CERC Formula Research Articles

PRELIMINARY INVESTIGATION OF SHORELINE RESPONSE IN SAN JUAN, LA UNION, PHILIPPINES

Coastal erosion has been affected by environmental factors and human development. The investigation of the coastal erosion in San Juan, La Union covers the analysis and quantitative data that can be applied to protect the coastal community, to minimize economic losses, and to plan for the improvement of coastal process response. The main objective of this study was to investigate the shoreline response based on the extent of the coastal erosion problem of the 5.36 km - coastline of San Juan La Union and predict the long-term erosion pattern and shoreline change. The characteristics of the triggering factors of coastal erosion were evaluated during normal and extreme weather conditions. The areas along the coastline were characterized whether it experienced dominant deposition or erosion. Changes in shoreline position were assessed to predict future shoreline change scenarios. Sediment transport analysis was conducted by using the Kamphuis Formula and the CERC Formula.

Derivation of governing equation for short-term shoreline response due to episodic storm wave incidence: comparative verification in terms of longshore sediment transport

The shoreline temporarily recedes significantly as incoming storm waves reach the beach and cause wave breaking and energy dissipation. However, since the existing shoreline change model simulates shoreline change based on the longshore sediment transport rate (LSTR) empirical formulae, which are derived using the correlation between energy flux and littoral drift, it is difficult to simulate this phenomenon, which is drafted with transverse drift. Therefore, in this study, by applying the concept of the horizontal behavior of suspended sediments, a set of governing equations were derived that can simulate short-term shoreline changes in which the shoreline temporarily recedes, and then recovers. Among the three variables of the governing equation, the two main physical variables related to transverse drift—the beach response factor and the beach recovery factor—can be obtained from the median grain size. However, in the present study, the third variable, the actual transport speed of littoral drift, was estimated by comparison with the CERC formula and discussed from the point of view of alongshore energy flux and wave duration. This was established by introducing the delay factor of longshore sediment transport (DFLST), which indicates how slowly suspended sediments move relative to the longshore current speed. It was found that the littoral sediment speed is inversely proportional to the square root of the beach scale factor. The LSTR formula derived in this study was compared with the observed LSTR values collected from 25 beaches in the United States and with the results of four existing empirical formulae. The proposed governing equation is expected to be widely used as a means of predicting short-term shoreline changes, unlike existing shoreline change models, because it can consider the temporal shoreline retreat and recovery due to storm wave incidence.

Sand Spit Morphology at an Inlet on Phu Quoc Island, Vietnam

Tidal inlets with attached sand spits are a very common coastal landform. Since the evolution of sand spits along coastlines influence the social-economic development of local coastal areas, sand spits have become the objects of numerous studies. However, previous studies have mainly focused on sand spits that are usually in the scale of hundreds of meters in width, whilst knowledge about the evolution of smaller-scale sand spits still remains limited. Therefore, in this study, the morphological change of a small and unexplored sand spit in front of Song Tranh Inlet on the west coast of Phu Quoc Island, Vietnam is investigated. Satellite images are first used to observe the morphological change of the sand spit and calculate the longshore sediment transport rates (LSTR) along the sand spit. Waves and beach sediments are collected at the study site to calculate the longshore sediment transport rate using the CERC formula. It is found that there is a seasonal variation in the evolution of the sand spit at Song Tranh Inlet. The longshore sediment transport rates along the spit calculated by image analysis are 39,000 m3/year, 66,000 m3/year, and 40,000 m3/year, whilst the longshore sediment transport rate calculated by the CERC formula is 72,000 m3/year. This study aims to contribute to the methodology for investigating the evolutions of small sand spits and, specifically, sustainable coastal management for Phu Quoc Island, which is well-known as the Pearl Island of Vietnam.

Revisiting the derivation of bulk longshore sediment transport rates using meta-heuristic algorithms

ABSTRACT During recent decades, different formulas have been developed to estimate longshore sediment transport rates through calibration using a wide variety of datasets, applicable for a range of particular wave and beach conditions. The equations that have shown the best capability to predict Bulk Longshore Sediment Transport Rate (BLSTR) are the formulas derived by CERC and by Kamphuis. In the present study, the five process parameters as used in the Kamphuis formula are accepted. The CERC formula includes only two of the five process parameters used in Kamphuis’ formula. A renewed optimization to derive the power of the five Kamphuis’ process parameters using an extensive dataset by Bayram was performed by Mil-Homens. In addition to this valuable effort, our contribution introduces two innovations. Firstly, the power coefficients of the five Kamphuis process parameters are optimized using a broad range of meta-heuristic algorithms. Secondly, the optimization is not based on the Bayram dataset as carefully collected and reviewed from published manuscripts but on a methodologically more homogeneous Iranian dataset acquired for port design and port management purposes. Independently from the results by Mil-Homens derived from the Bayram dataset, our study confirms these findings based on a totally different dataset. Specifically, the weaker impact of wave period and the stronger impact of the median grain diameter are in accordance with each other. The latter finding provides a stronger support for the mutual cancellation of the impact of slope and grain diameter in BLSTR, lending explanatory support to the CERC formula once beach slope and grain size are not known.

High‐efficiency gravel longshore sediment transport and headland bypassing over an extreme wave event

AbstractGravel beaches are common throughout the high latitudes, but few studies have examined gravel transport rates, in particular at high energy levels, and no studies have quantified gravel transport around headlands. Here, we present the first complete sediment budget, including supra‐, inter‐ and sub‐tidal regions of the beach, across multiple headland‐separated gravel embayments, combined with hydrodynamic observations, over an extreme storm sequence, representing at least a 1‐in‐50‐year event. Unprecedented erosion was observed (~400 m3 m−1, −6 m vertical), with alongshore flux of 2 × 105 m3, equivalent to annual rates. Total system volume change was determined to the depth of closure and then used to calculate alongshore flux rates. Alongshore wave power was obtained from a wave transformation model. For an open section of coastline, we derive a transport coefficient (CERC formula) of KHs = 0.255 ± 0.05, exceeding estimates in lower‐energy conditions by a factor of 5 or more. We apply this coefficient to rocky segments of the shoreline, determining rates of headland bypass from 0 to 31% of potential flux, controlled by headland extent and toe depth. Our results support the hypothesis that gravel is transported more efficiently at higher energy levels and that a variable rate or threshold approach may be required. Complete coverage and varying morphology make this dataset uniquely suited to improving model predictions of gravel shoreline change. © 2019 John Wiley & Sons, Ltd. © 2019 John Wiley & Sons, Ltd.

Performance Test of Parabolic Equilibrium Shoreline Formula by Using Wave Data Observed in East Sea of Korea

Lim, C.B.; Lee, J.L., and Kim, I.H., 2019. Performance test of parabolic equilibrium shoreline formula by using wave data observed in East Sea of Korea. In: Lee, J.L.; Yoon, J.-S.; Cho, W.C.; Muin, M., and Lee, J. (eds.), The 3rd International Water Safety Symposium. Journal of Coastal Research, Special Issue No. 91, pp. 101-105. Coconut Creek (Florida), ISSN 0749-0208.This study is the validity examination of an equilibrium shoreline formula of parabolic type, which was introduced by Hsu in 1987, for real phenomena. Hsu's formula of parabolic type is practical for estimation of shoreline change after coastal or harbor structure construction. The wave data observed at Maengbang beach of East Sea of Korea and the CERC formula on longshore sediment transport were used in the present study. Performance test was conducted for the case of a shoreline change after the construction of a groyne. It was reasonable between the observed wave data and the data obtained under a wave spreading parameter, S = 3.5. However, when S increased, significant changes were observed. Thus, it is required to apply an equilibrium shoreline formula of parabolic type carefully.

Coastal Processes and Longshore Sediment Transport Along Krui Coast, Pesisir Barat of Lampung

Longshore sediment transport is one of the main factors influencing coastal geomorphology along the Krui Coast, Pesisir Barat of Lampung. Longshore sediment transport is closely related to the longshore current that is generated when waves break obliquely to the coast. The growth of waves depends upon wind velocity, the duration of the wind, and the distance over which the wind blow called fetch. The daily data of wind speed and direction are forecast from European Centre for Medium-Range Weather Forecasts (ECMWF). This study examines for predicting longshore sediment transport rate using empirical method. The wave height and period were calculated using Shore Protection Manual (SPM) 1984 method and the longshore sediment transport estimation based on the CERC formula, which also includes the wave period, beach slope, sediment grain size, and breaking waves type. Based on the use CERC formula it is known that from the Southeast direction (Qlst(1) ) the sediment transport discharge is 2.394 m3/s, in 1 (one) year the amount of sediment transport reaches 75,495,718 m3/s. Whereas from the northwest direction of (Qlst(2)) the sediment transport debit is 2.472 m3/s, in 1 (one) year the amount of sediment transport reaches 77,951,925 m3/s.

Sandy sediment budget of the midcoast of Rio Grande do Sul, Brazil

Calculation of the coastal sediment budget involves estimation of the timing and intensity of processes of erosion, transport, and deposition, as well as an understanding of local and regional sediment dynamics. The modern sedimentary deposits present in the coastal zone constitute the physical basis of coastal ecosystems. Knowledge of the dynamics of these sediments from the source to sink area, through regional sediment management, is critical to understanding the long-term stability of the coastal zone and the fate of these important natural resources. In this article, the littoral cell concept has been applied to the midcoast of Rio Grande do Sul, a wave-dominated and dissipative-intermediate sandy coast in southern Brazil. To analyze littoral drift variations along the 275 km long study area, the shoreline was divided into 12 cells. Littoral drift rates were estimated and compared using the energy flux method. Wave parameters were obtained from WAVEWATCH III. The sand volume of the coastal dune field (4.20 billion m3) was quantified using satellite imagery and the aeolian transport rates estimated utilizing the sediment budget residual. The net annual longshore transport rates obtained with the Coastal Engineering Research Center equation range from 0.60 to 2.63 million m3 per year. The littoral drift rates obtained with the Van Rijn (2001) and Kamphuis (1991) equations range between 0.15 and 1.00 million m3 per year. Based on the sediment budget and dune field age, the CERC formula seems more appropriate to estimate longshore transport.

Simulation of Seasonal Bathymetric Change at Haeundae Beach with Two Representative Wave Settings

Kim, H.; Jin, J.Y.; Jang, C.; Yoo, H.J., and Hwang, D.H., 2014. Simulation of seasonal bathymetric change at Haeundae Beach with two representative wave settings.Long-term shoreline position of Haeundae Beach has been quite stable notwithstanding seasonal oscillatory movement. Bathymetry around Haeundae Beach was surveyed on 7 August 2007 and 12 November 2007 by using an echo-sounder, while wave, tide, and tidal current were measured between the two survey days, so that bathymetric change at Haeundae Beach was obtained from the two surveys. According to the surveys the east part of the beach was eroded, and the west part of the beach was accreted. Measured waves from SSE, SE, ESE, E during the period were stronger than measured waves from S, SSW, SW, WSW. A numerical model system CST3D was adopted to reproduce the bathymetric change at Haeundae Beach during the period. Two representative wave settings are chosen for the period as a minimum number to represent the time-series of wave record, based on equivalent sediment flux concept contained in the CERC formula. Wave field, wave-induced force field, wave-induced current field, sediment transport field, and bathymetric change are computed from individual modules, SWAN, WIF, FLOW, SED in CST3D, respectively. Computed bathymetric change agrees reasonably well with measured one. It is believed that selection of two representative wave settings is useful for simulation of seasonal bathymetric change for fairly straight morphology like Haeundae. CST3D is thought to effectively describe overall seasonal sediment transport pattern and consequent bathymetric change at Haeundae Beach.

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 (Ksig=0.39), the calibrated CERC formula (Ksig=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.

Calculation of longshore sediment transport

Calculation approaches to longshore transport of sandy sediments are discussed. The estimation of the total sediment transport rate is shown to be possibly based on the so-called CERC formula, where the proportionality factor K should be calculated from relationships of Bayram et al. [8] or Leont’yev [4]. In both cases, the results are very close to each other if the author’s determination of the wave breaking depth is used. Under the condition of contrasting variations in the sediment grain size over the coastal profile or in the case of fragmentary sand distribution on the surface of the bed, the local approach implying process-based modeling is more effective. A model is suggested to compute the local longshore sediment transport rates.

Modelling beach-structure interaction using a Heaviside technique: application and validation

ABSTRACT Valsamidis, A., Cai, Y., Reeve, D.E., 2013. Modelling beach-structure interaction using a Heaviside technique: application and validation In this study, an analytical solution, based on a Heaviside technique, is developed to model the shoreline evolution in the vicinity of a groyne due to a random sequence of waves. The beach at Borth, Wales, UK was used as a case-study. A wave time-series covering a time period of about 12 years, was used to test the performance of a recently constructed coastal defence scheme. Transformations of the wave time-series from offshore to nearshore were performed using a semi-empirical procedure. Three different wave breaking formulae were independently applied to the wave model, and their effects to the consequent shoreline evolution were investigated. In addition, three different longshore transport formulae were compared. These were the CERC, the Kamphuis and the Bayram formulae. Results showed that the CERC formula predicted a significantly greater amount of sedi...

NEAR-SHORE FLOATING WAVE ENERGY CONVERTERS: APPLICATIONS FOR COASTAL PROTECTION

Aim of this note is to analyse the possible application of a Wave Energy Converter (WEC) as a combined tool to protect the coast and harvest energy. Physical model tests are used to evaluate wave transmission past a near-shore floating WEC of the wave activated body type, named DEXA. Efficiency and transmission characteristics are approximated to functions of wave height, period and obliquity. Their order of magnitude are 20% and 80%, respectively. It is imagined that an array of DEXA is deployed in front of Marina di Ravenna beach (IT), a highly touristic site of the Adriatic Coast. Based on the CERC formula, long-shore sediment transport is evaluated in presence and in absence of this array of DEXAs. The sediment transport in this site is quite large and frequently changes directions during the year. The larger North directed contribution and the more persistent South directed one are similar in magnitude and almost compensate each other, with the latter only slightly prevailing. It is shown that the DEXA could be designed so that the effect on sediment transport becomes quite significant and the direction of the net transport can be reversed.

Verification of Longshore Sediment Transport Formulas at Some of the Southern Coastlines of Iran

A correct estimation of the sediment transport rate and the amount of sedimentation is among the important and effective factors to be considered in the design of ports and coastal structures. Although many research efforts are now conducted on the influencing parameters of the sediment transport to quantify the transport rate, the approximate and relatively simple formulas are still routinely used. CERC and Kamphuis are among the well-known formulas for the calculation of the potential longshore sediment transport (LST) rate. However, the accuracy of predictions of transport rates, based on the applications of these formulas at different locations of the world, has not been similar. In present paper, using a limited number of data related to local waves and characteristics of grain size distributions, the longshore sediment transport rates at some of the southern coastlines of Iran have been calculated and the results have been compared with the actual sediment impoundments at breakwaters and groins. The volumes of sedimentation are derived from the comparisons of hydrographic surveys. Verification of these formulas at southern coasts of the country reveals the higher accuracy of Kamphuis formula in comparison to CERC formula. A relationship was also presented for the calculation of K parameter of CERC formula as a function of the surf similarity parameter.

Long Term Change of Terrace Morphology and Longshore Sediment Transport around the Tenryu River Mouth

This study investigates long-term change of terrace morphology and longshore sediment transport around the Tenryu River mouth based on bathymetry data of past 50 years. Based on the sediment budget around the terrace and the assumption of little sediment supply from the river in recent years, CERC formula was calibrated to estimate the longshore sediment transport rates at both east and west boundaries of the focusing area. Obtained boundary conditions then yielded distribution of the longshore sediment transport around the terrace and estimations of sediment supply from the river. These results and additional numerical analysis clearly showed increasing impacts of the detached breakwaters and indicated that the terrace morphology in 1984 may be required for dynamic equilibrium of the sediment budget around the river mouth.

Dependence of Total Longshore Sediment Transport Rates on Incident Wave Parameters and Breaker Type

Abstract Experiments were conducted in the Large-scale Sediment Transport Facility (LSTF) at the U.S. Army Engineer Research and Development Center to investigate the importance of wave height, period, and breaker type (spilling and plunging breakers) on total rate of longshore sediment transport (LST) and the cross-shore distribution of LST. Estimates computed by the CERC formula and Kamphius were compared to the accurately measured total LST rates. Several K-values were used with the CERC formula, including the recommended value of 0.39 and calculated values by Kamphuis and Readshaw, Ozhan, Bailard, and Del Valle et al. The recommended K-value and most of the calculated K-values overpredicted the measured total LST rates, but methods that included parameters to indicate breaker type gave good estimates. The Kamphuis and Readshaw equation, in which K is a function of surf similarity parameter, gave consistent estimates with measurements. The Kamphuis equation, which includes wave period and beach slope t...

Numerical Model for Cross-shore Distribution of Longshore Sediment Transport Rate Including Suspended and Bed Loads in and outside the Surf Zone

A one-dimensional numerical model for predicting the cross-shore distribution of the longshore sediment transport rate was developed. The model predicts the suspended load due to wave breaking and bed load due to longshore current velocity and velocity skewness and atiltness. The model validity was examined for steady flows and for waves and wave-induced longshore currents. The sediment transport rates for steady flows estimated by the present model agreed with those by Ribberink's formula. The total longshore sediment transport rates estimated by the present model were smaller than those estimated by CERC's formula. However, because CERC's formula was found to overestimate the total longshore sediment transport rate, the present model likely predicts the longshore sediment transport in the field properly.

Predicting shoreline response to changes in longshore sediment transport for the Rio Grande do Sul coastline

Longshore sediment transport (LST) has been calculated using the CERC formula for the long (618 km), gently undulating, sandy shore of Rio Grande do Sul (RS) for wave climate scenarios typifying normal (i.e. non-ENSO years) and La Nina years. Predicted LST values have been validated with available field measurements. Whilst in most cases LST was directed to the north, simulations revealed large spatial variability in both the magnitude and direction of the net annual LST flux. This was related primarily to the orientation of the coastline relative to the incident waves and to the dominance of waves from different directions. Predicted net annual LST values were used in a simple model to calculate changes in the position of the shoreline. For normal years, results showed that areas of erosion predicted along the southern shores of the coastal projections and regions of accretion predicted in the embayments agreed well with shoreline surveys. The wavelength and amplitude of temporal and spatial oscillations in shoreline position measured by DGPS surveys were estimated well by a simple simulation of shoreline change. The simulation showed also that observed reversals in shoreline displacement from erosion to accretion or vice-versa could be explained by subtle changes in the annual wave climate. The present results provide strong evidence that slight changes to the wave climate can impact significantly on coastal processes along the RS shoreline. Similar impacts might be anticipated along other sandy shorelines worldwide.

Modelling of wave climate and sediment transport patterns at a tideless embayed beach, Pirita Beach, Estonia

Nearshore sand transport patterns along the tideless, embayed Pirita beach, Tallinn, Estonia, have been investigated utilizing high-resolution modelling of wave processes combined with bathymetric surveys and sediment textural analyses of the nearshore sea floor. Textural analysis showed the mean grain size is about 0.12 mm. Fine sand (0.063–0.125 mm) accounts for about 77% of the sediments. Coarser-grained sand (0.28 mm) dominates along the waterline. Based upon the spatial distribution of the mean grain size and basic features of the local wave activity, properties of the Dean Equilibrium Beach Profile were determined. Alongshore sediment transport was calculated based upon a long-term time series of wave properties along the beach, and the CERC formula applied to about 500 m long beach sectors. The time series of wave fields and the properties of the local wave climate were modelled using a triple nested WAM wave model with an extended spectral range for short waves. The model is forced by open sea wind data from Kalbådagrund for the years 1981–2002. Results indicate that typical closure depth at Pirita is 2.5 m. The width and mean slope of the equilibrium profile are 250 m and 1:100, respectively. Southward transport dominates in the northern sections of the beach whereas no prevailing transport direction exists in the southern sections. This pattern has several nontrivial implications for the planning of beach protection activities.

Application of the MPS Method for Prediction of Armor-Block Stability in front of Stepped Seawall with Drainage

At a low crown caisson seawall with a large-size wave overtopping drainage, overtopping water lump collides with a wall of drainage and the resultant return flow falls down to blocks in front of seawall. This falling water can pick blocks up, however, the velocity measurement around the blocks is difficult in a hydraulic experiment. In this study, using the MPS method, which is suitable to analyse wave overtopping process in a complicated setup of seawall, the velocity field was calculated and compared with the critical velocity of blocks based on CERC formula. The pick-up condition of blocks predicted by the MPS method with CERC formula showed good agreement with ones in a hydraulic experiment.