Shoreface profile
Definition of Shoreface profile:
The shoreface profile, often called beach profile, is the crossshore coastal depth profile extending from the lowwater line to the closure depth.
This is the common definition for Shoreface profile, other definitions can be discussed in the article

Contents
Introduction
The shoreface is the zone where offshore generated waves interact with the upward sloping seabed, in front of the shoreline. The width of sandy shorefaces typically ranges between a few hundred meters and a few kilometers and the average slope between 1/20 and 1/200. Incident waves are transformed and dissipate most of their energy on the shoreface, whereby large amounts of sediment are suspended and transported. Most energy is dissipated in the upper part of the shoreface, the surf zone (or breaker zone), where waves overturn and break. The lower part of the shoreface extends to the socalled closure depth; beyond this depth the seabed is hardly influenced by waves and waveinduced sediment transport is insignificant (see also Active coastal zone). The lower part of the shoreface is also called shoaling zone; wave shoaling is the process of wave amplification when waves travel from deep to shallow water before breaking (see Shallowwater wave theory). The division between upper and lower shoreface profiles is often marked by an inflexion point, a bar or a terrace, indicating transition of morphodynamics ^{[1]} (Fig. 1). Another transition exists at the shoreline where waves collapse and run up the beach; this socalled swash zone is dealt with in the article Swash zone dynamics. The surf zone profile is often undulated due to the presence of one or several bars. These bars have mainly a shore parallel orientation, but more complex threedimensional patterns are ubiquitous (see Rhythmic shoreline features and Fig. 2).
Morphodynamic feedback
Sediment transport on the shoreface depends on the local wave climate. By 'wave climate' is meant the description of incoming waves in terms of a statistical distribution of incident wave directions, wave heights and wave periods (see Statistical description of wave parameters). Sediment transport also depends on the characteristics of bed sediments and on the seabed bathymetry. For small wave incidence angles (close to the shorenormal direction) the relevant seabed bathymetry is the crossshore shoreface profile.
The shoreface profile influences crossshore sediment transport, but the inverse is also true: changes of the shoreface profile result from gradients in the crossshore sediment transport. This is called morphodynamic feedback: for a given incident wave field the shoreface profile determines the transformation of the wave field on the shoreface and therefore the resulting sediment transport, whereas the resulting sediment transport determines the shoreface profile. As a result of this morphodynamic feedback, the shoreface profile tends to an equilibrium shape for a given stable wave climate. A dynamic equilibrium is reached when onshore directed sediment transport and offshore directed transport are equal on average over a period exceeding the morphodynamic adaptation time. This holds for alongshore uniform coasts; the equilibrium requirement for nonuniform coasts is a vanishing divergence of the longterm average total sediment transport vector (crossshore and alongshore). It was realised already long ago that the shoreface of a sedimentary coast should not be regarded as a geologically inherited feature, but as the result of natural adaptation to modern hydrodynamic conditions ^{[2]} ^{[3]}.
Knowing how to determine the equilibrium shoreface profile has great practical interest. It provides quantitative insight in the response of the shoreface to changes in the local wave climate by human and natural causes; such insight is important for testing and improving the effectiveness of measures to combat coastal erosion and shoreline retreat.
Bedforms and sediment sorting
Morphodynamic feedback involves not only shoreface profile development, but also sediment grainsize and bed roughness. Grainsize and bed roughness strongly influence sediment transport ^{[4]}. Inversely, sediment transport strongly influences the grainsize distribution of bed sediments. Bed roughness depends on the presence of bedforms (ripples, dunes), which in turn depend on sediment transport and sediment grainsize. Consequently, shoreface profile development, wave transformation on the shoreface, sediment transport, grainsize sorting and bedform emergence are all dynamically coupled processes.
Grainsize sorting is primarily due to differences in transport modes of different grainsize fractions. The finer fractions are more easily brought and maintained in suspension than the coarser fractions. They are transported further away from their initial location and tend to settle on the lower shoreface zone where waveinduced bed shear stresses are lower than on the upper shoreface. The coarse fraction is transported partly as suspended load and partly as bedload in the wave boundary layer. Wave transformation in shallow water leading to wave skewness (stronger onshore than offshore wave orbital velocity) and wave asymmetry (stronger onshore than offshore wave orbital acceleration) favour net onshore transport in the wave boundary layer. Fine sediments are resuspended from the upper shoreface due to undertow currents and turbulent shear stresses generated by breaking waves. Sediments on the upper shoreface are therefore coarser than on the lower shoreface. Fine sediment particles can still be present on the upper shoreface if they are 'hidden' by overlying coarser sediment particles – a phenomenon called 'bed armouring'.
The largest bedforms on the shoreface, such as shorefaceconnected ridges (scale of several kilometers) and shoreoblique bars (scale of the order of hundred meters) are mainly related to morfodynamic feedback processes that interact with longshore transport, see the articles Sand ridges in shelf seas and Rhythmic shoreline features. Other large bedforms, the socalled breaker bars (scale also of the order of 100 meters) arise from morphodynamic coupling with the wave breaking process, through the resulting flow structure at the breaker bar and interaction with crossshore and longshore transport ^{[5]}^{[6]}. Bedforms at much smaller scales – ripples with wavelengths of the order of 1 m – are formed in the less exposed parts of the shoreface under low to moderate wave conditions. Morphodynamic feedback processes, leading to regular ripple patterns, involve rippleinduced nearbed flow circulation ^{[7]}, vortex shedding at ripple crests ^{[8]} and nonlinear rippleripple interactions ^{[9]}. For a more detailed discussion, see the articles Wave ripples and Wave ripple formation. The time lag of sediment suspension and settling related to vortex shedding at the ripple crests strongly influences the direction of residual crossshore sediment transport on the shoreface, see section #Onshore waveinduced sediment transport.
Beach classification
The beach profile in the upper shoreface zone can be highly variable. The profile tends to steepen in periods of lowenergy waves (especially longperiod swell waves) and to flatten under highenergy storm waves (see Active coastal zone). Sediment characteristics also play an important role. Coarsegrained beaches, typical for highenergy coasts, have steeper slopes than finegrained beaches, typical for moderatetolowenergy coasts ^{[10]}. Gently sloping beaches dissipate almost completely the energy of incident waves, whereas steepsloping beaches tend to reflect (partly) incident waves. For distinguishing between reflective and dissipative beaches the Deanparameter [math]\Omega[/math] is often used ^{[11]}^{[12]}:
[math]\Omega = \Large \frac{H}{wT} \normalsize , \qquad(1)[/math]
where [math]H[/math] is the offshore wave height before breaking, [math]T[/math] is the peak spectral wave period and [math]w[/math] is the mean sediment fall velocity. By analysing beach profiles in Australia, Wright and Short (1984) ^{[13]} found that beach types could be characterised by the parameter [math]\Omega[/math]:
 reflective beaches correspond to [math]\Omega \lt 1 [/math];
 intermediate beaches correspond to [math]1\lt \Omega \lt 6 [/math];
 dissipative beaches correspond to [math]\Omega \gt 6 [/math].
The tidal range also influences the beach profile, because the surf zone is shifted across the shoreface with tidal level. For large tides (tidal range much larger than wave height) the surf zone covers during the tidal cycle a much larger area than for small tides. Beaches with large tides therefore have smaller upper shoreface slopes compared to beaches with the same [math]\Omega[/math] and small tides.
Crossshore sediment transport
Sediment transport on the shoreface depends on many processes. We focus on processes relevant for crossshore transport. It should be realised, however, that longshore transport processes can also play an important role. Shifts in the crossshore position of the shoreface profile and the generation of bars on the shoreface are strongly influenced by longshore transport processes. See for example the articles: Natural causes of coastal erosion, Littoral drift and shoreline modelling and Rhythmic shoreline features. In the following we consider sandy beaches, with grain sizes typically between 0.2 and 0.5 mm (fine to medium sand). Coarse sedimentary beaches are dealt with in the article Gravel Beaches.
Onshore waveinduced sediment transport
Wave transformation in shallow water (see Shallowwater wave theory) is a major factor for onshore sediment transport ^{[14]}. Waves become skewed and asymmetric, producing nearbed shear stresses which are stronger in onshore direction than in offshore direction ^{[15]} ^{[16]}^{[17]}. Phase lags between bed shear stress and sediment suspension determine to which degree wave skewness induces onshore transport; in some situations (rippled bed, sheet flow) a large phase lag can reverse the net sediment transport direction. A large time lag implies that sediment particles that are stirred up by turbulent eddies during onshore orbital motion are transported offshore after reversal of the wave orbital velocity ^{[18]}^{[19]}^{[15]}^{[20]}. Onshore transport is stimulated by wave breaking that generates turbulent fluid motions and sediment resuspension under the wave crest ^{[21]}. The development of forward streaming at the top of the wave boundary layer also contributes to onshore transport ^{[22]}, but this only holds for smooth beds and not in cases where the seabed is rippled, in cases of strongly skewed waves or for sheet flow conditions ^{[23]}^{[24]} (see also Sediment transport formulas for the coastal environment). Another, but generally lesser contribution to onshore sediment transport is further due to net mass transport in the upper layer between wave trough and wave crest.
Offshore waveinduced sediment transport
Offshore transport is due to socalled undertow: the compensating return current for the net onshore mass transport in the layer between wave trough and wave crest ^{[25]}^{[26]}^{[27]}. The undertow current is particularly strong just in front of the location where waves are breaking and where much sediment is brought into suspension^{[28]}. Bound infragravity waves may also contribute to net offshore sediment transport, as discussed in the article Infragravity waves.
Downslope sediment transport
Downslope transport occurs when sediment particles roll down the shoreface slope. However, this is not the primary cause of downslope sediment transport for fine to medium sandy beaches ^{[29]}. Gravityinduced sediment transport is a minor effect for two reasons: (1) the shoreface slope is small and (2) sediment particles are mainly transported in suspension, more than as bedload, especially on the upper shoreface. When a sediment particle is lifted from the bed to a certain level [math]z[/math] into the fluid, it moves with the wave orbital flow over a net distance [math]l[/math] until it settles again onto the bed. The net distance [math]l[/math] travelled by the sediment particle depends on the settling time; the longer the settling time, the greater the distance. The settling time is inversely proportional to the sediment fall velocity [math]w[/math]. Because the shoreface has a seaward dipping slope, the net travelled distance by an offshore moving sediment particle is larger than for a flat bottom; the inverse holds for an onshore moving sediment particle. The slope effect thus requires a correction to the net sediment transport over a flat bottom, which depends on the slope [math]S[/math] and the fall velocity [math]w[/math]. Formulas for suspended sediment transport assume in general that the slope effect can be represented by a correction factor to the waveinduced transport components of the form ^{[30]}
[math](1 S \, \gamma \Large \frac{u }{w} \normalsize ) , \qquad(2)[/math]
where [math]S[/math] is the bed slope, [math]u[/math] the instantaneous wave orbital velocity, [math]w[/math] the sediment fall velocity and [math]\gamma[/math] an efficiency parameter. Although not proven, it is often assumed that the slope effect is a major factor compensating for net waveinduced onshore transport (sum of waveinduced onshore and offshore transport components) in situations close to equilibrium. This implies that the equilibrium shoreface slope [math]S[/math] will be steeper (larger [math]S[/math]) for a coarser seabed (large fall velocity [math]w[/math]) than for a finer sediment bed (small fall velocity [math]w[/math], smaller [math]S[/math]). This is expressed by the correction factor (2) and is in general agreement with field observations. When averaging over the wave period (or, more precisely, the wave climate), the bedslope effect on the total net sediment transport can be related to the equilibrium bed slope [math]S_{eq}[/math] by the correction factor [math](1 – S / S_{eq})[/math] ^{[31]}.
Sediment transport modelling
The processes involved in sediment transport on the shoreface, as described above, are complicated and not yet fully understood. Even the most sophisticated processbased mathematical models, like XBEACH ^{[32]}, make use of approximate empirical formulations for several processes contributing to sediment transport and involve parameters that need to be tuned. Empirical formulas for waveinduced sediment transport on the shoreface that are often used in practice are given in the articles Sediment transport formulas for the coastal environment and Sand transport. These formulas are based on laboratory and field measurements for a large range of conditions. Rough estimates can be obtained with the empirical default parameters given in these articles. For better estimates it is necessary to tune these parameters to field data.
Equilibrium shoreface profile
For a given stable wave climate the shoreface profile tends after a long period to an equilibrium profile. This equilibrium profile can be computed by applying sediment transport formulas to an initial profile for a period comprising all wave conditions according to local wave climate statistics. This requires heavy calculations that are moreover subject to large uncertainty margins. Therefore, equilibrium profiles derived from field observations are generally used. From analysis of a large number of beach profiles of the Californian and Danish coasts ^{[33]}^{[34]} and the US Atlantic and Gulf coasts ^{[35]} Bruun (1954) and Dean (1977) derived an equilibrium profile (often called the Dean/Bruun profile) of the form (Fig. 3)
[math]h(x)=A \; x^{2/3}, \qquad(3)[/math]
where [math]h[/math] is the water depth [m], [math]x[/math] the crossshore distance [m] ([math]x=0[/math] at the shoreline) and [math]A [/math] a coefficient depending on the sediment fall velocity [math]w[/math] [m/s], [math] \quad A \approx 0.5 \; w^{0.44} [m^{1/3}][/math].
Dean ^{[35]} showed that the exponent 2/3 is consistent with the assumption of constant wave energy dissipation per unit volume throughout the surf zone.
Because the Bruun/Dean profile has an infinite slope at the shoreline, an alternative form was proposed by Bodge (1992) ^{[36]},
[math]h(x)=B \; (1 – e^{kx}) , \qquad(4)[/math]
where [math]k[/math] is an empirical coefficient in the range [math]3 \; 10^{5}  1.16 \; 10^{3} \; [m^{1}][/math].
From an analysis of terraceshaped shoreface profiles in northern Spain, Bernabeu et al. (2003) ^{[37]} found that the Bruun/Dean profile was adequate only for the upper shoreface; for the lower shoreface they proposed the form
[math]h(x)=A' \; (xx_0)^{2/3} , \qquad(5)[/math]
where [math]x_0[/math] is determined such that the two profiles (3) and (5) match at the inflexion point between the upper and lower shoreface.
Inman et al. (1993) ^{[38]} used a similar procedure for the analysis of beach profiles for the coasts of south California, North Carolina and the Nile delta. They found best fits with exponents ranging between 0.3 and 0.45 instead of 2/3.
Analytical equilibrium models
Because of the earlier mentioned difficulties to derive model estimates of the equilibrium shoreface profile, taking into account the full wave climate, analytical models have been developed in which the wave climate is replaced by a single representative monochromatic incident wave. An alongshore uniform shoreface is assumed with perpendicular wave incidence. In these models a simple wave transformation model is used based on depth saturation of broken waves (wave height limited by depth) and shallowwater wave theory. An analytical expression for the equilibrium shoreface slope can be derived by requiring that the total waveintegrated crossshore sediment flux equals zero throughout the shoreface zone ^{[39]} ^{[29]} ^{[40]}. Although these models reproduce certain properties also observed in the field, such as increasing profile steepness with increasing grain size and with increasing wave period, a more detailed comparison of computed profiles with observations exhibits large discrepancies. The computed concavity of the upper shoreface profile is much stronger than generally observed in the field and much stronger than for the Bruun/Dean profile. This is perhaps not surprising in view of the simplicity of the model for waveinduced sediment transport, which ignores many of the processes described in the previous paragraphs. These analytical models also ignore the influence of extreme storms, which can flatten the profile out to great depths within a few days. The profile adaptation time scale for the entire shoreface being quite long (order of centuries ^{[29]}), it is plausible that observed shoreface profiles generally correspond to transient profiles ^{[40]}.
Related articles
Further reading
Komar, P.D. 1998. Beach processes and sedimentation. Prentice Hall, London, pp. 544.
Woodroffe, C.D. 2002. Coasts, form, processes and evolution. Cambridge Univ.Press, 623 pp.
Dronkers, J. 2017. Dynamics of Coastal Systems. World Scientific Publ. Co. 753 pp.
References
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