Nearshore Wave Height Research Articles

An integrated model system for coastal flood prediction with a case history for Walcott, UK, on 9 November 2007

AbstractAn integrated model system is based on downscaling from climate models, to wave climate and continental shelf models for tides and surge, to coastal models for waves and water levels, to beach levels and overtopping of sea defences and inundation. Present operational practice in the UK is described. The model system is applied to the prediction of flooding at Walcott on 9 November 2007. Inundation levels are predicted in reasonable agreement with those at certain residential properties in Walcott as reported by the occupants. The effect of time‐varying and time‐averaged overtopping discharge is considered. Sensitivity of overtopping and inundation to uncertainties in nearshore wave height and water level is analysed, with the greatest sensitivity being to water level. Extreme joint probability analysis is undertaken, showing the event to be close to a 1 in 100‐year event. Finally, the effects of different rates of sea level rise and a climate change scenario are investigated for 2100; the simulations indicate that the return period of the equivalent 2007 event could reduce to less than 2 years with a 0.5m sea level rise.

Microseisms and hum from ocean surface gravity waves

Ocean waves incident on coasts generate seismic surface waves in three frequency bands via three pathways: direct pressure on the seafloor (primary microseisms, PM), standing waves from interaction of incident and reflected waves (double‐frequency microseisms, DF), and swell‐transformed infragravity wave interactions (the Earth's seismic hum). Beamforming of USArray seismic data shows that the source azimuths of the generation regions of hum, PM and DF microseisms vary seasonally, consistent with hemispheric storm patterns. The correlation of beam power with wave height over all azimuths is highest in near‐coastal waters. Seismic signals generated by waves from Hurricane Irene and from a storm in the Southern Ocean have good spatial and temporal correlation with nearshore wave height and peak period for all three wave‐induced seismic signals, suggesting that ocean waves in shallow water commonly excite hum (via infragravity waves), PM, and DF microseisms concurrently.

Tsunami flood modelling for Aceh & west Sumatra and its application for an early warning system

For implementation of a regional Tsunami Early Warning System (EWS) in Sumatra island in Indonesia, a set of detailed and accurate tsunami propagation and flooding models using Delft3D were developed. The purpose of the models was not only to reproduce the 2004 Indian Ocean tsunami, but also to determine tsunami flood hazard maps with different return periods. The model outputs have then been used to build a tsunami flooding database covering 1250 hypothetical sources for different earthquake parameters along the Sunda Trench for an EWS called RiskMap. The model simulations produced detailed information of near-shore tsunami wave height, tsunami inundation length and run-up. Smart storage of computational results, in a geo-referenced database, allows quick access to the requisite information. The result is a system capable of issuing a warning within few minutes after a detection of an earthquake. The system has been successfully installed and tested in the last two years at national and regional emergency coordination centres, National Agency for Meteorology, Climatology and Geophysics (BMKG) and at Tsunami Disaster Mitigation Research Centre (TDMRC) in Banda Aceh.

Extreme values of coastal wave overtopping accounting for climate change and sea level rise

An integrated modelling system is presented for determining the wave overtopping of a sea wall due to offshore hydrodynamic conditions; the overtopping discharge depends mainly on the water level and the nearshore wave height. The modelling system enables joint probabilities for overtopping discharge to be assessed for different future climate scenarios with different rates of sea level rise. For the test case of a sea wall at Walcott, UK, where extensive flooding occurred on 9th November 2007, it is shown how the frequency of flooding of a given magnitude would increase with time, dependent on future climate projections and sea level rise, and, correspondingly, how the magnitude of flooding with a given return period would increase. For example, for an event with a return period of 100years (similar to the 2007 Walcott event), the return period, estimated by the proposed extreme event analyses, reduces to 5years with 0.35m sea level rise in 2100, thought to be the most likely level, and just over 1year with 1m sea level rise. The methodology applied here, based on state-of-the-art modelling of wave overtopping, shows that the future projected rates are more influenced by changes in water level than by changes in significant wave height.

Pressure-gradient-driven nearshore circulation on a beach influenced by a large inlet-tidal shoal system

[1] The nearshore circulation induced by a focused pattern of surface gravity waves is studied at a beach adjacent to a major inlet with a large ebb tidal shoal. Using a coupled wave and wave-averaged nearshore circulation model, it is found that the nearshore circulation is significantly affected by the heterogeneous wave patterns caused by wave refraction over the ebb tidal shoal. The model is used to predict waves and currents during field experiments conducted near the mouth of San Francisco Bay and nearby Ocean Beach. The field measurements indicate strong spatial variations in current magnitude and direction and in wave height and direction along Ocean Beach and across the ebb tidal shoal. Numerical simulations suggest that wave refraction over the ebb tidal shoal causes wave focusing toward a narrow region at Ocean Beach. Due to the resulting spatial variation in nearshore wave height, wave-induced setup exhibits a strong alongshore nonuniformity, resulting in a dramatic change in the pressure field compared to a simulation with only tidal forcing. The analysis of momentum balances inside the surf zone shows that, under wave conditions with intensive wave focusing, the alongshore pressure gradient associated with alongshore nonuniform wave setup can be a dominant force driving circulation, inducing heterogeneous alongshore currents. Pressure-gradient-forced alongshore currents can exhibit flow reversals and flow convergence or divergence, in contrast to the uniform alongshore currents typically caused by tides or homogeneous waves.

An analysis of wave dissipation at the Hendijan mud coast, the Persian Gulf

Effects of non-rigid muddy bed on the wave climate at the Hendijan coast along the northwestern part of the Persian Gulf have been examined through field measurements and numerical wave transformation modeling. The field survey included measurements of wave characteristics at an offshore and a nearshore station, and mud sampling to obtain the thickness of the fluid mud layer and its rheological properties. Comparisons of wave spectra at the two stations show energy dissipation along the wave trajectory with higher dissipation in the wave period band around 6 s, because depending on the site a given frequency band tends to be more effective in wave–mud interaction. Dissipation induced by the non-rigid bed is introduced into the REF/DIF wave transformation model through the application of viscoelastic constitutive equations for fluid mud. Numerical outputs of the nearshore wave height, for which the viscoelastic parameters included in the model were obtained independently from oscillatory frequency-sweep tests, are found to be comparable with measured values at the nearshore station. This implies that the model is useful for estimating the design wave conditions in the study area.

Nearshore wave height variation in unsaturated surf

The nearshore evolution of wave height is presented from field observations during unsaturated surf conditions from 10 different beaches characterized by microtidal conditions and predominantly swell‐dominated wave climates. Wave evolution is presented in terms of wave height to water depth ratio (γ) for comparison with previous data from saturated surf. Both conventional time‐averaged (γrms) and a new wave‐by‐wave analysis (γw) are performed. Values of γ increase with increasing offshore wave height, indicating unsaturated surf. The observations show a variation in γ values from near constant values in the mid surf zone to rapidly and asymptotically increasing γ values in the inner surf zone. In contrast to previous data from saturated surf, γ shows no dependence on either the absolute beach slope or the relative beach slope β/k. The skewness of the distributions of γw is consistent with waves that are not depth limited. The inner surf zone wave heights are approximately equally dependent on the water depth and offshore wave height. The previous observations of γ from saturated surf are shown to be consistent with a terminal bore height at the shoreline which is in excellent agreement with a previously derived value for the Miche parameter. In contrast, for the present unsaturated surf conditions, the terminal bore height at the shoreline can be approximated by Hb ≈ 0.12Ho, which is consistent with recent laboratory data sets.

Estimation of infragravity waves at intermediate water depth

The accuracy of nearshore infragravity wave height model predictions has been investigated using a combination of the spectral short wave evolution model SWAN and a linear 1D SurfBeat model (IDSB). Data recorded by a wave rider located approximately 3.5 km from the coast at 18 m water depth have been used to construct the short wave frequency-directional spectra that are subsequently translated to approximately 8 m water depth with the third generation short wave model SWAN. Next the SWAN-computed frequency-directional spectra are used as input for IDSB to compute the infragravity response in the 0.01 Hz–0.05 Hz frequency range, generated by the transformation of the grouped short waves through the surf zone including bound long waves, leaky waves and edge waves at this depth. Comparison of the computed and measured infragravity waves in 8 m water depth shows an average skill of approximately 80%. Using data from a directional buoy located approximately 70 km offshore as input for the SWAN model results in an average infragravity prediction skill of 47%. This difference in skill is in a large part related to the under prediction of the short wave directional spreading by SWAN. Accounting for the spreading mismatch increases the skill to 70%. Directional analyses of the infragravity waves shows that outgoing infragravity wave heights at 8 m depth are generally over predicted during storm conditions suggesting that dissipation mechanisms in addition to bottom friction such as non-linear energy transfer and long wave breaking may be important. Provided that the infragravity wave reflection at the beach is close to unity and tidal water level modulations are modest, a relatively small computational effort allows for the generation of long-term infragravity data sets at intermediate water depths. These data can subsequently be analyzed to establish infragravity wave height design criteria for engineering facilities exposed to the open ocean, such as nearshore tanker offloading terminals at coastal locations.

An application of Boussinesq modeling to Hurricane wave overtopping and inundation

Wave and combined wave-and-surge overtopping was significant across a large portion of the hurricane protection system of New Orleans during Hurricane Katrina. In particular, along the east-facing levees of the Mississippi River-Gulf Outlet (MRGO), the overtopping caused numerous levee breaches. This paper will focus on the MRGO levees, and will attempt to recreate the hydrodynamic conditions during Katrina to provide an estimate of the experienced overtopping rates. Due to the irregular beach profiles leading up to the levees and the general hydrodynamic complexity of the overtopping in this area, a Boussinesq wave model is employed. This model is shown to be accurate for the prediction of waves shoaling and breaking over irregular beach profiles, as well as for the overtopping of levees. With surge levels provided by ADCIRC and nearshore wave heights by STWAVE, the Boussinesq model is used to predict conditions at the MRGO levees for 10 h near the peak of Katrina. The peak simulated overtopping rates correlate well with expected levee damage thresholds and observations of damage in the levee system. Finally, the predicted overtopping rates are utilized to estimate a volumetric flooding rate as a function of time for the entire 20 km stretch of east-facing MRGO levees.

Numerical hindcast of extreme waves

The cyclone wave parameters are predicted using Young’s parametric hurricane wave prediction model. The input cyclone tracks for this work are obtained from Fleet Naval Meteorology and Oceanography Center, USA. Extreme value analysis is carried out to obtain the wave heights and periods for 1 in 5, 10, 50 and 100 years return periods, respectively. The deep-water hindcast wave corresponding to 100 years from probable directions are allowed to propagate to Visakhapatnam coastal waters using nearshore spectral wind-wave mode. The offshore wave height for one in 100-year return period is 11.9 m, and the corresponding nearshore wave height at 10-m water depth varies between 4.6 and 5.6 m depending on the directional spreading. Weibull distribution is chosen to fit the 24 cyclonic data sets over a total period of 30 years (September 1972 to November 2002). This paper demonstrates usefulness of Young’s wave model for deep-water extreme wave hindcasting. Further, the results of the present study would be highly useful for assessing the design wave height for Visakhapatnam coast.

A probabilistic approach for determining submarine landslide tsunami hazard along the upper east coast of the United States

Tsunami hazard assessment is critical for coastal communities, emergency services, and industry, to develop regional risk and response management plans, for catastrophic tsunami events (such as the recent 1998 Papua New Guinea (PNG) and 2004 Indian Ocean tsunamis). Along the northeastern United States coastline, tsunami hazard assessment is in its infancy, mostly due to the lack of historical tsunami record and the uncertainty regarding the return periods of potential large-scale events. The latter includes large transoceanic tsunamis, such as could be caused by a collapse of the Cumbre Vieja volcano in the Canary Islands or a large co-seismic tsunami initiated in the Puerto Rican trench, as well as large local tsunamis, such as could be caused by a Submarine Mass Failure (SMF) occurring on the nearby continental slope. In this region, considerable geologic and some historical (e.g., the 1929 Grand Bank landslide tsunami) evidence suggests that the largest tsunami hazard may arise from tsunamigenic SMFs, triggered by moderate seismic activity. The coastal impact of SMF (or landslide) tsunamis, indeed, can potentially be narrowly focused and affect specific communities. This research presents the development, validation, and results of a probabilistic geomechanical and coastal tsunami impact analysis, of tsunami hazard on the upper northeast coast of the United States. Results are presented in terms of nearshore breaking wave height and runup, caused by seismically induced tsunamigenic SMF, with a given return period. A Monte Carlo approach is employed, in which distributions of relevant parameters (seismicity, sediment properties, type and location, volume, and dimensions of slide, water depth, etc.) are used to perform large numbers of stochastic stability analyses of submerged slopes (along actual shelf transects), based on standard pseudo-static limit equilibrium methods. The distribution of predicted slope failures along the upper U.S. East Coast is found to match published data quite well. For slopes that are deemed unstable for a specified ground acceleration (with given return period), the tsunami source characteristic height is found using empirical equations (based on earlier numerical simulation work), and corresponding breaking height and runup are estimated on the nearest coastline. For a 0.2% annual-probability ground acceleration, for instance, simulations yield a return period of tsunamigenic SMFs of 3350-yr (i.e., a 0.03% annual probability of occurrence). The resulting estimate of the overall coastal hazard, from 100 and 500-yr SMF tsunami events, is found to be quite low at most locations, as compared to the typical 100 yr hurricane storm surge in the region (~ 4–5 m). Specifically, for the 100 yr event, SMF tsunami hazard is quite low with no coastal region exceeding a 1 m runup. For the 500 yr event, however, two regions of relatively elevated hazard are found: (1) near Long Island, NY, with a peak runup of 3 m; and (2) near the New Jersey coast, with a peak runup of 4 m. It should be stressed that these are only first-order estimates and detailed tsunami inundation modeling is required to fully quantify tsunami runup (and inundation) at these sites. This will be the object of more detailed studies in future work.

A performance test of nearshore wave height prediction with CLASH datasets

The CLASH database was analyzed for extraction of a set of data having the measured wave heights at both the deep station and the toe of the structure for wave overtopping tests, yielding 1214 data from 29 datasets. Wave heights in front of the toe of the structure were estimated with the Goda formulas and compared with the measured ones. Comparison yielded the overall mean of 1.106 with the standard deviation of 0.155 for the ratio of the estimated to the measured heights, which support the use of the Goda formulas for prediction of nearshore wave heights. Another set of 1215 data having the measured wave heights at the deep station and the wave heights calculated with the SWAN model was also extracted from the CLASH database. A comparative test of the SWAN model using the wave height estimated with the Goda formulas in lieu of the measured height indicated the performance of the SWAN model being similar to that of the Goda formulas, but a tendency of underestimation was noticed in shallow water on a beach of very gentle slope.

Southern California Deep-Water Wave Climate: Characterization and Application to Coastal Processes

We consider the effect of decadal climate change on the historic wave climate of the Southern California Bight (SCB) using a 50 year hindcast record (1948–98) for waves generated in the North Pacific winter. Deep-water wave height, period, and direction are examined with respect to the Southern Oscillation Index (SOI) and the Pacific Decadal Oscillation (PDO). Storms occurring during strong La Niña intervals, when the SOI is greater than 1.0, concurrent with either a cool or warm phase of the PDO, are indistinguishable in wave character. In marked contrast, wave conditions arising from storms during strong El Niño intervals, when the SOI is less than −1.0, concurrent with the PDO cool phase (1948–77), differ greatly from wave conditions of storms during strong El Niño intervals concurrent with the PDO warm phase (1978–98). Our statistical analyses characterize the deep-water winter wave climate as consistent during La Niña intervals (mean values Hs =3.3 m, Ts =13.0 s, α =293°, for the highest 5% of waves), but variable during El Niño intervals depending on PDO phase (Hs =3.64 m, Ts =13.8 s, α =292°during the PDO cool phase, and Hs =4.82 m, Ts =15.1 s, α =284°during the PDO warm phase, for the highest 5% of waves). The dominant characteristics for the different operational modes of wave climate determined in this study provide realistic inputs for numerical models aimed at understanding past and future coastal change within the SCB. Simulating WAves Nearshore (SWAN)-modeled wave transformations for the southern portion of the Oceanside littoral cell show that nearshore wave heights during westerly wave conditions are roughly twice those of northwesterly wave conditions for the same deep-water wave heights and periods, indicating increasing wave energy flux at the beach during the westerly storm-source conditions by an average of 320% (74 kW/m vs. 23 kW/m).

Parameterisation of clastic sediments including benthic structures

The sediment transport processes in the south-western Baltic Sea are predicted by means of a numerical model in the project DYNAS. There are two sediment parameters that influence the results of modelling remarkably: critical shear stress velocity and bottom roughness. This paper presents the way how to parameterise these factors and extrapolate them into the investigation area. The critical shear stress velocity is parameterised basing on grain size data, combining approximations after Hjulström [Hjulström, F., 1935: Studies in the morphological activity of rivers as illustrated by the river Fyris. Geological Institution of University of Uppsala: Bulletin (25): 221–528.], Shields [Shields, A., 1936: Anwendung der Ähnlichkeits-Mechanik und der Turbulenzforschung auf die Geschiebebewegung. Mitteilungen der Preussischen Versuchsanstalt für Wasserbau und Schiffahrt (26): 26 pp.] and Bohling [Bohling, B., 2003: Untersuchungen zur Mobilität natürlicher und anthropogener Sedimente in der Mecklenburger Bucht. unpublished doctoral thesis, Mathematisch-Naturwissenschaftliche Fakultät, Ernst-Moritz-Arndt-Universität Greifswald/Germany, 156 pp.]. The roughness length, in the case of absence of macro zoo-benthos and their structures, is parameterised basing on grain size too employing Soulsby [Soulsby, R.L., 1997: Dynamics of Marine Sands: a Manual for Practical Applications. London, Thomas Telford Publications. 249 pp.], Nielsen [Nielsen, P., 1983: Analytical determination of nearshore wave height variation due to refraction shoaling and friction. Coastal Engineering 7, 233–251.] and Yalin [Yalin, M.S., 1977: Mechanics of Sediment Transport. Pergamon Press, New York. 298 pp.]. No equivalent simple parameterisations for biologically caused bed roughness exist. Here, findings of Friedrichs [Friedrichs, M., 2004: Flow-induced effects of macro zoo-benthic structures on the near-bed sediment transport. Dissertation, Universität Rostock, 80 S.] and estimations by the DYNAS biologists group were combined in order to derive roughness lengths from abundance measurements of four previously selected key species which represent the originators of the dominating benthic structures at the sea floor in the south-western Baltic Sea. Critical shear stress velocity and bed roughness are known at few sample sites only. They were extrapolated into the larger investigation area using a proxy-target concept. The mean near bottom milieu (bathymetry, median grain size, salinity, oxygen) which was derived using results from numerical modelling serves as the proxy. Since the milieu parameters are measured at the sampling sites for which the target parameters have been determined, a combined hierarchical and supervised classification was employed to transfer the local knowledge into the unknown investigation area.

Geological and oceanographic data determining the foreshore zone according to the Greek legislation

The available scientific field data of the marine and the coastal enviroment, (wind and wave field data, shallow area bathymetry, coastal area geomorphology and topography, etc.), in addition to deep and shallow wave prediction numerical modelling (by means of wind and bathymetry measurements), calculation of the nearshore wave height and maximum wave run up, were used to support the mapping of the innermost limit of the foreshore zone according to Greek legislation which defi nes that ‘the foreshore is the zone of land wetted by the highest however unexceptional sea wave run up’ and the Supreme Administrative Court standard case law. These methods were applied for two areas, which completely differ as regards the wind and the wave field, the geomorphological and topographical characteristics of the coastal area, suggesting different procedures for the determination of the innermost limit of the foreshore zone. The limits of the foreshore zones for both areas, resulting from the study, are compared to the limits set out by the authorised Administrative Commissions, which were published in the Official Gazette and also were applied by the local authorities for the management of the coastal area.

A predictive relationship for the spacing of beach cusps in nature

Modeling is carried out to obtain a relationship that enables the prediction of the spacing of beach cusps using wave and sediment parameters. The modeling is based on the concepts that: (1) the path of wave uprush flow diverging at a cusp horn has a close connection with the cusp spacing, and (2) the flow path is affected by the grain size of beach sediment. The following equation is derived: λ = A ϕ T g ⁢ H , in which λ is the cusp spacing, H is the nearshore wave height, T is the wave period, ϕ is a dimensionless quantity representing the effect of sediment grain size: ϕ=exp(−0.23 D 0.55), where D is the grain size in mm-units, g is the gravitational acceleration, and A=1.35. The value of A is determined using a large amount of existing field data. Applicability of the predictive equation is examined by using the data from an embayed beach in New South Wales, Australia. The result indicates that this equation is capable of reasonably explaining a general trend of the alongshore variation in cusp spacings.

Prediction of nearshore wave energy distribution by analysis of numerical wave model output, East Sussex coastline, UK

Abstract Prediction of wave energy distribution in coastal areas is necessary if an assessment of the likelihood of cliff collapse is to be undertaken. Use has been made of numerical modelling to predict relative wave heights along the chalk cliff coastline of East Sussex between Brighton and Eastbourne, UK. In this study, wave modelling has been undertaken using the University of Delaware REFDIF-1 software with a 100m mesh size to predict nearshore wave heights for boundary unit wave height conditions from a range of different incident directions. The results from this wave modelling have been combined with the frequency distribution of incident waves obtained from analysis of time series of 12 years of hindcast wave data in the English Channel, obtained from the UK Meteorological Office. The resulting distribution of nearshore wave heights is presented as a surrogate for the distribution of wave energy over the 12-year period. Some concern exists about the quality of the output data, in particular of the effect of the relatively coarse bathymetry grid used for the model. Some wave focusing is evident from the model output, caused by the presence of local shoals in the model grid, leading to a ‘banding’ effect in the model output. Some suggestions are made for the improvement of the modelling scheme, including the use of finer mesh size, bathymetric smoothing and the use of a spectral model such as REFDIF-S.

Estimating palaeowind strength from beach deposits

Abstract The geological record of past wind conditions is well expressed in the coarse gravel, cobble and boulder beach deposits of Quaternary palaeolakes in the Great Basin of the western USA and elsewhere. This paper describes a technique, using the particle‐size distribution of beach deposits, to reconstruct palaeowind conditions when the lakes were present. The beach particle technique (BPT) is first developed using coarse beach deposits from the 1986–87 highstand of the Great Salt Lake in Utah, combined with instrumental wind records from the same time period. Next, the BPT is used to test the hypothesis that wind conditions were more severe than at present during the last highstand of Lake Lahontan (≈ 13 ka), which only lasted a decade or two at most. The largest 50 beach clasts were measured at nine beach sites located along the north, west and south sides of Antelope Island in the Great Salt Lake, all of which formed in 1986–87. At these sites, the largest clast sizes range from 10 to 28 cm (b‐axis), and fetch lengths range from 25 to 55 km. Nearshore wave height was calculated by assuming that the critical threshold velocity required to move the largest clasts represents a minimum estimate of the breaking wave velocity, which is controlled by wave height. Shoaling transformations are undertaken to estimate deep‐water wave heights and, ultimately, wind velocity. Wind estimates for the nine sites, using the BPT, range from 6·5 to 17·4 m s−1, which is in reasonable agreement with the instrumental record from Salt Lake City Airport. The same technique was applied to eight late Pleistocene beaches surrounding the Carson Sink sub‐basin of Lake Lahontan, Nevada. Using the BPT, estimated winds for the eight sites range from 9·7 to 27·1 m s−1. The strongest winds were calculated for a cobble/boulder beach with a fetch of 25 km. Instrumental wind records for the 1992–99 period indicate that wind events of 9–12 m s−1 are common and that the strongest significant wind event (≥ 9 m s−1 for ≥ 3 h) reached an average velocity of 15·5 m s−1. Based on this preliminary comparison, it appears that the late Pleistocene western Great Basin was a windier place than at present, at least for a brief time.

Long–wave forcing by the breaking of random gravity waves on a beach

This paper presents new laboratory data on long-wave (surf-beat) forcing by the random breaking of shorter gravity water waves on a plane beach. The data include incident and outgoing wave amplitudes, together with shoreline oscillation amplitudes at long-wave frequencies, from which the correlation between forced long waves and short-wave groups is examined. A detailed analysis of the cross-shore structure of the long-wave motion is presented, and the observations are critically compared with existing theories for two-dimensional surf-beat generation. The surf beat shows a strong dependency on normalized surf-zone width, consistent with long-wave forcing by a time-varying breakpoint, with little evidence of the release and reflection of incident bound long waves for the random-wave simulations considered. The seaward-propagating long waves show a positive correlation with incident short-wave groups and are linearly dependent on short-wave amplitude. The phase relationship between the incident bound long waves and radiated free long waves is also consistent with breakpoint forcing. In combination with previous work, the present data suggest that the breakpoint variability may be the dominant forcing mechanism during conditions with steep incident short waves.

Simplified Dean's Method for Beach-Fill Design

A simplified approach is presented to use Dean's method for determining dry-beach (subaerial) width after equilibrium for arbitrary sediment size. A simple equation is developed relating a key parameter in Dean's method to sediment diameter. Closure depth is shown to be simply related to nearshore mean annual significant wave height. Dean's equations for dry-beach width are dimensionalized and simplified. The key parameter, closure depth, and the equations for dry-beach width are all presented in simple forms that can be solved easily using a hand calculator. Examples are presented for all cases including fill sediment with a mean diameter the same size, larger, and smaller than the native sediment. When the fill sediment is finer than the native sediment a minimum quality of sediment has to be placed before there is any resulting dry beach, and an equation is provided to determine this minimum quantity. The simplified method presented allows an engineer to easily evaluate a large number of scenarios at the feasibility stage of a project.