Prediction of berm geometry using a set of laboratory tests combined with teaching–learning-based optimization and artificial bee colony algorithms

Understanding sediment movement in coastal areas is crucial in planning the stability of coastal structures, the recovery of coastal areas, and the formation of new coast. Accretion or erosion profiles form as a result of sediment movement. The characteristics of these profiles depend on the bed slope, wave conditions, and sediment properties. Here, experimental studies were performed in a wave flume with regular waves, considering different values for the wave height (H₀), wave period (T), bed slope (m), and mean sediment diameter (d₅₀). Accretion profiles developed in these experiments, and the geometric parameters of the resulting berms were determined. Teaching–learning-based optimization (TLBO) and artificial bee colony (ABC) algorithms were applied to regression functions of the data from the physical model. Dimensional and dimensionless equations were found for each parameter. These equations were compared to data from the physical model, to determine the best equation for each parameter and to evaluate the performances of the TLBO and ABC algorithms in the estimation of the berm parameters. Compared to the ABC algorithm, the TLBO algorithm provided better accuracy in estimating the berm parameters. Overall, the equations successfully determined the berm parameters.     

Determination of bar parameters caused by cross-shore sediment movement

Waves, topographic features and material properties are known as the most important factors affecting the sediment movement and coastal profiles. In this study, considering wave height (H=6.5, 17, 16, 20, 23, 26 and 30 cm) and period (T=1.46 and 2.03 s), bed slope (m=1/10, 1/15 and 1/25) and sediment diameter (d₅₀=0.18, 0.26, 0.33 and 0.40 mm), cross-shore sediment movement was investigated using a physical model and various offshore bar geometric parameters were determined by the resultant erosion profile. The offshore bar geometric characteristics are the distance between the bar crest and the shoreline, the depth from bar crest to the still-water level, the distance between the equilibrium point and the shoreline, the distance between the closure point and the shoreline, and the bar volume. Dimensional and non-dimensional equations were obtained by using non-linear regression methods through the experimental data and compared with those of previously developed equations. The results have indicated that the proposed equations fit to experimental data better than previously developed equations.     

An experimental study on geometric characteristics of beach erosion profiles

The beach profile and sediment transport are very important factors in the design of coastal structures, and the beach profile is mainly affected by a number of parameters, such as wave height and period, beach slope, and the material properties of the bed. In this study, considering wave height (H₀=6.5, 11.5, 16, 20, 23, 26 and 30 cm), wave period (T=1.46 and 2.03 s), beach slope (m=1/10 and 1/15) and mean sediment diameter (d₅₀=0.18, 0.26, 0.33 and 0.40 mm), an experimental investigation of coastal erosion profile (storm profile) was carried out in a wave flume using regular waves, and geometric characteristics of erosion profile were determined by the resultant erosion profile. Dimensional and non-dimensional equations were obtained by using linear and non-linear regression methods through the experimental data and were compared with previously developed equations in the literature. The results have shown that the experimental data fitted well to the proposed equations with respect to the previously developed equations.     

Prediction of scour depth at breakwaters due to non-breaking waves using machine learning approaches

Coastal structures may cease to function properly due to seabed scouring. Hence, prediction of the maximum scour depth is of great importance for the protection of these structures. Since scour is the result of a complicated interaction between structure, sediment, and incoming waves, empirical equations are not as accurate as machine learning schemes, which are being widely employed for the coastal engineering modeling. In this paper, which can be regarded as an extension of Pourzangbar et al. (2016), two soft computing methods, a support vector regression (SVR), and a model tree algorithm (M5′), have been implemented to predict the maximum scour depth due to non-breaking waves. The models predict the relative scour depth (S_max/H₀) on the basis of the following variables: relative water depth at the toe of the breakwater (h_toe/L₀), Shields parameter (θ), non-breaking wave steepness (H₀/L₀), and reflection coefficient (Cr). 95 laboratory data points, extracted from dedicated experimental studies, have been used for developing the models, whose performances have been assessed on the basis of statistical parameters. The results suggest that all of the developed models predict the maximum scour depth with high precision, the M5′ model performed marginally better than the SVR model and also allowed to define a set of transparent and physically sound relationships. Such relationships, which are in good agreement with the existing empirical findings, show that the relative scour depth is mainly affected by wave reflection.     

Predicting wave run-up on rubble-mound structures using M5 model tree

Prediction of run-up level is a key task in design of the coastal structures. For the design of the crest level of coastal structures, the wave run-up level with a 2% exceedance probability, R_u2%, is most commonly used. In this study, the performance of M5 model tree for prediction of the wave run-up on rubble-mound structures was investigated. The main advantage of model trees, unlike the other soft computing tools, is their easier use and more importantly their understandable mathematical rules. Experimental data set of Van der Meer and Stam was used for developing model trees. The conventional governing parameters were selected as the input variables and the obtained results were compared with Van der Meer and Stam’s formula, recommended by the Coastal Engineering Manual (CEM, 2006). The predictive accuracy of the model tree approach was found to be superior to that of Van der Meer and Stam’s empirical formula. Furthermore, to judge the generalization capability of the model tree method, the model developed based on laboratory data set was validated with the prototype run-up measurements on the Zeebrugge breakwater, Belgium. Results show that the model tree is more accurate than empirical formulas and TS Fuzzy approach in estimating the full-scale run-up.     

Application of a fuzzy inference system for the prediction of longshore sediment transport

A fuzzy inference system (FIS) and a hybrid adaptive network-based fuzzy inference system (ANFIS), which combines a fuzzy inference system and a neural network, are used to predict and model longshore sediment transport (LST). The measurement data (field and experimental data) obtained from Kamphuis [1] and Smith et al. [2] were used to develop the model. The FIS and ANFIS models employ five inputs (breaking wave height, breaking wave angle, slope at the breaking point, peak wave period and median grain size) and one output (longshore sediment transport rate). The criteria used to measure the performances of the models include the bias, the root mean square error, the scatter index and the coefficients of determination and correlation. The results indicate that the ANFIS model is superior to the FIS model for predicting LST rates. To verify the ANFIS model, the model was applied to the Karaburun coastal region, which is located along the southwestern coast of the Black Sea. The LST rates obtained from the ANFIS model were compared with the field measurements, the CERC [3] formula, the Kamphuis [1] formula and the numerical model (LITPACK). The percentages of error between the measured rates and the calculated LST rates based on the ANFIS method, the CERC formula (K_sig = 0.39), the calibrated CERC formula (K_sig = 0.08), the Kamphuis [1] formula and the numerical model (LITPACK) are 6.5%, 413.9%, 6.9%, 15.3% and 18.1%, respectively. The comparison of the results suggests that the ANFIS model is superior to the FIS model for predicting LST rates and performs significantly better than the tested empirical formulas and the numerical model.     

Comparison between M5′ model tree and neural networks for prediction of significant wave height in Lake Superior

Prediction of wave height is of great importance in marine and coastal engineering. Soft computing tools such as artificial neural networks (ANNs) are recently used for prediction of significant wave height. However, ANNs are not as transparent as semi-empirical regression-based models. In addition, neural networks approach needs to find network parameters such as number of hidden layers and neurons by trial and error, which is time consuming. Therefore, in this work, model trees as a new soft computing method was invoked for prediction of significant wave height. The main advantage of model trees is that, compared to neural networks, they represent understandable rules. These rules can be readily expressed so that humans can understand them. The data set used for developing model trees comprises of wind and wave data gathered in Lake Superior from 6 April to 10 November 2000 and 19 April to 6 November 2001. M5′ algorithm was employed for building and evaluating model trees. Training and testing data include wind speed (U₁₀) as the input variable and the significant wave height (H_s) as the output variable. Results indicate that error statistics of model trees and feed-forward back propagation (FFBP) ANNs were similar, while model trees was marginally more accurate. In addition, model tree shows that for wind speed above 4.7 m/s, the wave height increases nonlinearly by the wind speed.     

Processes affecting long-term changes in <Superscript>137</Superscript>Cs concentration in surface sediments off Fukushima

Temporal changes in cesium-137 (¹³⁷Cs) concentrations in the surface (0–10 cm) layer of seabed sediment were quantified from continuous observation data at 71 stations within a 150-km radius of the Fukushima Daiichi Nuclear Power Plant, and the primary processes affecting temporal changes were identified. From March 2011 to the end of 2015, about 80% of the initially deposited ¹³⁷Cs in the surface sediment in the coastal region (bottom depth ≤100 m) region has dissipated (radioactive decay is not included). Such a remarkable change in the ¹³⁷Cs concentration was not observed in the offshore (>100 m) region. This paper focuses on the following three processes that affected the decrease in the ¹³⁷Cs concentrations, and assesses their relative importance; (1) resuspension and transport of ¹³⁷Cs-bound sediment, (2) desorption of ¹³⁷Cs from the sediment, and (3) dilution of ¹³⁷Cs by vertical mixing of sediment. Consequently, it was estimated that the first two processes together have potentially contributed to reduce the ¹³⁷Cs inventory in the top 10 cm of the coastal region by at most 35%. Furthermore, by applying a pulse input sediment mixing model to the observed vertical distribution of sedimentary ¹³⁷Cs, it was also estimated that more than 43% of the ¹³⁷Cs in the surface sediment was transported to deeper sediment layers by vertical mixing of the sediment. This indicates that the decrease of ¹³⁷Cs concentrations in coastal sediments was mainly affected by mixing of ¹³⁷Cs-bound surface sediment with less contaminated sediment in the deeper layers.     

Generation mechanism of an alongshore bar on a sandy beach slope

A model explaining the mechanism of alongshore bar formation from the point of view of the sediment balance in the surf zone is considered. A cloud of suspended matter that appears during wave breaking is transported shoreward and simultaneously sediments forming a vertical material flux directed to the bottom (S). Simultaneously, an undertow generates a horizontal offshore flux of suspended matter q _x . Under these conditions, the sediment balance is determined by the equality of the flux -S and the gradient dq _x /dx. The bottom profile satisfying the balance equation is a bar profile with the crest at the point of the flux maximum -S. The model predicts a concave profile of the seaside slope and a concave-convex profile of the slope in the trough. A conclusion is reached on the basis of the calibration and verification of the model based on the field data that the suggested mechanism manifests itself differently in the outer and inner zones of the coastal zone. In the inner zone, the horizontal size of the bar is determined by the length of short wind waves, while, in the outer one, it is determined by the length of the infragravity waves related to the groups of short waves. It is shown that the model can be applied to estimate the parameters of the largest bar in the inner part of the coastal zone.     

A test of the ADV-based Reynolds flux method for in situ estimation of sediment settling velocity in a muddy estuary

Under conditions common in muddy coastal and estuarine environments, acoustic Doppler velocimeters (ADVs) can serve to estimate sediment settling velocity (w _s) by assuming a balance between upward turbulent Reynolds flux and downward gravitational settling. Advantages of this method include simple instrument deployment, lack of flow disturbance, and relative insensitivity to biofouling and water column stratification. Although this method is being used with increasing frequency in coastal and estuarine environments, to date it has received little direct ground truthing. This study compared in situ estimates of w _s inferred by a 5-MHz ADV to independent in situ observations from a high-definition video settling column over the course of a flood tide in the bottom boundary layer of the York River estuary, Virginia, USA. The ADV-based measurements were found to agree with those of the settling column when the current speed at about 40 cm above the bed was greater than about 20 cm/s. This corresponded to periods when the estimated magnitude of the settling term in the suspended sediment continuity equation was four or more times larger than the time rate of change of concentration. For ADV observations restricted to these conditions, ADV-based estimates of w _s (mean 0.48±0.04 mm/s) were highly consistent with those observed by the settling column (mean 0.45±0.02 mm/s). However, the ADV-based method for estimating w _s was sensitive to the prescribed concentration of the non-settling washload, C _wash. In an objective operational definition, C _wash can be set equal to the lowest suspended solids concentration observed around slack water.     

Suspended-sediment reference concentration under waves: field observations and critical analysis of two predictive models

Two commonly adopted but fundamentally different approaches for predicting time-averaged suspended-sediment reference concentration (C̄_REF) under waves are tested against field measurements and compared with each other. The first model relates C̄_REF to the cube of the non-dimensional skin friction, whereas the second model adopts a more complex function of excess skin friction incorporating the empirical constant γ₀. The dataset is from the zone of wave shoaling seaward of an open-coast surfzone and includes measurements of waves, currents, suspended sediment and bedforms. Estimates of C̄_REF are derived from acoustic backscatter data, and the seabed and suspension process are described from video footage. When waves were energetic, the bed was deformed into large hummocks; during less energetic conditions, the bed was rippled. The time-averaged concentration profiles over the ripples were consistent with settling flux balanced by pure gradient diffusion and a sediment diffusivity that is constant with elevation above the bed. C̄_REF in that case is shown to apply at z=0, where z is the elevation above the bed. Over the hummocks, there was a sheet flow at the base of the suspension and C̄_REF is shown to apply at z=1 cm. The concentration profiles over the hummocks implied sediment diffusivity that varied linearly with elevation within ∼10 cm of the bed and constant sediment diffusivity above that level. For both rippled and hummocky beds, γ₀ derived from the field data was found to be sensitive to the value assumed for critical stress for initiation of sediment motion, which could explain the range of values reported in the literature for γ₀. γ₀ was also found to vary in a complex way with skin friction, which suggests that the reference-concentration model based on excess skin friction is not correctly formulated. Nevertheless, two functions for γ₀ (one applying to rippled beds and the other to hummocky beds) were contrived to make the model fit the data. The model based on non-dimensional skin friction was found to be a good predictor of C̄_REF when a correction was made for flow contraction over ripples. The correction was not required for the hummocky bed, where sediment was being entrained in a thin sheet flow layer. The model based on non-dimensional skin friction correctly portrayed the relationship between flow and sediment response without contrivance and therefore should be the favoured approach in predicting reference concentration.     

Two-dimensional,two-phase granular sediment transport model with applications to scouring downstream of an apron

We present a two-dimensional, two-phase model for non-cohesive sediment transport. This model solves concentration-weighted averaged equations of motion for both fluid and sediment phases. The model accounts for the interphase momentum transfer by considering drag forces. A collisional theory is used to compute the sediment stresses, while a two-equation (k–ε) fluid turbulence closure is implemented. A benchmark sediment transport problem concerning the scouring downstream of an apron is carried out as an example and numerical results agree with existing experimental data.     

Partitioning particulate absorption coefficient into contributions of phytoplankton and nonalgal particles: A case study in the northern South China Sea

We measured the absorption coefficients of suspended particles (a_p(λ)) during three cruises from coastal waters to open ocean in the northern South China Sea (NSCS). The absorption contributions of phytoplankton (a_ph(λ)) and nonalgal particles (a_NAP(λ)) were determined using the methanol extraction method. Based on the dataset of about 360 samples, we examined the spectral relationships of the particle absorption coefficients. The results show that a_p(λ) spectra are well linearly correlated with a_p(443) over the wavebands between 420–650 nm; a_ph(λ) could be well expressed as the second-order quadratic equations of a_ph(443) among the blue-green wavebands, and a_NAP(λ) follows the general exponential function. Based on these spectral relationships, a model was proposed for partitioning the total particulate absorption coefficients into the contributions of phytoplankton and nonalgal particles using the nonlinear optimization method. The model was validated by comparing the computed results with in situ absorption coefficients. In some wavebands, such as 412 nm, 443 nm, 490 nm and 683 nm, we obtained good correlations with the percentage root mean square error (RMSE) values being controlled within 25% and the slopes being closer to 1.0. For samples from coastal waters, the discrepancy was a little large, which might be due to the higher absorption contributions from certain pheopigments. Overall, this model provides us much insight into phytoplankton absorption retrieval from in situ measurements and remote sensing ocean color data.     

Phase-lag effects in sheet flow transport

The inception of the sheet flow regime as well as the effects of the phase lag when the sheet flow regime is established were investigated for oscillatory flows and combined steady and oscillatory flows. A new criterion for the inception of sheet flow is proposed based on around 300 oscillatory flow cases from experiments. This criterion was introduced in the Camenen and Larson [Camenen, B., Larson, M., 2005. A bedload sediment transport formula for the nearshore. Estuarine, Coastal and Shelf Science 63, 249–260.] bed load formula in order to take into account phase-lag effects in the sheet flow regime. The modification of the Camenen and Larson formula significantly improves the overall agreement with data and yields a correct behavior in relation to some of the main governing parameters, which are the median grain size d₅₀, the orbital wave velocity U_w, and the wave period T_w. The calibration of the new formula was based on more than 200 experimental data values on the net sediment transport rate for a full wave cycle. A conceptual model was also proposed to estimate the ratio between sediment transport rate with and without phase lag, (r_pl = q_s,net / q_s,net,ϕ=0). This simple model provides accurate results and may be used together with any quasi-steady model for bed load transport.     

Medium-term frequency distributions of cross-shore suspended sediment transport rates in water depths of 3 to 9 m

A data set of several thousands of hours of near-bed flow, obtained at three cross-shore positions in 3- to 9-m water depth in the multiple bar system of Terschelling (Netherlands), was used to estimate the medium-term (≈years) frequency distribution of the cross-shore suspended sediment transport rates induced by short waves, infragravity waves and cross-shore mean flows. Predictions of an energetics-based transport model were categorised into groups of the local height-over-depth ratio with a width of 0.02 and were subsequently coupled to the discrete medium-scale probability distribution of this ratio. At all depths, the estimated medium-scale sediment transport rate by the short waves, q_ms,h, and mean flows, q_ms,mf, were of approximately equal magnitude and were about three times as large as that of the infragravity waves. In general, the medium-term sediment transport rates were dominated neither by the most extreme conditions nor by day-to-day situations. This was related to the infrequent recurrence of the most energetic events and by the predicted negligible transport rates under daily conditions. In 9-m depth, breaking conditions contributed to about 90% of both q_ms,h and q_ms,mf. In shallower water (3–5 m), non-breaking conditions became increasingly important for q_ms,h, whereas q_ms,mf remained fully dominated by surf zone conditions. This observation as well as literature findings for water depths less than about 3 m suggest that the range of small-scale conditions that contribute most to q_ms,h and q_ms,mf changes in the onshore direction from mainly breaking conditions at depths in excess of 5–7 m towards prolonged non-breaking periods for q_ms,h and short breaking events for q_ms,mf on the beach.     

Testing and calibrating parametric wave transformation models on natural beaches

To provide coastal engineers and scientists with a detailed inter-comparison of widely used parametric wave transformation models, several models are tested and calibrated with extensive observations from six field experiments on barred and unbarred beaches. Using previously calibrated (“default”) values of a free parameter γ, all models predict the observations reasonably well (median root-mean-square wave height errors are between 10% and 20%) at all field sites. Model errors can be reduced by roughly 50% by tuning γ for each data record. No tuned or default model provides the best predictions for all data records or at all experiments. Tuned γ differ for the different models and experiments, but in all cases γ increases as the hyperbolic tangent of the deep-water wave height, H_o. Data from two experiments are used to estimate empirical, universal curves for γ based on H_o. Using the new parameterization, all models have similar accuracy, and usually show increased skill relative to using default γ.     

Lipid biomarkers in surface sediments from the Gulf of Genoa,Ligurian sea (NW Mediterranean sea) and their potential for the reconstruction of palaeo-environments

A series of molecular organic markers were determined in surface sediments from the Gulf of Genoa (Ligurian Sea) in order to evaluate their potential for palaeo-environmental reconstructions. Allochthonous input can be characterized by the distributions of n-C₂₉ and n-C₃₁ alkanes, n-C₂₆ and n-C₂₈ alkanols and branched glycerol dialkyl glycerol tetraethers (GDGTs), whose concentrations are generally highest near the river mouths. In the open basin however, terrestrial n-alkanes and n-alkanols may have an additional, eolian source. Autochthonous input is represented by crenarchaeol and isoprenoid GDGTs. Their concentrations are highest in the open basin showing the preference of Thaumarchaeota for oligotrophic waters. Indications of a significant degradation of sterols and C₃₇ alkenones exclude these lipids as reliable productivity proxies. Using terrestrial and aquatic lipids as end-members allows estimating the percentage of terrestrial organic matter between 20% and 58% in the coastal area decreasing to 1–30% in the deep basin. The spatial distribution of sea surface temperature (SST) estimates using the alkenone-based U^K′₃₇ index is very similar to the autumnal (November) mean satellite-based SST distribution. Conversely, TEX^H₈₆-derived SST estimates are close to winter SSTs in the coastal area and summer SSTs in the open basin. This pattern reflects presumably a shift in the main production of Thaumarchaeota from the coastal area in winter to the open basin in summer. This study represents a major prerequisite for the future application of lipid biomarkers on sediment cores from the Gulf of Genoa.     

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.