The effect of temporal wave averaging on the performance of an empirical shoreline evolution model

The effect of using time-averaged wave statistics in a simple empirical model for shoreline change is investigated. The model was first calibrated with a six-year time series of hourly wave conditions and weekly shoreline position at the Gold Coast, Australia. The model was then recalibrated with the hourly waves averaged over intervals up to 1 year. With wave averaging up to 2 days, model performance was approximately constant (squared correlation r² ~ 0.61–0.62), with only small changes in the values of empirical model parameters (e.g. the beach response coefficient c varied by less than 4%). With between 2 and 40 day averaging, individual storms are not resolved; model skill decreased only modestly (r² ~ 0.55), but c varied erratically by up to 40% of the original value. That is, optimal model coefficients depend on wave averaging, an undesirable result. With increased averaging (> 40 days) seasonal variability in the wave field is not resolved well and model skill declined markedly. Thus, temporal averaging of wave conditions increases numerical efficiency, but over-averaging degrades model performance and distorts best-fit values of model free parameters.     

Sub-weekly to interannual variability of a high-energy shoreline

Sixty-one Global Positioning System (GPS), sub-aerial beach surveys were completed at 7 km long Ocean Beach, San Francisco, CA (USA), between April 2004 and March 2009. The five-year time series contains over 1 million beach elevation measurements and documents detailed changes in beach morphology over a variety of spatial, temporal, and physical forcing scales. Results show that seasonal processes dominate at Ocean Beach, with the seasonal increase and decrease in wave height being the primary driver of shoreline change. Storm events, while capable of causing large short-term changes in the shoreline, did not singularly account for a large percentage of the overall observed change. Empirical orthogonal function (EOF) analysis shows that the first two modes account for approximately three-quarters of the variance in the data set and are represented by the seasonal onshore/offshore movement of sediment (60%) and the multi-year trend of shoreline rotation (14%). The longer-term trend of shoreline rotation appears to be related to larger-scale bathymetric change. An EOF-based decomposition technique is developed that is capable of estimating the shoreline position to within one standard deviation of the range of shoreline positions observed at most locations along the beach. The foundation of the model is the observed relationship between the temporal amplitudes of the first EOF mode and seasonally-averaged offshore wave height as well as the linear trend of shoreline rotation. This technique, while not truly predictive because of the requirement of real-time wave data, is useful because it can predict shoreline position to within reasonable confidence given the absence of field data once the model is developed at a particular site.     

Application of one-line model to the prediction of shoreline change

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Determination and control of longshore sediment transport: A case study

The fishery harbor of Karaburun coastal village is located at the south west coast of the Black Sea. The significant waves coming from north eastern direction cause considerable rate of sediment transport along 4 km sandy beach towards the fishery harbor in the region. The resulting sediment deposition near and inside the harbor entrance prevents the boat traffic and cause a vital problem for the harbor operations. In order to determine the level and reasons of the sediment transport, the long-term observations of shoreline changes, the long-term statistical analysis of wind and wave characteristics in the region, and sediment properties have been performed. The data obtained from observations, measurements and analysis were discussed. The long-term statistics of deep water significant wave heights for each direction was discussed by comparing the results obtained from different data sources and methods. For shoreline evolution, the numerical study using one-line model was applied to describe the shoreline changes with respect to probable wave conditions. Initial shoreline was obtained from the digitized image in 1996 since there was no previous shoreline measurement of the site. The results were compared using the techniques of remote sensing obtained from sequent images using IKONOS and IRS1C/D satellites.     

Determination of wave–shoreline dynamics on a macrotidal gravel beach using Canonical Correlation Analysis

This paper describes the application of Canonical Correlation Analysis (CCA) to derive forcing–response relations between the wave climate and shoreline position on a macrotidal gravel barrier located in the southwest of the U.K., and to develop a tool to determine shoreline positions from wave records. The data sequences comprise wave climate recorded by a nearshore directional wave buoy and video-derived shorelines over a time span of one year and a half. The hydrodynamic conditions are used to determine the probability density function of wave heights and alongshore energy fluxes. These are then related to shoreline change through a CCA analysis. The CCA analysis identifies patterns of behaviour of the wave conditions and the shoreline position, and the relation between both patterns is found to provide useful information about the beach response to wave action. The analysis shows that the movement of sediment is greater at the southern end of the study area and that there is an immediate shoreline response to the wave action. In the case of coastal management it is more often the case that wave forecasts are available on a routine basis. The ability of the CCA to provide useful estimates of shorelines from wave conditions was tested by using measured waves to calculate the corresponding shoreline position from additional data at the end of the sequences. Shoreline positions determined with the CCA agreed well with the measured ones. Thus, the CCA is found to be a useful tool to determine unknown shoreline positions and support effective coastal management if good quality hydrodynamic and morphological data are available to input into the initial set-up of the technique.     

Modelling analysis of the sensitivity of shoreline change to a wave farm

Change of shoreline wave climate caused by the installation of a wave farm is assessed using the SWAN wave model. The 30 MW-rated wave farm is called the ‘Wave Hub’ and will be located 20 km off the north coast of Cornwall, UK. Changes in significant wave height and mean wave period due to the presence of the Wave Hub are presented. The results suggest that the shoreline wave climate will be affected, although the magnitude of effects decreases linearly as wave energy transmitted increases. At probable wave energy transmission levels, the predicted change in shoreline wave climate is small.     

Megacusps on rip channel bathymetry: Observations and modeling

The formation of beach megacusps along the shoreline of southern Monterey Bay, CA, is investigated using time-averaged video and simulated with XBeach, a recently developed coastal sediment transport model. Investigations focus on the hydrodynamic role played by the bay's ever-present rip channels. A review of four years of video and wave data from Sand City, CA, indicates that megacusps most often form shoreward of rip channels under larger waves (significant wave height (H_s) = 1.5–2.0 m). However, they also occasionally appear shoreward of shoals when waves are smaller (H_s ~ 1 m) and the mean water level is higher on the beach. After calibration to the Sand City site, XBeach is shown to hindcast measured shoreline change moderately well (skill = 0.41) but to overpredict the erosion of the swash region and beach face. Simulations with small to moderate waves (H_s = 0.5–1.2 m) suggest, similar to field data, that megacusps will form shoreward of either rip channels or shoals, depending on mean daily water level and pre-existing beach shape. A frequency-based analysis of sediment transport forcing is performed, decomposing transport processes to the mean, infragravity, and very-low-frequency (VLF) contributions for two highlighted cases. Results indicate that the mean flow plays the dominant role in both types of megacusp formation, but that VLF oscillations in sediment concentration and advective flow are also significant.     

Shoreline accretion and sand transport at groynes inside the Port of Richards Bay

The south-western shoreline along the entrance channel inside the Port of Richards Bay has experienced continued erosion. Four groynes were constructed to stabilise the shoreline. Monitoring of shoreline evolution provided valuable data on the accretion adjacent to two of the groynes and on the sediment transport rates at these groynes. Tides, beach slopes, winds, wave climate, current regime, and sand grain sizes were documented. The one site is “moderately protected” from wave action while the other is “protected” according to the Wiegel [Wiegel, R. L. (1964). Oceanographical engineering. Prentice Hall, Inc., Englewood Cliffs, NJ.] classification. The shoreline accreted progressively at the two groynes at 0.065 m/day and 0.021 m/day respectively. The shorelines accreted right up to the most seaward extremity of the groynes. Equilibrium shorelines were reached within about 3.5 years to 4 years, which compare well with other sites around the world. The mean wave incidence angle is large and was found to be about 22°. The median sand grain sizes were 0.33 mm and 0.37 mm. The groynes acted as total traps, the beach surveys were extended to an adequate depth, and cross-shore sediment transport did not cause appreciable net sand losses into the entrance channel. The net longshore transport rate along the study area, which is north-westbound, is only slightly lower than the gross longshore transport. The actual net longshore transport rates are 18 000 m³/year and 4 600 m³/year respectively at the two groynes. A rocky area limits the availability of sand at one groyne. There is fair agreement between the predicted and measured longshore transport rates at the other groyne.     

Seasonal-scale nearshore morphological evolution: Field observations and numerical modeling

A coupled waves–currents-bathymetric evolution model (DELFT-3D) is compared with field measurements to test hypotheses regarding the processes responsible for alongshore varying nearshore morphological changes at seasonal time scales. A 2001 field experiment, along the beaches adjacent to Grays Harbor, Washington, USA, captured the transition between the high-energy erosive conditions of winter and the low-energy beach-building conditions typical of summer. The experiment documented shoreline progradation on the order of 10–20 m and on average approximately 70 m of onshore sandbar migration during a four-month period. Significant alongshore variability was observed in the morphological response of the sandbar over a 4 km reach of coast with sandbar movement ranging from 20 m of offshore migration to over 175 m of onshore bar migration, the largest seasonal-scale onshore migration event observed in a natural setting. Both observations and model results suggest that, in the case investigated here, alongshore variations in initial bathymetry are primarily responsible for the observed alongshore variable morphological changes. Alongshore varying incident hydrodynamic forcing, occasionally significant in this region due to a tidal inlet and associated ebb-tidal delta, was relatively minor during the study period and appears to play an insignificant role in the observed alongshore variability in sandbar behavior at kilometer-scale. The role of fully three-dimensional cell circulation patterns in explaining the observed morphological variability also appears to be minor, at least in the case investigated here.     

Estimation of shoreline position and change from satellite images considering tidal variation

This paper presents the one-line shift method of determining mean sea level datum-based shoreline positions from three sequential satellite images that take into account tidal variations. Tidal correction through data interpolation on originally computed tides to accurately predict tidal level with a root mean squared error less than 10 cm. The determined mean sea level datum-based shoreline positions of the Waisanding Sandbar by the proposed method differ from those by RTK GPS by about 43.09–193.58 m. Based on the acceptable shoreline positions from satellite images, the whole area of the Waisanding Sandbar is proven to be decreasing since 1999 and migrating landward to the west of Taiwan.     

Meteorological forcing of long-term temperature variations of the Dutch coastal waters

Time series of observations of the sea surface temperature (SST) at 12 stations in the Dutch coastal zone are analyzed to establish whether an earlier published nearly 150 year long SST time series from the Marsdiep tidal inlet is representative for the whole Dutch coastal zone. The annual cycles (SST range and phase) as well as the long-term SST trends at decadal scales from other estuaries agree with the Marsdiep time series. An increasing SST trend since 1982 is a phenomenon of the whole Dutch coastal zone. In order to increase the understanding of the causes of the observed SST variability, a multiple linear regression model is constructed, which links locally determined seasonal meteorological and oceanographic forcing factors to the seasonal mean SST. The oceanographic forcing factor is the SST value from the preceding season, representing persistence due to thermal inertia of the sea. Season to season changes of the atmospheric circulation, connected with SST variability, are represented by seasonal mean wind components as forcing factors, e.g. the western winds in winter which bring relatively warm air masses to Western Europe. For the seasons where shortwave solar radiation is the dominant term in the local heat budget (spring and summer), the number of bright sun hours is used as forcing factor, roughly representing the effects of changing cloudiness. The annual mean SST, derived from the regression models for the four seasons, applied to 4 locations along the Dutch coast, correlates quite well, not only for the year to year variability (R = 0.88) but also for the longer-term SST trends (R = 0.95). An explicit local greenhouse effect is not required as separate forcing factor to explain the recent warming trend of Dutch coastal waters starting in the early 1980s; coincident variations in wind statistics and cloudiness are a sufficient explanation.     

A simple equilibrium model for predicting shoreline change

This contribution describes the development, calibration and verification of a 1-D behaviour-orientated shoreline prediction model. The model primarily encapsulates shoreline displacement forced by wave-driven cross-shore sediment transport. Hysteresis effects are shown to be important and are included in the model, whereby present shoreline change is influenced by past hydro-/morpho-dynamic conditions. The potential magnitude of shoreline change increases with incident wave power and the degree of disequilibrium. The latter disequilibrium term (Ω_eq − Ω) is expressed in terms of the time-evolving equilibrium (Ω_eq) and instantaneous (Ω) dimensionless fall velocities and dictates the direction of shoreline movement. Following Wright et al. (1985) the equilibrium fall velocity is defined as a function of the weighted antecedent conditions and is a proxy for the evolving beach state. The decay rate of the weighting function used to compute Ω_eq is a model free parameter determined by calibration against measured data, which physically reflects the degree of observed ‘memory’ of the system. The decay in amplitude of this weighting function with time is controlled by a ‘memory decay’ term (ϕ), where the weighting reaches 10%, 1% and 0.1% at ϕ, 2ϕ and 3ϕ days prior to the current calculation time. The model is applied to two multi-year (6 + years) data sets incorporating hourly wave and weekly shoreline measurements, from two contrasting energetic sites in SE Australia. The first is the relatively dissipative, straight Gold Coast (QLD) and the second is a more intermediate embayed beach at Narrabeen (NSW). The model shows significant skill at hindcasting shoreline change at both sites, predicting approximately 60% of the total shoreline variability. The Gold Coast shoreline is dominated by a strong seasonal signal. Conversely, at the Narrabeen embayment, shoreline variability (and morphology) is more dynamic, responding at storm frequency. Evidence suggests that there is a strong coherence between the shoreline position and morphodynamic state and that both have response times characterised by ϕ. It is hypothesised that optimised ϕ values in the shoreline model physically relate to the efficiency of sediment exchanges between the shoreface and offshore bars and the prevalence of one- or two-dimensional horizontal circulation. The general success of this new shoreline model for hindcasting the observed shoreline behaviour at two distinctly different open-coast sites suggests that this approach may be suitable for broader application.     

Comparison of long-, medium- and short-term variations of beach profiles with and without submerged geological control

Victoria Beach (Cadiz, Spain) comprises a rocky flat outcrop in its northern zone and a sand-rich southern zone. These natural features allowed for a 5-year monitoring period and subsequent analysis of two different profiles (one in each zone) based on differences in bottom contours. Topo-bathymetric data were analysed using empirical orthogonal functions (EOFs) to determine changes over the short-, medium- and long-term. Several morphologic phenomena were identified (generalised erosion, seasonal or summer–winter tilting of the profile around different hinge points, berm development and its posterior destruction, etc.) in terms of their importance in explaining the variability of the collected data for both profiles. It is worth mentioning that both profiles undergo parallel regression in the medium-term. Thus, the 1st eigenfunction enabled us to identify the true regression of the beach shoreline, independent of seasonal or summer–winter slope changes. Reconstruction of profiles using EOF components demonstrated that though accretion periods in the medium-term were similar for both types of profiles, the accretion speed was much faster in the sand-rich profile than in the reef-protected profile (1.01 m³/day versus 0.33 m³/day). Moreover, the seasonal erosion rate and the subsequent shoreline retreat for the sand-rich profile were much larger than for the reef-protected profile (121 m³/year versus 29 m³/year). Analysis in the short-term (changes induced by a single day's storm) showed an instantaneous tilting of the profile, with the mobilised sand volume being much greater for the sand-rich than for the reef-protected profile (68 m³/m versus 12 m³/m).     

Influence of ENSO variability on sinking-particle fluxes in the northeastern equatorial Pacific

A time-series sediment trap was operated from July 2003 to July 2008 at a station located in the 10°N thermocline ridge of the northeastern equatorial Pacific (10°30′N, 131°20′W), with the aim of understanding variations in natural background sinking-particle flux and the influence on such fluxes of ENSO (El Niño-Southern Oscillation). Each one of weak El Niño, moderate El Niño and moderate La Niña were observed during the monitoring period. During non-ENSO periods, total mass fluxes varied from 4.1 to 36.9 mg m⁻² d⁻¹, with a distinct seasonal variation, ranging from an average flux of 14.0 mg m⁻² d⁻¹ in the warm season (June-November) to 25.3 mg m⁻² d⁻¹ in the cold season (December-May). This seasonal fluctuation was characterized by a distinct difference in CaCO₃ flux between the two seasons. The enhanced particle fluxes during the cold season are attributed to the supply of nutrient-enriched subsurface water by wind-driven vertical mixing, supported by a simultaneous reduction in sea surface temperature and enhanced trade winds. The weak El Niño event occurred in the monitoring period had no recognizable effect on particle fluxes in the study area, but the moderate El Niño event was accompanied by a significant reduction in particle fluxes to 60% of the average background value in the warm season. In contrast, particle fluxes during the moderate La Niña increased to a maximum value of 129.9 mg m⁻² d⁻¹, almost three times the average background value. Organic carbon and biogenic silica fluxes were most sensitive to the El Niño and La Niña conditions. The observed variations of particle fluxes are synchronized with those of chlorophyll-a, suggesting primary productivity for the main cause of flux change. The present data indicate that marked seasonal variability in background fluxes commonly exceeds the variability associated with ENSO and post-ENSO signals, which should be taken into account when evaluating the influence of ENSO on sinking particle fluxes in the 10°N thermocline ridge area.     

Forecast of wave run-up on coastal structure using offshore wave forecast data

In this paper, first we introduce the wave run-up scale which describes the degree of wave run-up based on observed sea conditions near and on a coastal structure. Then, we introduce a simple method which can be used for daily forecast of wave run-up on a coastal structure. The method derives a multiple linear regression equation between wave run-up scale and offshore wind and wave parameters using long-term photographical observation of wave run-up and offshore wave forecasting model results. The derived regression equation then can be used for forecasting the run-up scale using the offshore wave forecasting model results. To test the implementation of the method, wave run-up scales were observed at four breakwaters in the East Coast of Korea for 9 consecutive months in 2008. The data for the first 6 months were used to derive multiple linear regression equations, which were then validated using the run-up scale data for the remaining 3 months and the corresponding offshore wave forecasting model results. A comparison with an engineering formula for wave run-up is also made. It is found that this method can be used for daily forecast and warning of wave run-up on a coastal structure with reasonable accuracy.     

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.     

Forecasting ocean wave energy: Tests of time-series models

This paper evaluates the ability of time-series models to predict the energy from ocean waves. Data sets from four Pacific Ocean sites are analyzed. The energy flux is found to exhibit nonlinear variability. The probability distribution has heavy tails, while the fractal dimension is non-integer. This argues for using nonlinear models. The primary technique used here is a time-varying parameter regression in logs. The time-varying regression is estimated using both a Kalman filter and a sliding window, with various window widths. The sliding window method is found to be preferable. A second approach is to combine neural networks with time-varying regressions, in a hybrid model. Both of these methods are tested on the flux itself. Time-varying regressions are also used to forecast the wave height and wave period separately, and combine the forecasts to predict the flux. Forecasting experiments are run at an hourly frequency over horizons of 1-4 h, and at a daily frequency over 1-3 days. All the models are found to improve relative to a random walk. In the hourly data sets, forecasting the components separately achieves the best results in three out of four cases. In daily data sets, the hybrid and regression models yield similar outcomes. Because of the intrinsic variability of the data, the forecast error is fairly high, comparable to the errors found in other forms of alternative energy, such as wind and solar.     

Modelling of sand transport under wave-generated sheet flows with a RANS diffusion model

A 1DV-RANS diffusion model is used to study sand transport processes in oscillatory flat-bed/sheet flow conditions. The central aim is the verification of the model with laboratory data and to identify processes controlling the magnitude and direction (‘onshore’/‘offshore’) of the net time-averaged sand transport. The model is verified with a large series of measured net sand transport rates, as collected in different wave tunnels for a range of wave-current conditions and grain sizes. Although not all sheet flow details are represented in the 1DV-model, it is shown that the model is able to give a correct representation of the observed trends in the data with respect to the influence of the velocity, wave period and grain diameter. Also detailed mean sediment flux profiles in the sheet flow layer are well reproduced by the model, including the direction change from ‘onshore’ to ‘offshore’ due to a difference in grain size from 0.34 mm (medium sand) to 0.13 mm (fine sand). A model sensitivity study with a selected series of net transport data shows that the stirring height of the suspended sediment ε_s/w_s strongly controls the magnitude and direction of the net sediment transport. Inclusion of both hindered settling and density stratification appears to be necessary to correctly represent the sand fluxes for waves alone and for waves + a superimposed current. The best agreement with a large dataset of net transport measurements is obtained with the 1DV-RANS model in its original settings using a Prandtl–Schmidt number σ_ρ = 0.5.     

Surface salinity in the Atlantic Ocean (30°S–50°N)

Sea surface salinity (SSS) data in the Atlantic Ocean is investigated between 50°N and 30°S based on data collected mostly during the period 1977–2002. Monthly mapping of SSS is done to extract the large-scale variability. This mapped variability indicates fairly long (seasonal) time scales outside the equatorial region. The spatial scales of the seasonal anomalies are regional, but not basin-wide (typically 500–1000 km). These seasonal SSS anomalies are found to respond with a 1–2 month lag to freshwater flux anomalies at the air–sea interface or to the horizontal Ekman advection. This relation presents a seasonal cycle in the northern subtropics and north-east Atlantic indicating that the late-boreal spring/summer season is less active than the boreal winter/early-spring season in forcing the seasonal SSS variability. In the north-eastern mid-latitude Atlantic, SSS is positively correlated to SST, with SSS slightly lagging SST. There are noticeable long-lasting larger-scale signals overlaid on this regional variability. Part of it is related to known climate signals, for example ENSO and NAO. A linear trend is present during the first half of the period in some parts of the basin (usually towards increasing salinities, at least between 20°N and 45°N). Based on a linear regression analysis, these signals combined can locally represent up to 20% of SSS variance (in particular near 30°N/60°W or 40°N/10–30°W), but usually represent less than 10% of the variance.