Surf Zone Conditions Research Articles

Suspended sand concentration models under breaking waves: Evaluation of new and existing formulations

A total of 7 reference concentration (C0) models (6 existing and 1 newly proposed) were validated against 119 test cases from 4 recently published datasets collected under the LIP, CROSSTEX, SandT-Pro and SINBAD experimental studies. These models were evaluated for performance in different cross-shore regions: the shoaling zone, breaking (outer surf) zone and inner surf zone, under regular and irregular breaking wave conditions. In almost all existing C0 models, substantial under-prediction was found particularly around the wave plunging point (point at which breaking wave plunges and surface generated turbulent kinetic energy, TKE, is injected into the water column) where strong localised increases in C0 were observed. This strong increase in concentration was attributed to the large-scale breaking-generated turbulent vortices invading the wave bottom boundary layer (WBBL) and entraining dense clouds of sediment near the plunging point. Models that were directly or indirectly driven by local wave climate such as the local wave height (H), breaker height (Hb) or local water depth (d), were found to perform quite poorly in the breaking region under regular and irregular plunging breaker waves. Formulations that related C0 to the sand pickup rate (i.e. depending on exerted bed shear exceeding critical bed shear for entrainment) were adept in regions unaffected by external breaking-induced TKE (e.g. the shoaling zone) but could not account for the high levels of concentration observed at the plunging point. This is because these formulations were based on the implicit assumption that sediment entrainment is only induced by the local TKE generated by bed shear; not taking surface-generated breaking-induced TKE into account. This assumption was addressed in more recent studies, by including breaking-induced TKE into sediment pickup rate or reference concentration formulations. Though latest studies have shown promising relationships between near-bed TKE (kb) and reference concentration/sediment pickup, such formulations also face inherent limitations. These formulations are highly dependent on the accuracy of measured or modelled kb and are also sensitive to the magnitude of kb. For example, the magnitude of measured kb was found to vary by a factor of 1.1–1.3 between regular and irregular wave conditions, with kb being smaller under irregular wave conditions. This resulted in varied performance between datasets in kb-driven reference concentration formulations. The Froude-scaled TKE produced smaller deviations in magnitude of TKE between datasets, suggesting that it may be a more suitable driving parameter for reference concentration models than kb. A new reference concentration model, L19, was empirically derived from an inverse relationship observed between d and C0, and from the roller energy dissipation rate. The newly proposed L19 model shows good agreement with measured C0 (with RMSE ranging between 0.36 and 1.79 kg/m3 over the different datasets) in regular and irregular wave conditions, even at the plunging point where concentration is highest. The modified concentration profile [C(z)] equation also performs well, generally capturing the vertical concentration profile accurately throughout the whole water column.

Video-Based Remote Sensing of Surf Zone Conditions

Coastal engineers design harbors, coastal structures, and beach protection measures to guard infrastructure and communities located in coastal zones. The accurate forecasting of coastal erosion and inundation is crucial for planning the protection of existing and new coastal zone infrastructure.

Sediment suspension events in the inner surf and swash zone. Measurements in large-scale and high-energy wave conditions

The present study presents a database of hydrodynamic properties and suspended sediment concentration collected within the inner surf and swash zones aiming to improve the current understanding of the sediment dynamics occurring within the beach area closest to the shoreline. Experimental measurements were conducted in a large-scale wave flume under high-energy wave conditions at three cross-shore locations, representing inner surf and swash zone conditions. 47 tests, each one comprising 500 wave trains with identical wave conditions were measured. Obtained hydrodynamic properties and suspended sediment concentrations were observed to be highly repeatable between successive tests despite the sediment suspension event-like pattern, the beach evolution between tests, and the apparent randomness of the sediment suspension phenomenon. The hydrodynamics close to the shoreline (inner surf and swash zone) is dominated by short incident broken waves and long-wave water level oscillations induced by wave grouping. The analyzed time series of measured water surface elevation, horizontal velocity, computed Turbulent Kinetic Energy (TKE), and sediment concentration revealed that the suspended sediment concentration in this coastal zone does not correlate strongly with either the incident bore height, or the short-wave horizontal velocity or the TKE; in other words high/low values of these variables do not always promote high/low values of sediment suspension. In contrast, the highest suspended sediment concentrations were observed to occur by the combined action of incident bores and the trough of long-period water level oscillations. This pattern was more apparent in the inner surf than in the swash zone. High suspended sediment concentrations were also observed to coincide with negative peaks in long-wave horizontal velocity modulation resulting in enhanced negative sediment transport rates and beach erosion close to the shoreline.

Modeling of depth‐induced wave breaking under finite depth wave growth conditions

Recent studies have shown that the spectral wind wave model SWAN (Simulating Waves Nearshore) underestimates wave heights and periods in situations of finite depth wave growth. In this study, this inaccuracy is addressed through a rescaling of the Battjes and Janssen (1978) bore‐based model for depth‐induced breaking, considering both sloping bed surf zone situations and finite depth wave growth conditions. It is found that the variation of the model error with the breaker index γBJ in this formulation differs significantly between the two types of conditions. For surf zones, clear optimal values are found for the breaker index. By contrast, under finite depth wave growth conditions, model errors asymptotically decrease with increasing values of the breaker index (weaker dissipation). Under both the surf zone and finite depth wave growth conditions, optimal calibration settings of γBJ were found to correlate with the dimensionless depth kpd (where kp is the spectral peak wave number and d is the water depth) and the local mean wave steepness. Subsequently, a new breaker index, based on the local shallow water nonlinearity, expressed in terms of the biphase of the self‐interactions of the spectral peak, is proposed. Implemented in the bore‐based breaker model of Thornton and Guza (1983), this breaker index accurately predicts the large difference in dissipation magnitudes found between surf zone conditions and finite depth growth situations. Hence, the proposed expression yields a significant improvement in model accuracy over the default Battjes and Janssen (1978) model for finite depth growth situations, while retaining good performance for sloping bed surf zones.

Distribution patterns of interstitial polychaetes in sandy beaches of southern Brazil

AbstractThis study describes the distribution patterns of interstitial polychaetes along morphodynamic gradients on six exposed sandy beaches in Santa Catarina and Paraná (South Brazil). Three random transects were sampled at two points on each beach, one at the swash and another at the surf zone, in winter and summer conditions. Six sediment replicates were collected at each sampling point using a corer of 4.6 cm internal diameter that removed 10 cm into the sediment. Abundance and composition of interstitial polychaete were correlated to wave height, slope, grain size, CaCO3, chlorophyll a, omega indexes, temperature and relative tide range using a canonical correspondence analysis (CCA). A factorial ANOVA showed that taxa richness, mean density and Shannon’s diversity were significantly higher at the reflective beaches, but average values differ significantly between transects and these differences change according to the beach zones on both sampling dates. PERMANOVA showed that polychaete associations differ among transects according to the beach zones. The composition of interstitial polychaete associations was significantly correlated to beach morphodynamics and features (P < 0.01). Polychaete associations of reflective beaches were more diverse than in other morphodynamic states. Intermediate beaches may also sustain diverse associations due to temporal variability of the morphodynamic patterns. Beaches presenting extreme dissipative morphodynamics and compacted sediments appear to be unfavourable for the occurrence of interstitial polychaetes.

Field observations of nearshore bar formation

AbstractThe formation of an inner nearshore bar was observed during a high‐energy event at the sandy beach of Vejers, Denmark. The bar accreted in situ during surf zone conditions and the growth of the bar was associated with the development of a trough landward of the bar. Measurements of hydrodynamics and sediment fluxes were obtained from electromagnetic current meters and optical backscatter sensors. These process measurements showed that a divergence in sediment transport occurred at the location of the developing trough, and observed gradients in cross‐shore net sediment flux were consistent with the morphological development. The main cause for the flux gradients were cross‐shore gradients in offshore‐directed mean current (undertow) speed which depended upon local relative wave height and local bed slope. Copyright © 2007 John Wiley & Sons, Ltd.

A note on wave energy dissipation over steep beaches

This paper revisits the derivation of the parametric surf zone model proposed by Baldock et al. [Baldock, T. E., Holmes, P., Bunker, S. & Van Weert, P. 1998 Cross-shore hydrodynamics within an unsaturated surf zone. Coast. Eng. 34, 173–196.]. We show that a consistent use of the proposed Rayleigh distribution for surf zone wave heights results in modification of the expressions for the bulk dissipation rate and enhanced dissipation levels on steep beaches and over-saturated surf zone conditions. As a consequence, the modification proposed herein renders the model robust even on steep beaches where it could otherwise develop a shoreline singularity.

Improved representation of breaking wave energy dissipation in parametric wave transformation models

An improved formulation to describe breaking wave energy dissipation is presented and incorporated into a previous parametric cross-shore wave transformation model [Baldock, T.E., Holmes, P., Bunker, S., Van Weert, P., 1998. Cross-shore hydrodynamics within an unsaturated surf zone. Coastal Engineering 34, 173–196]. The new formulation accounts for a term in the bore dissipation equation neglected in some previous modelling, but which is shown to be important in the inner surf zone. The only free model parameter remains the choice of γ, the ratio of wave height to water depth at initial breaking, and a well-established standard parameter is used for all model runs. The proposed model is compared to three sets of experimental data and a previous version of the model which was extensively calibrated against field and laboratory data. The model is also compared to the widely used model presented by Thornton and Guza (1983) [Thornton, E.B., Guza, R.T., 1983. Transformation of wave height distribution. Journal of Geophysical Research 88 (No.C10), 5925–5938]. The new formulation leads to an important improvement in predicting wave height condition close to the shoreline in non-saturated surf zone conditions. The approach overcomes a problem in the original model, where amplification by shoaling could exceed energy dissipation by breaking in very shallow water, i.e. approaching the swash zone. In dissipative conditions an improvement is also noticeable. Of the four models considered, the new model gives the smallest error between predicted and measured wave heights for all three data sets presented.

Direct Estimation of the Reynolds Stress Vertical Structure in the Nearshore

Abstract Measurements of the vertical Reynolds stress components in the wave-dominated nearshore are required to diagnose momentum and turbulence dynamics. Removing wave bias from Reynolds stress estimates is critical to a successful diagnosis. Here two existing Reynolds stress estimation methods (those of Trowbridge, and Shaw and Trowbridge) for wave-dominated environments and an extended method (FW) that is a combination of the two are tested with a vertical array of three current meters deployed in 3.2-m water depth off an ocean beach. During the 175-h-long experiment the instruments were seaward of the surfzone and the alongshore current was wind driven. Intercomparison of Reynolds stress methods reveals that the Trowbridge method is wave bias dominated. Tests of the integrated cospectra are used to reject bad Reynolds stress estimates, and the Shaw and Trowbridge estimates are rejected more often than FW estimates. With the FW method, wave bias remains apparent in the cross-shore component of the Reynolds stress. However, the alongshore component of Reynolds stress measured at the three current meters are related to each other with a vertically uniform first EOF containing 73% of the variance, indicating the presence of a constant stress layer. This is the first time the vertical structure of Reynolds stress has been measured in a wave-dominated environment. The Reynolds stress is, albeit weakly, related to the wind stress and a parameterized bottom stress. Using derived wave bias and bottom stress parameterizations, the effect of wave bias on Reynolds stress estimates is shown to be weaker for more typical surfzone conditions (with both stronger waves and currents than those observed here).

Intertidal beach change during storm conditions; Egmond, The Netherlands

The processes responsible for sediment transport and morphological change in the intertidal zone of natural beaches are not well known. Consequently, factors determining whether the intertidal beach erodes/accretes or remains stable in the face of significant wave impact, and the mechanisms behind the elusive concept of ‘equilibrium beach slope’ are poorly understood. A field experiment was designed to measure suspended sediment transport in the swash and inner surf zone through successive tidal cycles in the intertidal zone at Egmond Beach, The Netherlands, using a stack of fiberoptic backscatter sensors (UFOBS-7). The experimental period comprised three large storm events, including an extreme storm with offshore significant wave heights in excess of 7 m. Surveys spanning a >1 km long section of the beach as well as observations from an ARGUS video camera system showed that gently sloping shoreline salients (megacusps) were highly stable in position and displayed only minor slope adjustments through the storm period, whereas steeply sloping embayments were eroded significantly. The sediment transport measurements at a shoreline salient indicated that the subdued net beach response was because offshore sediment transport occurring under surf zone conditions at high tide was compensated by onshore sediment transport at low tide when swash zone processes dominated. Such temporally varying, tidally modulated sediment transport rates and directions are suggested to be able to maintain a quasi-equilibrium intertidal beach slope and the results indicate that a negative feedback existed between initial beach slope and net sediment transport patterns.

Shoaling transformation of wave frequency‐directional spectra

A Boussinesq model for the nonlinear transformation of the frequency‐directional spectrum and bispectrum of surface gravity waves propagating over a gently sloping, alongshore uniform beach is compared with field and laboratory observations. Outside the surf zone the model predicts the observed spectral evolution, including energy transfers to harmonic components traveling in the direction of the dominant waves, and the cross‐interactions of waves traveling in different directions that transfer energy to components with the vector sum wavenumber. The sea surface elevation skewness and asymmetry, third‐order moments believed to be important for sediment transport, also are predicted well. Effects of surf zone wave breaking are incorporated with a heuristic frequency‐dependent dissipation term in the spectral energy balance equation and an empirical relaxation of the bispectrum to Gaussian statistics. The associated coefficients are calibrated with observations that span a wide range of surf zone conditions. With calibrated coefficients, the model predicts observed surf zone frequency spectra well and surf zone skewness and asymmetry fairly well. The observed directional spectra inside the surf zone are broader than the predicted spectra, suggesting that neglected scattering effects associated with the random onset of wave breaking or with higher‐order nonlinearity may be important.

Wave transformation in the nearshore zone: comparison between a Boussinesq model and field data

Abstract A numerical model based on the Boussinesq equations was developed to simulate wave transformation in the nearshore zone with emphasis on describing the effects of wave breaking. Two different formulations for estimating additional momentum due to depth-limited wave breaking, namely one proposed by Watanabe and Dibajnia [Watanabe, A., Dibajnia, M., 1988. A numerical model of wave deformation in the surf zone. Proceedings of the 21st Coastal Engineering Conference, ASCE, pp. 578–587] and another one by Schaffer et al. [Schaffer, H.A., Madsen, P.A., Deigaard, R., 1993. A Boussinesq model for waves breaking in shallow water. Coastal Engineering 20, 185–202], were incorporated and tested in the numerical wave model. Detailed, high-quality data from Duck, NC, collected during the DUCK85 and SUPERDUCK field experiments using photographic means were employed to evaluate the applicability of the Boussinesq model to surf-zone conditions. Also, comparison with the field data allowed for an assessment of how well the two formulations could describe the effects of wave breaking on the evolution of the waveform. Model simulations were compared with measured time series of water surface elevation as well as with derived statistical quantities, such as the skewness, kurtosis and root-mean-square wave height. Overall, the model results were satisfactory, although the Boussinesq model failed to accurately reproduce the strong nonlinear shoaling that occurred prior to breaking. The roller model developed by Schaffer et al. produced somewhat better agreement with the data than the model proposed by Watanabe and Dibajnia. However, the difference was small and both formulations are judged to yield acceptable results, although improvements are needed before the predictions can be used for calculating the sediment transport rate in intra-wave models.

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.

The systematic contribution of transporting mechanisms to the cross-shore sediment transport in water depths of 3 to 9 m

The systematic contributions of short waves, infragravity waves and mean flows to the cross-shore sediment transport were studied with direct measurements of instantaneous near-bed sediment concentrations and velocities as well as with an energetics-based sediment transport model using measured time series of near-bed cross-shore flow as input. The study was conducted at four cross-shore positions in the multiple bar system of Terschelling, Netherlands during three field campaigns, each with a five-week duration. The data were collected in 3- to 9-m water depth during a wide range of conditions, from low-energy non-breaking conditions to almost fully saturated breakers. The height over depth ratio H s/ h was applied at all four measuring stations as a local conditional parameter. All model predictions were grouped into H s/ h classes with a width of 0.02 to highlight the generality of the data. The energetics approach predicted that the suspended load dominated over the bedload at all four stations. Both the sediment flux measurements as well as the model predictions showed that the largest contributors to the gross suspended sediment transport were made by the short waves and the undertow, inducing an onshore and offshore transport, respectively. Their contributions to the gross suspended transport were about 40 to 50% under surf zone conditions. Bound infragravity waves were observed and predicted to result in an offshore directed transport that was of subordinate magnitude compared to the observed and estimated magnitudes by the short waves and the undertow. However, as these transports almost cancelled out because of their about equal magnitude but opposite sign, the suspended transport by bound infragravity waves may not be ignored and may, rather paradoxically, have a relatively large influence on the net suspended sediment transport. Hydrodynamical processes that do not seem to be of importance to the onshore and offshore sediment transport in 3- to 9-m water depth in the long run are mean flows under non-breaking conditions and free infragravity motions. A direct comparison between measured sediment fluxes and the model predictions suggests that simple energetics models are suitable for predicting cross-shore sediment transport in 3- to 9-m water depth.

Vertical profiles and horizontal scales of bubble clouds in the surf zone as measured with a distributed array of upward-looking sonars

A collaborative, multi-institute experiment was recently performed in the vicinity of the Scripps Pier, whose goal was the study of bubble-field generation, transport, and distribution, as influenced by surf zone conditions. The collaboration produced an ensemble of instrumentation at the site for measuring bubbles, ambient noise, temperature and salinity, currents, and surface waves. This paper emphasizes data gathered by APL-UW using a set of four upward-looking transducers (frequency 240 kHz), which simultaneously measured vertical profiles of acoustic volume scattering from bubbles from four locations. The primary locus of measurement activity was defined by NRL-SSC’s triangular frame (Delta Frame) and the four transducer locations for the APL-UW system bracketed this region. The transport of bubbles via rip currents emerged as a key feature surf zone bubble environment. Images of volumetric backscattering strength versus time and depth reveal episodic events (by way of increased scattering level) which last O(100) s and can occur in intervals of O(10) min. Time lags for increased scattering at the four locations were consistent with a seaward flow of rip currents equal to ∼0.25 m/s. Other features of the data that complement the single-depth measurements made from the Delta Frame will be discussed. [Work supported by ONR.]

The temporal and spatial variability of infragravity energy in a barred nearshore zone

Recordings of near-bottom pressure at six cross-shore positions in a gently sloping multiple bar system were analysed to study the temporal and spatial variability of infragravity (0.004–0.04 Hz) energy. The temporal variations in infragravity levels at each position were, as expected, strongly related to those in the offshore incident wave energy. Furthermore, infragravity energy was better correlated to swell than to sea energy and, under non-breaking conditions, was tidally modulated with larger values during low water than during high water. During low-energy conditions infragravity energy was almost constant over the profile, suggesting a dominance of free long-wave motions; however, it rapidly grew in the onshore direction during more energetic, though non-breaking conditions, caused by significant bound-wave contributions to the total long-wave field. Infragravity energy was significantly damped under surf-zone conditions, even causing a decline in the onshore direction. The data indicates that the release of bound long waves during the breaking process of the incident sea and swell may be the main source of free infragravity motions.

Suspended sediment transport and morphological response on a dissipative beach

This paper reports on some results from a field experiment conducted under highly dissipative surf zone conditions, occurring during a storm in Lake Huron, Ontario, Canada. Measurements of sediment resuspension and sediment flux were conducted at a number of stations across a nearshore bar. This bar moved approximately 25 m offshore during the storm, at a rate of ≈2.5 m h −1. The maximum erosion depth over the former bar crest was 0.92 m, with simultaneous accretion on the lakeward slope of the bar reaching 0.63 m. During the early hours of the storm, the accretion rate over the lakeward slope was approximately 0.05 m h −1. Mean sediment concentrations were up to 6.4 g 1 −1, time series of sediment concentration were characterized by low-frequency fluctuations and the sediment resuspension was strongly constrained by infragravity waves. The major mechanism responsible for the offshore sediment flux was an offshore directed mean current, which reached a velocity of −0.34 m s −1. However, the reason for the erosion and the offshore migration of the bar was the strong spatial gradient in the cross-shore suspended sediment flux. This gradient was induced mainly by the infragravity waves, which transported sediment onshore at the former bar crest where the oscillatory flux balanced the mean flux, and offshore over the lakeward slope, reinforcing the mean flux at this location.

Dynamics of large and small scale bedforms on a macrotidal shoreface under shoaling and breaking waves

Bedform dimensions, bed position changes, near-bed velocities and suspended sand concentrations are analyzed from measurements at a single location on a macro tidal beach in the south west of England. The study was conducted in 0.5-2.25 m water depth under both swell and wind-generated storm waves with both weak and strong currents present. Bed positions and suspended sand concentrations were measured using the 3 transducers of a multi-frequency acoustic backscatter sensor with 5 mm vertical resolution. Two distinct bed types, based on wavelength (λ), were observed, each with two or more subtypes possible: (I) small-scale bedforms ( λ < 20 cm) which include two-dimensional pre-vortex (1), vortex (2), post-vortex (3) and three-dimensional vortex (4) forms; (II) large-scale bedforms ( λ > 20 cm) which include two-dimensional (5) forms and three-dimensional vortex (6) forms. Small-scale forms were dominant under non-breaking conditions while the large-scale forms occurred under both non-breaking and breaking waves; the large-scale forms dominate under breaking conditions. Both types, but particularly low steepness forms, were highly mobile with maximum horizontal migration rates of 5 cm min −1. Large (upto 15 cm) and rapid (upto 3.0 cm min −1) changes in vertical bed elevation were also observed in association with the development and migration of large-scale forms. Large-scale bedforms were also highly variable spatially, often being interspersed with smaller scale forms under decaying flow regimes and with areas of flat bed under increasing regimes. Observations suggest these forms are present even under high energy surf zone conditions (wave Shields ⩾ 1). Models for predicting ripple dimensions did not perform well in this environment. This lack of agreement reflects the complex hydrodynamic regimes associated with random (grouped) shoaling and breaking waves together with the presence of currents, often at large angles to the waves, as well as the rapid rates of change in the wave forcing associated with tidal cycle oscillations in this macrotidal environment. Suspended sediment concentrations and transport rates are particularly sensitive to the bedforms present and also to bed position changes associated with ripple migration. Estimates of transport rates are subject to potentially large errors (upto 30%) without compensation for bed elevation changes relative to sensor position.

APPLICABILITY OF SOLUTIONS FOR TRANSIENT WAVE-INDUCED POREWATER PRESSURES IN SEABED AND LIQUEFACTION CONDITIONS OF SEABED

There exist three solutions for the transient wave-induced porewater pressures in seabed, the seepage flow solution, the exact solution and the boundary region approximation solution of Biot's consolidation equations. Applicability of three solutions is shown graphically in terms of non-dimensional parameter for surf zone conditions. One of the important parameters is the ratio of the shear modulus of solid skelton to the effective bulk modulus of porewater. Another is a non-dimensional quantity proportional to the permeability coefficient and the shear modulus. As the former becomes large and the latter becomes small, the seepage flow solution can not be used but the boundary region approximation solution becomes applicable. Under such situation, the possibility of the vertical effective stress of solid skelton being zero under the wave trough increases. The maximum depth of zero stress is about one half of the wave height.

Statistical Description of Longshore Transport Environment

The longshore transport environment at a coastal site is represented in terms of six parameters. The total population of longshore transport-rate observations at a site is separated into two populations, positive transport and negative transport, each of which canbe described by a log-normal probability distribution. The six parameters describing the environment are the two means and standard deviations that define the two log-normal distributions and the fractions of time the transport is positive and negative. The log-normal distribution appears to fit data from a wide variety of sites and for a wide range of types of wave data. Longshore transport rates calculated from longshore current observations depend on surf-zone width; thus the coefficient relating longshore transport rates to surf-zone conditions varies from site to site. Annual net longshore transport rates are normally distributed. Synthetic net transport-rate data at Indian River Inlet, Delaware, was generated having the same statistical parameters as the observed transport rates.