the solution of 2D extended Boussinesq equations in the surf zone

In this paper, a hybrid finite volume-finite difference scheme is applied to study surf zone dynamics. The numerical model solves the 2DH extended Boussinesq equations proposed by Madsen and Sørensen (1992) where nonlinear and dispersive effects are both relevant whereas it solves NSWE equations where nonlinearity prevails. The shock-capturing features of the finite volume method allow an intrinsic representation of wave breaking and runup; therefore no empirical (calibration) parameters are necessary. Comparison with laboratory measurements demonstrates that the proposed model can accurately predict wave height decay and mean water level setup, for both regular and solitary wave breaking on a sloping beach. The model is also applied to reproduce two-dimensional wave transformation and breaking over a submerged circular shoal, showing good agreement with experimental data.