Beach face and berm morphodynamics fronting a …Beach face and berm morphodynamics fronting a coastal lagoon Felicia M. Weir a,⁎, Michael G. Hughes a, Tom E. Baldock b a School

2006) 331–346www.elsevier.com/locate/geomorph

Geomorphology 82 (

Beach face and berm morphodynamics fronting a coastal lagoon

Felicia M. Weir a,⁎, Michael G. Hughes a, Tom E. Baldock b

a School of Geosciences and Institute of Marine Science, The University of Sydney, NSW, 2006, Australiab Division of Civil Engineering, The University of Queensland, St. Lucia, QLD, 4072, Australia

Received 1 December 2005; received in revised form 19 May 2006; accepted 19 May 2006Available online 20 July 2006

Abstract

This study documents two different modes of berm development: (1) vertical growth at spring tides or following signif icant beach cutdue to substantial swash overtopping, and (2) horizontal progradation at neap tides through the formation of a proto-berm located lowerand further seaward of the principal berm. Concurrent high-frequency measurements of bed elevation and the associated wave runupdistribution reveal the details of each of these berm growth modes. In mode 1 sediment is eroded from the inner surf and lower swashzone where swash interactions are prevalent. The net transport of this sediment is landward only, resulting in accretion onto the upperbeach face and over the berm crest. The f inal outcome is a steepening of the beach face gradient, a change in the profile shape towardsconcave and rapid vertical and horizontal growth of the berm. Inmode 2 sediment is eroded from the lower two-thirds of the active swashzone during the rising tide and is transported both landward and seaward. On the falling tide sediment is eroded from the inner surf andtransported landward to backf ill the zone eroded on the rising tide. The net result is relatively slow steepening of the beach face, a changeof the profile shape towards convex, and horizontal progradation through the formation of a neap berm. The primary factor determiningwhich mode of berm growth occurs is the presence or absence of swash overtopping at the time of sediment accumulation on the beachface. This depends on the current phase of the spring-neap tide cycle, the wave runup height (and indirectly offshore wave conditions)and the height of the pre-existing berm. A conceptual model for berm morphodynamics is presented, based on sediment transport shapefunctions measured during the two modes of berm growth.© 2006 Elsevier B.V. All rights reserved.

Keywords: Berm; Morphodynamics; Swash; Wave runup; Sediment transport shape function; Intermittently closed and open lagoon (ICOL)

1. Introduction

The wave-dominated coastline of New South Wales,Australia, has approximately 130 estuaries.Many of theseare coastal lakes or lagoons with entrances that naturallycycle between being briefly open to the ocean and beingclosed off by a wave-built berm for extended periods oftime (Roy et al., 2001). The beach berms responsible forclosing off coastal lagoons are created through the depo-

⁎ Corresponding author. Tel.: +61 2 93514050; fax: +61 2 93510184.E-mail address: [email protected] (F.M. Weir).

0169-555X/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.geomorph.2006.05.015

sition of sediment at the landward extent of wave runup,resulting in the beach face profile growing both verticallyand horizontally seaward. This tends to produce an in-creasing profile gradient approaching the berm crest onthe seaward side and a horizontal to gently dipping back-beach profile on the landward side.

Berms are ubiquitous on steep, coarse-grained beachesand several early studies proposed a simple relationshipbetween berm height above mean sea level and waveheight (Bagnold, 1940; Bascom, 1953; King, 1972).Subsequent studies have proposed relationships thatinclude not only wave height but also wavelength (period)

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332 F.M. Weir et al. / Geomorphology 82 (2006) 331–346

(Sunamura, 1975; Takeda and Sunamura, 1982). Tidalf luctuations through the spring-neap cycle also influenceberm development, with greatest growth occurring whenovertopping is taking place, which typically occurs withelevated still water levels during springs (Bascom, 1953;Strahler, 1966; Austin and Masselink, 2006). The inf lu-ence of grain size on berm height remains ambiguous.While the studies of Sunamura (1975) and Takeda andSunamura (1982) concluded that berm height was inde-pendent of grain size in the range 0.22–1.30 mm, Okazakiand Sunamura (1994) found it necessary to include a ‘re-duction factor’ in their predictive equation for berm heightin order to account for bed roughness and permeability,which are both directly related to grain size.

The dependence of berm height upon wave runupleads to what is known as the ‘berm-height paradox’, i.e.,increasing offshore wave heights increase the wave runupheight and therefore the berm crest height, but the largestwaves ultimately erode the beach face and result in areduction in berm height (e.g. Bascom, 1953; Komar,1998; Hughes and Turner, 1999). The key element toresolving the berm height paradox is through improvedprediction of the direction of cross-shore sediment trans-port (onshore versus offshore). Early laboratory workshowed that the initiation of offshore sediment transportand switching from a berm-to a bar-profile occurs at acritical value of deepwater wave steepness, though thisvalue varied between studies (e.g.King andWilliam, 1949;Rector, 1954; Watts, 1954; Saville, 1957). Later studiesconsidered the effect of the sediment fall velocity, whichimproved the predictive capability for initiation of offshoresediment transport and the switch to a bar-profile (Dean,1973; Kraus and Larson, 1988; Larson and Kraus, 1989).A different approach was investigated by Kemp (1975)who showed that swash interaction, specifically imped-ance, has a controlling effect on the sediment transportdirection and resulting beach profile (bar or berm). Whilesome nearshore morphodynamic models have tried toaccount for swash zone processes (e.g. Larson and Kraus,1995; Masselink and Li, 2001), the transition to an accre-tionary berm type profile requires accretionary transportabove the still water level, for which there is still no vali-dated sediment transport model (see Elfrink and Baldock,2002, for a recent review).

Hine (1979) described three mechanisms for bermgrowth. The f irst mechanism is attributed to the land-ward migration and welding of an intertidal swash bar tothe beach face. This creates a gently seaward dippingbeach-face terrace, which rapidly steepens to create anew berm (e.g. Aagaard et al., 2006). A second, similarmechanism involves rapid vertical growth of an inter-tidal swash bar. During neap tides overtopping is in-

hibited and results in the steepening of the seaward faceof the swash bar. Later inf illing of the landward runnelby overtopping during spring tides subsequently devel-ops a wide berm ridge. In the case of the third mecha-nism, differences in tidal elevations over a spring-neapcycle are again crucial. During neap tides, wave runup isunable to overtop the pre-existing berm crest, resulting inthe accumulation of sediment lower on the beach face inwhat is termed a ‘neap-berm’. At spring tide, the sedimentscomposing the neap-berm are transported onto the top andover the crest of the higher ‘spring-berm’. Although Hine(1979) argued that differences in the longshore sedimenttransport rate determined which berm growth mechanismoccurred at a given site, all of the mechanisms describedare effectively the result of cross-shore sediment transport.

The controlling inf luence of the tide onmaximumbermheight is not limited to whether the beach accretion occursduring spring or neap tides. Grant (1948) hypothesised thaton the f looding tide the beach face should accrete, par-ticularly above the landward limit of the groundwatereff luent zone (water table exit point) where swash infil-tration is enhanced and the transport competency of theuprush is superior to the backwash. Similarly, on theebbing tide he hypothesised that the beach should erode,particularly below the landward limit of the groundwatereff luent zone where swash infiltration is impeded and thetransport competency of the backwash is superior to theuprush. This hypothesis is consistent with subsequent fieldmeasurements presented in Duncan (1964) and Strahler(1966). In a recent study, Austin and Masselink (2006)present concurrent hydrodynamic and sediment transportmeasurements demonstrating reduced transport competen-cy and deposition due to swash infiltration above the watertable exit point on a gravel beach. They concluded that bothtidal elevation and sediment deposition linked to swashinfiltration controlled berm positioning on their beach.

Beyond these early qualitative studies and that byAustin and Masselink (2006) on a gravel beach, therehas been no study of berm development on a sandybeach that integrates both morphological and hydrody-namic data with a temporal resolution suff icient to ex-plore behavioral response of the berm at both inter- andintra-tidal timescales. This represents a signif icant gapin our understanding of beach morphodynamics. Whilethe processes relating to beach erosion (elevated waterlevels at the shoreline and largely surf processes) havebeen widely studied and are reasonably well-describedby broad-scale numerical engineering models, the pro-cesses relating to beach accretion (swash processes) arepoorly understood and are largely excluded from suchmodels (e.g. Schoonees and Theron, 1995; Elfrink andBaldock, 2002). This paper addresses this point by

333F.M. Weir et al. / Geomorphology 82 (2006) 331–346

presenting integrated hydrodynamic and morphologicaldata collected during two different accretionary periods ofberm growth. Field data and methods are described inSection 2. The data presented in Section 3 delimit hydro-dynamic zones and related (localised) erosion and accre-tion that, when migrated across the beach with the tide,ultimately lead to berm growth. Two modes of bermgrowth are documented. Section 4 quantifies the sedimenttransport shape functions responsible for each of thesemodes and presents a conceptual model for berm mor-phodynamics. Discussion and conclusions follow inSections 5 and 6.

2. Field site and methods

2.1. Avoca Beach

Two field campaigns were conducted over the periods13–22 October, 2003, and 15–18 November, 2004, atAvoca Beach, New South Wales, Australia. The NSWcoast is a high energy,wave-dominated environment, witha long-term offshore average significant wave heightand period of 1.59 m and 8.0 s, respectively (Short andTrenaman, 1992). The coastline experiences semi-diurnalmicrotides, with an average spring tidal range of 1.6 mand a maximum spring range of 2 m (Easton, 1970).Avoca is a 1.5 km long beach facing east–southeast andbounded by two large sandstone headlands (Fig. 1). Theentrance to Avoca Lagoon is situated approximately half-way along the beach and is intermittently open to theocean during and following times of heavy rainfall. Toavoid f looding of properties along the lagoon foreshore,

Fig. 1. Sketch map showing the location of the experiment site at Avoca BeaAustralia.

the entrance is usually opened artif icially when waterlevel inside the lagoon reaches 2.1 m Australian HeightDatum (0 m AHD is approximately mean sea level).

The field measurements reported here were obtainedimmediately in front of Avoca Lagoon. The beach face atthis site is uniformly composed of coarse sand. A surfacesediment sample collected from themid-swash zone had amean grain diameter of 0.525mm, and is representative ofthe entire profile. During the first experiment, the beachmorphology was characterized by a steep beach face witha gradient (tanβ) that ranged from 0.097 to 0.133. Duringthe second experiment the beach face gradient rangedfrom 0.067 to 0.100.

2.2. Field experiments

The first f ield campaign was conducted over neaptides and the second over spring tides. During each cam-paign the beach morphology between the lagoon andinner surf zone was surveyed daily with a total stationalong shore-normal transects. Additional higher resolu-tion measurements of morphological change in the swashzone were obtained from a single line of bed elevationrods inserted at 2-m intervals across the beach face. Therod heights were measured to within half a centimetreevery 15 min over most or all of a semi-diurnal tide cycleon 8 occasions during the two field campaigns. Themethodology is sufficiently accurate to resolve changesin bed elevation of 1 cm or greater (Masselink et al.,1997). The tops of the rods were surveyed at the start ofeach experiment and reduced to a common datum (AHD).Thus, the measured rod heights provided beach profiles

ch, on the central coast of New South Wales (shaded region of inset),

Fig. 2. Example of an observed wave runup height exceedencedistribution (symbols) measured at 11:00, October 16, 2003, and theRayleigh distribution (solid line).

Fig. 3. Example of a pressure record showing two swash events, the firstcontaining an overrunning wave (measured at 09:14, October 16, 2003).


measured every 15 min throughout the tide cycle. In total310 profiles from 8 separate tidal cycles are presentedhere. Diff icult wave conditions or failing daylight some-times prevented logging over a full tide cycle.

Concurrent with collection of the high-resolutionmorphology data, the wave runup height distribution wasmeasured using a shore-normal array of pressure sensorsinstalled across the beach face. In the first experimentthis array consisted of 12 pressure sensors of varyingmakes (Druck, Van Essen Diver, In-Situ Mini Troll) andsampling capabilities, which were logged at a rate ofeither 2 or 10 Hz for 30-min bursts each hour over theperiod that the morphology was being monitored. In thesecond experiment the shore-normal array contained 13Druck PTX pressure sensors, logged at a rate of 10Hz for15-min bursts every half hour with an additional VanEssen Diver self-logging pressure sensor logging con-tinuously at 2 Hz. The latter was deployed at the bermcrest to record the number of swash overtopping events.All pressure sensors were deployed at or just below thesand surface. The pressure sensor data were only used totally the number of waves arriving at each elevation inorder to construct a wave runup height distribution (seebelow), so the difference in sampling rates between theinstruments is not problematic.

Intersection of the groundwater table with the beachface (water table exit point) was also measured in thesecond experiment. Four stilling wells were inserted intothe sand and periodically moved up and down the beachface with the tide in order to identify the elevation of themean water surface through the swash zone and into thebeach. Linear interpolation of the water surface betweenwells was used to obtain the water table exit on thebeach face. Measurements were made every 15 min.

2.3. Data processing

Wave runup exceedence statistics were obtained fromthe wave runup height distribution constructed from each15-min pressure record. The highest elevation on the beachthat was continuously inundated in each 15-min record,Zo,was determined first. The elevation of each pressure sensorZi relative to Zo was obtained from the survey data. Thenumbers of waves passing each pressure sensor, ni, and thetotal number of waves, N, were then counted. Wave runupheights are expected to be well-described by the Rayleighdistribution (Battjes, 1971; Nielsen and Hanslow, 1991), inwhich case, measurements of the number of waves trans-gressing each elevation plotted against elevation shouldfollow a straight line if the former is scaled as

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi−lnðni=NÞp

and the latter as (Zi−Zo) (Fig. 2). A total of 134wave runupheight distributions obtained over 8 separate days showedthat the Rayleigh distribution provides a good descriptionof wave runup at Avoca Beach, with correlation coeffi-cients (R2-values) from linear regression ranging from0.907 to 0.986. Given that the Rayleigh distribution is agood description of the wave runup on Avoca Beach, weassume that the following relations exist:

Z50% ¼ Zo þ 0:83Lz ð1Þ

Zsig ¼ Zo þ 1:42Lz ð2Þ

Z2% ¼ Zo þ 1:98Lz ð3Þ(e.g. Nielsen and Hanslow, 1991) where Lz is the verticalscale of the distribution, which equals the root mean square(rms) of the runup elevations, Z50% is the elevationexceeded by 50% of waves, Zsig is the significant runupelevation (i.e. exceeded by 33.3% of waves) and Z2% is theelevation exceeded by 2% of waves.

Fig. 4. Demonstration of the method used to determine the landwardlimit of wave–swash interaction (see text for explanation). Solid linewith crosses represents the tally of waves recorded at each pressuresensor and the dotted line with circles represents the tally of swashevents. The elevation at which these two lines converge corresponds tothe landward limit of wave–swash interaction.


Swash motion is not always simply the uprush andbackwash of a single wave on the beach face. If theincident wave period is shorter than the swash period,then a second wave may arrive before the swash cycle ofthe previous wave is completed, resulting in swash inter-action (e.g. Kemp, 1975; Hegge and Eliot, 1991). Anexample of one swash event experiencing overrunning bya subsequent wave is shown in Fig. 3. The swash event isidentif ied by the bed being ‘dry’ at the start and finish ofthe event and waves are identif ied as one or more sec-ondary peaks in the water depth. It was considered im-

Fig. 5. (a) Monthly survey data showing berm crest height (solid line) and bsignificant wave height, Hsig.

portant in this study to determine the landward limit ofinteracting swash, since flow accelerations, turbulencelevels, hydraulic jumps and the potential for enhancedsuspended sediment transport are all likely to be whereswash interactions are occurring. To quantify the land-ward limit of swash interactions, the total tally of waves(solid line) and the total tally of swash events (dotted line)recorded by each pressure sensor were plotted againstsensor elevation (Fig. 4). The point of convergence ofthese two lines is considered to be the maximum elevationof swash interaction (Zint). Seaward of this elevation thereare more waves than swash events so several waves mustoverrun the swash lens. Landward of this elevation thereis one swash event associated with each wave.

3. Experimental results

3.1. Typical berm dimensions at Avoca Beach

To place the detailed experimental data describedbelow into a broader context, monthly surveys (made atspring tide) of berm height and width fronting AvocaLagoon for the period July 2003 to August 2005 areshown together with the corresponding deepwater sig-nif icant wave height in Fig. 5. From a lagoon manage-ment viewpoint it is interesting to note that the maximumberm height at Avoca is largely constant across a widerange of offshore wave conditions (Fig. 5). Our visualimpression from monthly survey visits is that when ero-sion occurs the berm crest (swash limit) migrates land-ward as the beach face is cut back and the berm width isreduced. There is rarely a large reduction in the bermcrest height, however, since the back-beach slopes at less

erm width (dashed line) in front of Avoca lagoon. (b) Daily deepwater

Fig. 6. (a) Significant deepwater wave height, Hsig (solid line), and period Tsig (dashed line); (b) offshore wave direction; and (c) ocean tide levels forthe experiment period 14–20 November, 2004. The same parameters are repeated in panels (d) to (f ) for the experiment period 13–22 October, 2003.Tide levels are expressed in metres relative to the Australian Height Datum (AHD).


than 1° between the berm crest and the lagoon. Anymajor change in the maximum berm height that doesoccur is related to the opening (mechanical or natural)and subsequent closure of the lagoon entrance. Forexample, October–November 2004 and July 2005, bothof which coincide with artif icial openings (Fig. 5). Theseartificial openings are followed by rapid berm growth, asthe lower berm height allows large swash overtoppingvolumes (see Weir et al., in press). In summary, the bermcrest height at Avoca Lagoon is typically 2.8 to 3.0 mAHD except briefly during lagoon opening and sub-sequent closure events. The horizontal position of theberm crest (and beach face) is far more dynamic, mi-grating up to 25 m horizontally. There appear to be twomodes of berm response during periods of beach accre-tion: (1) vertical growth following opening of the lagoonentrance, and (2) horizontal growth during periods ofextended lagoon closure. Both of these modes aredocumented in the experimental data presented below.

Fig. 7. (a) Daily beach face prof iles surveyed at low tide over the period 15–consecutive beach profiles measured quarter-hourly, plotted as a function of ti2004, (d) 17 November, 2004, and (e) 18 November, 2004. (f) Color bar indipanels. The locations of Zo (thick solid line), Z50% (thin solid line), Z2% (daeffluent zone (hatched line) are also shown.

3.2. Berm Growth Mode 1: vertical growth (swashovertopping)

The mechanism for vertical berm growth was docu-mented during a f ield campaign that commenced 2weeks after an artif icial opening of Avoca Lagoon. Overthe course of the campaign deepwater signif icant waveheight ranged between 0.77 m and 1.95 m (Fig. 6a).Wave direction was dominantly from the southeast quad-rant, which is the direction of maximum exposure forAvoca Beach (Fig. 6b). Berm height at the start of thecampaign was 1.2 m AHD, which is substantially lowerthan the typical berm height at Avoca Beach and con-sistent with the recent opening of the lagoon (see Section3.1). Spring tides (Fig. 6c) and the lower berm heightduring this period resulted in frequent overtopping of theberm crest by swash.

Detailed measurements of beach face morphologyover 4 consecutive days (15–18November) during spring

18 November, 2004. Color mapping of bed elevation change betweenme and cross-shore distance; (b) 15 November, 2004, (c) 16 November,cating magnitude of bed elevation changes represented in the previoussh-dotted line), Zint (dashed line) and upper limit of the groundwater




tides showed a consistent pattern in berm developmentand profile response to wave forcing (Fig. 7). The prin-cipal feature of Berm Growth Mode 1 is a net accumu-lation of sediment on the upper beach face and berm crestat high tide. The largest net accumulation was immedi-ately seaward of the berm crest and resulted in vertical andhorizontal growth of the berm (Fig. 7a). There is alsosignificant deposition up to 15 m landward of the bermcrest. This mode of berm growth is strongly dependentupon swash overtopping, with larger amounts of over-topping resulting inmore rapid berm growth. For example,onNovember 15, the berm crest grew7.5 cmvertically and1.95 m horizontally over 10 h in response to 40% of swashevents surpassing the berm crest at high tide. In com-parison, on November 18, the berm crest only grew 3 cmvertically and 0.90m horizontally in response to only 10%of swash events overtopping the berm crest.

The main source of sediment during this mode of bermgrowth appears to be the lower half of the active swashzone and, thus, ultimately the inner surf zone. During theflooding tide on 15 November (07:30 to 10:30 in Fig. 7b)erosion occurred at the landward end of the surf zone andseaward end of the swash zone (i.e. immediately eitherside of Zo). Accretion occurred slightly seaward andeverywhere landward of Zint and Z50%, which follow eachother closely through most of the tide cycle. During therising tide the boundary between erosion in the lowerswash and accretion in the upper swash is abrupt. Duringthe falling tide such a boundary is less obvious (12:00 to16:00 in Fig. 7b), as indicated by mottled coloring in thefigure across the entire swash zone. The heightened de-gree of morphological variability indicated by the mottledcoloring may represent the passage across the swash zoneof small ridges up to 5 cm high with a period of severalminutes, as first noted by Sallenger and Richmond (1984)and frequently observed by the authors on steep beaches.Generally accretion occurred across most of the swashzone and erosion occurred in the inner surf zone. At hightide (10:30 to 12:00 in Fig. 7b) there is erosion in the innersurf zone and accretion across most of the swash zone aswell as over the berm crest. Note that at high tide Zint andZ50% diverge, due to a large number of swashes over-topping the berm crest. At all times bed elevation changeswere insignificant (<1 cm) landward of Z2%.

The pattern just described is generally repeated overthe next 3 days, although it does differ in detail. On the

Fig. 8. (a) Daily beach face profiles surveyed at low tide over the period 14–22003. Color mapping of bed elevation change between consecutive beach proshore distance; (b) 14 October, 2003, (c) 16 October, 2003, (d) 20 October, 20elevation changes represented in the previous panels. The line representationspoint and with the addition of Zsig (solid line with dots).

16 November the erosion/accretion boundary is strongeron the falling rather than the rising tide and follows thelocation of Zint over the entire tide cycle, whereas on the17 and 18 November the behavior is almost exactly thesame as the 15 November. There is a clear trend towardsthe 18 November of a reduced range in bed elevationchanges on the beach face and reduced accretion overthe berm crest. This is consistent with the reduction inswash overtopping mentioned previously.

In summary, Berm Growth Mode 1 involves erosionof the lower beach face and accretion of the upper beachface and berm crest. The erosion/accretion boundary onthe beach face is most marked during periods of risingand high tide when there is substantial swash over-topping. This is analogous with berm behavior at springtide reported by Hine (1979) on a sandy beach and byAustin and Masselink (2006) on a gravel beach. Thedifference here is that berm overtopping is not neces-sarily restricted to spring tides, due to the presence of alagoon entrance. The final outcome is a steepening of thebeach face gradient, a change in the profile shape towardsconcave and both vertical and horizontal growth of theberm. In the case documented here the gradient steepenedfrom 0.067 to 0.100, the berm crest increased in elevationby a total of 30 cm and grew horizontally seaward by atotal of 2.6 m over a 4-day period (8 tide cycles).

3.3. Berm Growth Mode 2: horizontal growth (no swashovertopping)

The mechanism for horizontal berm growth was docu-mented during an extended period of lagoon closure,when the elevation of the pre-existing berm crest was2.93 m AHD (close to the modal elevation). Deepwaterwave conditions varied substantially throughout the fieldcampaign. The largest deepwater significant wave heightof 3.48 m occurred at the beginning then decreased to aminimum of 0.62 m on the 18 October, followed by anincrease to 2.42 m on the 20 October (Fig. 6d). Waveswere mostly from the southeast quadrant (Fig. 6e). Al-though waves were large early in the campaign there wasno overtopping of the pre-existing berm crest, primarilybecause neap tides occurred during this period (Fig. 6f).

Daily measurements of the beach profile during thiscampaign indicated no significant change in the pre-existing berm elevation. Horizontal progradation of the

2 October, 2003, plus an additional profile surveyed on 28 November,files measured quarter-hourly, plotted as a function of time and cross-03, and (e) 22 October, 2003. (f ) Color bar indicating magnitude of bedare the same as those in Fig. 7, with the exception of the water table exit


beach face is clearly evident, however, through the devel-opment of a prominent lower or neap berm (Fig. 8a). Abeach profile surveyed approximately 1 month later atspring tide (28 November) shows that this lower bermappears to have migrated landward and accreted onto thepre-existing berm (Fig. 8a).

The principal feature of Berm Growth Mode 2 is a netaccumulation of sediment on the mid to upper beachface resulting in horizontal progradation of the beachface, but no vertical growth of the pre-existing berm.The details of this behavior are evident in Fig. 8b–e. Thedata coverage is not as comprehensive as that availablefrom the November 2004 experiment (Fig. 7), becauseof diff icult wave conditions in the inner surf zone andthe tide cycles not falling neatly within daylight hours.During the f looding tide on the 14 October erosionoccurred across the entire zone extending from Zo toZsig, i.e. across the entire lower two-thirds of the activeswash zone (07:30 to 10:30 in Fig. 8b). A relativelysmall amount of accretion occurred in the zone betweenZsig and Z2%. Landward of Z2% bed elevation changesare insignif icant (<1 cm). Although we do not haveprofile closure on the upper beach on this day, given therelatively minor amounts of change recorded in thisregion it is reasonable to conclude that the large amountof sediment eroded from the mid and lower swash zoneon the rising tide moved offshore. During the falling tidethe beach face recovered with accretion occurring acrossthe entire active swash zone (11:30 to 15:00 in Fig. 8b).The only possible source for this accreted sediment isthe inner surf. The development of the neap-berm wasinitiated on this day through the minor accretion thatpersisted during almost the entire tide cycle landward ofZsig. The total amount of net accretion cannot be deter-mined because the profile data are not closed at thelandward end in this case. This problem was rectified onsubsequent days.

The general pattern observed on the 14 October wasrepeated on the 16 October (Fig. 8c), although the rangeof bed elevation changes was reduced in the latter case,probably due to the 50% reduction in offshore waveheight over the 3 days (Fig. 6d). On the 20 October weonly have data for the rising tide (Fig. 8d), but the patterndiffers from the rising tides in the previous two panels.Accretion occurred across the region between the innersurf and Zint, erosion occurred across the zone betweenZint and Zsig, and further accretion occurred between Zsigand Z2%. Again, there were no signif icant bed elevationchanges landward of Z2%. This pattern is repeated on the22 October (Fig. 8e).

In summary, Berm Growth Mode 2 involves erosionof sediment from the lower swash zone and deposition

in the mid to upper swash zone to develop a neap bermbelow the principal berm. This is also consistent withberm behavior reported by Hine (1979) on a sandybeach and by Austin and Masselink (2006) on a gravelbeach. The final outcome is a steepening of the beachface, a change of the profile shape towards convex, andonly horizontal growth of the principal berm (wellbelow its crest). Sediment accumulation rates responsiblefor this profile change are significantly less than for BermGrowth Mode 1. In the case documented here the gradientsteepened from 0.097–0.133, the neap berm achieved amaximum thickness of only 40 cm and maximumhorizontal progradation seaward of only 2.1 m over a 9-day period (18 tide cycles).

4. Sediment transport shape functions and conceptualberm growth model

Sediment transport shape functions have previouslybeen used with some success in investigating beachmorphodynamics (e.g. Russell and Huntley, 1999;Masselink, 2003). These shape functions describe thesediment transport rate as a function of distance across thebeach profile, and have been calculated here to aid thedevelopment of a conceptual (and ultimately numerical)model for the morphodynamic behavior of berms duringaccretionary growth. The net cross-shore sediment trans-port rates at specific locations along the beach face profilewere calculated using the quarter-hourly beach elevationmeasurements and the mass conservation equation:

Qi ¼ Qi−1 þ 1−pð ÞDxDt

Zi−Zi−1ð Þ ð4Þ

where Qi is the sediment transport rate in (m3/m.s) at thecross-shore position i, Zi is the bed level at different timesteps, Δx is the cross-shore distance step, Δt is the timestep and p is the sediment porosity. Positive and negativevalues ofQi indicate onshore and offshore sediment trans-port, respectively. A total of 247 sediment transport shapefunctions were calculated from the available data sum-marized in Figs. 7 and 8, one for each quarter-hourly beachprofile.

For the purpose of developing the conceptual modelpresented here, the magnitudes associated with the shapefunctions are irrelevant, only the form of the shape func-tion is important. All 247 calculated sediment transportshape functions could be classified as one of three basicshapes, with one shape including subgroups. The basicshapes are represented by the curves shown in Fig. 9. All247 shape functions were assigned to one of the 3 groups(plus one subgroup). The position in the swash zone wasnormalized against the vertical extent of the runup

Fig. 9. The three types of sediment transport shape function that all 247measured shape functions could be classified as. Shape Function IIincludes two subtypes. The curves are ensemble-means for each groupand the vertical bars one standard deviation about the mean.


distribution corresponding to each shape function and thesediment transport rate was normalized against the maxi-mum for each shape function. The normalized shapefunctionswere then ensemble-averagedwithin eachgroup.This was done by first interpolating the value of the sedi-ment transport rate at successive increments of 0.1 of theswash height and then averaging the values for eachincrement across all functions in the group. The verticalbars in Fig. 9 indicate one standard deviation about theensemble-mean. The variability in the magnitudes is rea-sonably large and due at least in part to the fact thatcalculation of the ensemble-averaged transport rates in-volved interpolation between data points. Further discus-sion of the variability in magnitude of the transport rates ispresented in Section 5. Here we are most concerned withthe predominance of the 3 basic shapes. Shape I is char-acterized by a relatively large onshore sediment transportrate in the lower swash zone and a gradual decline to zeroseaward of the upper swash limit (Fig. 9a). In the case ofShape II onshore sediment transport takes place across theentire swash zone, including close to the upper swash limit,with Shape IIb characterized by substantially larger sedi-ment transport rates at the upper swash limit than Shape IIa(Fig. 9b and c). The sediment transport rate does not drop

to zero at the upper swash limit, because Shape II occursduring swash overtopping.When swash overtops the bermit can carry considerable sedimentwithout climbing higherin elevation, since the beach becomes close to horizontallandward of the berm crest. While Shape IIa and IIb arequalitatively similar there is a considerable difference inthe relative magnitude of the sediment transport rate at thetop of the beach −20% versus 60% of the peak transportrate. This has a profound effect on the rate of vertical bermgrowth, and it will be seen below that the two shapes alsocorrespond to different berm growthmodes, thus justifyingtheir inclusion as individual subtypes. Shape III is char-acterized by offshore sediment transport in the lower tomid-swash zone and a narrow region of onshore transportin themid-to upper swash zone that diminishes to zerowellseaward of the upper swash limit (Fig. 9d).

The columns on the right hand side of Figs. 7 and 8indicate when each shape function occurs over themonitored tide cycles. During Berm Growth Mode 1(vertical growth with swash overtopping), Shape Func-tion I occurred on the rising and falling tides and ShapeFunction II occurred at high tide (Fig. 7). Shape FunctionIII rarely occurred. In contrast, during Berm GrowthMode 2 (horizontal growth with no swash overtopping),Shape Function I generally occurred on the falling tidesand Shape Function III on the rising tides (Fig. 8). ShapeFunction II was absent, consistent with the absence ofswash overtopping the berm.

Fig. 10 depicts a conceptual model for the growth ofberms fronting coastal lagoons on energetic, relativelysteep, intermediate-type beaches (see Wright and Short(1984) for a full description of this beach type). In eachpanel the dashed profile represents the existing profilefrom the previous stage and the solid profile representsthe new profile developed in the current stage of the cycle.Following a lagoon opening (or simply a significanterosional event in the absence of a lagoon) the beach faceprofile is characterized by a lower than typical beach facegradient and berm crest height (Fig. 10a).On some beachesthe berm form (i.e. steep beach face, crest and subhor-izontal back-beach) may disappear entirely, particularly onsediment starved beaches backed by cliffs or seawalls. Onthe relatively steep and wide beaches characteristic of thecentral New South Wales coast, however, the beach faceprofile maintains a crest and gently sloping back-beacheven during considerable beach cut (Section 3.1).

As wave conditions become conducive to onshoresediment transport following the period of beach cut,berm growth occurs in both the vertical and horizontaldirection (Fig. 10b). Sediment transport Shape FunctionI operates during the rising and falling tide, deliveringsediment from the inner surf and lower swash zones to

Fig. 10. Diagram showing a conceptual model for berm growth following a lagoon breakout event (or a significant erosional event in the absence of alagoon) on steep intermediate-type beaches with an energetic wave climate. (a) Stage 1, the beach face profile is characterized by a lower than typicalbeach face gradient and berm crest height; (b) Stage 2, rapid vertical growth of the berm crest during swash overtopping, with additional horizontalprogradation of the berm; (c) Stage 3, slower horizontal progradation of the principal berm through accretion of a lower neap berm when swashovertopping ceases; (d) Stage 4, migration of the neap berm onto the principal berm on the following spring tide.


higher up the beach face, resulting in horizontal prograda-tion. Shape Function II operates at high tide when swashovertopping of the bermdelivers this sediment landward ofthe berm crest, resulting in vertical accretion. Shape Func-tion IIb occurs when overtopping is substantial and IIawhen it is limited. This stage continues until the berm crestheight has increased sufficiently or the high tide level hasdropped sufficiently towards neaps for swash overtoppingof the berm crest to cease.

Once swash overtopping of the berm ceases the nextstage begins where only horizontal growth occurs(Fig. 10c). Shape Function III occurs on the rising tideswith offshore transport in the lower swash zone causingsteepening of the profile and minor onshore transport in themid-upper swash zone contributing to the development of aneap berm. Shape Function I occurs on the falling tidesdelivering sediment from the inner surf zone to the lowerbeach and from the lower beach to the neap berm. No


change in the elevation or horizontal location of theprincipal berm occurs during this stage.

The neap berm ultimately migrates upwards as swashaction is translated higher up the beach face with the suc-cessively more elevated high tides approaching springs.During spring tides Shape Function III operates on therising tide, eroding the neap berm and depositing materialhigher up the beach (Fig. 10d). Shape Function II operatesat high tide when swash overtopping deposits this materialonto the berm crest to produce vertical growth. Shapefunction I operates on the falling tide, so there is no sedi-ment lost seaward. At any stage in the described cycle, thesituation may revert to Fig. 10a, thus re-initiating the cycle.A complete cycle through all four stages is only possiblegiven sufficient time between lagoon openings (or sig-nificant erosion events in the absence of a lagoon). For theenergetic Avoca Beach sufficient time is one spring-neaptide cycle. Once the berm is re-established to its maximumcrest height then only horizontal progradation of the beachcontinues, by cycling between stages 3 and 4 (with theabsence of significant overtopping at spring tides).

This conceptual model represents intra-tidal processesoccurring over the rising versus the falling limbs of the tideand stage changes occurring over the growth of the bermthat occur on the timescale of a neap-spring tide cycle atAvoca Beach. The model is based on 310 beach profilesmeasured quarter-hourly over both the rising and fallinglimbs of the tide, corresponding wave runup height dis-tributions for each beach profile, and a sediment transportshape function determined from the bed elevation changesbetween each consecutive beach profile. These concurrentdata were obtained from eight separate semi-diurnal tidecycles spread over the neap-spring cycle. The processesand stage changes represented in the model are thereforesubstantiated at the level of the data.

5. Discussion

This study has documented berm morphodynamics atAvoca Beach on the central coast of New South Wales,Australia. The results of this study indicate that the bermheight on this intermediate-type beach can be remark-ably constant. This is largely due to (1) the broad, nearlyhorizontal back-beach zone that accommodates extensivebeach cut without any change in the maximum elevationon the beach, and (2) the rapid re-establishment of theberm crest height when rare lagoon openings do occur(usually within one spring-neap tide cycle). This hassignificant implications for the management of this andother intermittently closed and open lagoon entrances(ICOLs), which are characteristic of New South Walesand many other wave-dominated coasts of the world.

Management plans for these systems usually must balanceconflicting outcomes, for example, the desire tomaintain anopen entrance for flood mitigation and improved flushingand the desire to maintain natural cycling of the entrancecondition (i.e. alternating periods of opening and closure) tosustain existing ecosystems.

Avoca Beach is a relatively short, pocket beach withlimited capacity for longshore sediment transport. Theseconditions contrast with those occurring on the beachstudied by Hine (1979), where longshore transport wasidentified as the controlling parameter in determining bermgrowth rates. Our data demonstrate that, following a nat-ural or artificial lagoon opening, subsequent closure can beachieved solely through cross-shore transport of sedimentand re-establishment of the berm to its modal height,usually within one spring-neap tide cycle. Stages in thisclosure process have been described here in terms of sedi-ment transport shape functions. A logical next step is toincorporate these shape functions into a numerical mod-eling framework to make predictions on rates of entranceclosure for different initial conditions. This next step is nottrivial. The general form of the shape functions is wellconstrained to 3 basic types at least during berm growth,but the actual magnitudes of the sediment transport ratesrepresented by these basic types vary widely. The magni-tudes related to each shape function are controlled in part bythe wave runup distribution, and given the random waveconditions driving runup on a natural beach the variabilityin magnitude of the shape functions is perhaps not sur-prising. The complexity inherent in the strong Markovianbehavior characteristic of beach systems will no doubt alsobe a factor (see Sonu and James, 1973).

It is important to note that although the transport shapefunctions are non-zero at the seaward boundary that doesnot necessarily imply the lower beach face will be con-tinuously eroded. Sediment delivery from the inner surfzone can partially or completely offset this. The highdegree of bed mobility in the inner surf zone of inter-mediate beach types like Avoca is therefore also expectedto contribute variability to the magnitudes of the transportshape functions. A detailed process description for sedi-ment delivery from the inner surf to the swash zone,suitable for model development, is beyond the currentstate of the art. Possible candidate processes includevelocity skewness beneath bores, boundary-layer stream-ing, sediment advection and long wave effects. Develop-ing the conceptual model in Fig. 10 into a predictive,quantitative model is, therefore, work in progress.

During some of the tide cycles monitored in this studythere is an asymmetry in morphological behavior abouthigh tide, i.e. for a given tidal elevation the morphologybehaves differently on the rising versus the falling limb of


the tide. This is particularly noticeable in Figs. 7d, e, 8band c where erosion of the swash zone is predominant onthe rising tide and deposition on the falling tide. Thismorphodynamic asymmetry corresponds with a similarasymmetry with respect to the runup distribution. In all ofthe cases just mentioned, for a given tidal level Z50% sitsrelatively higher up the beach (i.e. closer to Z2%) on therising compared to the falling limb of the tide. Thiseffectively means that more waves penetrate deeper intothe swash zone on the rising limb of the tide, whichprobably leads to greater swash interaction, enhancedturbulence and sediment suspension. The reason whymore waves penetrate the swash zone on the rising versusthe falling tide remains an open question.

Based on Grant's (1948) hypothesis for beach profilebehavior due to swash infiltration and its effect on sedimenttransport competency (Section 1), we might expect that theerosion/accretion boundary would migrate in concert withthe water table exit point. Indeed, Austin and Masselink(2006) observed this to be the case on their gravel beach.On the 3 occasions thatwe tracked thewater table exit pointacross the beach face at Avoca Beach the results weremixed (Fig. 7c to e). On the rising tides of the 16 and 17November the water table exit point coincided with theboundary as expected. On the falling tides of these 2 days,however, both zones of erosion and accretion existed in thegroundwater eff luent zone (seaward of the water table exitpoint). Moreover, erosion occurred landward of the watertable exit point at high tide on the 17 November, which isalso contrary to Grant's hypothesis. On the 18 Novemberthe water table exit point does not coincide with theboundary between beach face erosion/accretion at all.

Despite widespread acceptance of Grant's hypoth-esis, our data from a sandy beach are inconsistent withits predictions over a wide range of wave conditions(0.7–2.0 m offshore signif icant wave height). Similardata presented by Holland and Puleo (2001) also showbeach profile behavior on a sandy beach that is contraryto Grant's hypothesis. On many occasions the boundarybetween swash erosion/accretion in our data correspondedmore closely to the landward limit of swash interactionsZint (Figs. 7c, d, 8b–e), consistent with results reported byHolland and Puleo (2001). Kemp (1975) was the first topropose that wave–swash interactions might be importantin determining the net direction of sediment transport andprofile change. Where wave–swash interaction occurs onsandy beaches there will be increased sediment entrain-ment, due to greater turbulence and the frequent occur-rence of hydraulic jumps (e.g. Butt and Russell, 2005).This suspended sediment is swept landward when ShapeFunctions I and II are active and seaward when ShapeFunction III is active. The fact that gravel is less likely to be

raised into suspension may explain why the data reportedby Austin and Masselink (2006) concur with Grant'shypothesis. The detailed hydrodynamics determining thenet transport direction in the swash interaction zone stillneed to be established before quantitative predictions ofprofile behavior can be achieved.

6. Conclusions

On relatively steep, intermediate-type beaches with awide back-beach area, the beach can experience consid-erable cut and f lattening of the gradient without anysignificant change in elevation at the top of the beach face.That is to say, a berm-like profile persists during periodsof beach cut, due to the broad approximately horizontalback-beach area. A significant reduction in berm heightdoes occur on these beaches when the beach is cut nat-urally or artif icially by an open lagoon entrance, usuallyduring periods of prolonged heavy rainfall. When thelagoon has a small tidal prism and the beach is exposed toan energetic wave climate, then the lagoon entrance rap-idly closes off through vertical accretion of the bermfronting the lagoon. Depending on the phase of the neap-spring tide cycle closure can be achieved in a couple ofdays and almost always within one neap-spring tide cycle.As a consequence Avoca Lagoon, and others like it on theNew SouthWales coast, are intermittently open to the seabut typically closed for most of the time.

Two modes of berm growth were identified: (a) rapidvertical growth of the berm crest (associated with somehorizontal progradation), and (b) slower horizontal pro-gradation through the formation of a lower neap berm onthe face of the principal berm. The primary factor deter-mining which mode of berm growth occurred was thepresence or absence of swash overtopping of the pre-existing berm at the time of sediment delivery to the beachface. This depends on the prevailing phase of the spring-neap tide cycle, the wave runup height (and indirectlyoffshorewave conditions) and the height of the pre-existingberm. Sediment transport shape functions were calculatedand could be classified into 3 basic shapes. The two bermgrowth modes are clearly distinguished and characterizedby unique combinations of these shape functions.

A conceptual model for berm growth is presented(based on the transport shape functions) that is con-sidered to be generally applicable on steep, microtidal,intermediate-type beaches exposed to an energetic waveclimate. Following Stage 1, erosion of the berm, a com-plete accretionary path through the model involves:(Stage 2) rapid vertical growth of the berm crest duringswash overtopping with additional horizontal prograda-tion of the berm, particularly during spring tides; (Stage 3)


slower horizontal progradation of the principal bermthrough accretion of a lower neap berm when swashovertopping ceases; and (Stage 4) migration of the neapberm up onto the principal berm on the following springtide. During extended periods between erosional eventsthe beach face probably cycles back and forth betweenStages 3 and 4, but producing only horizontal prograda-tion once the berm reaches its maximum possible crestelevation at springs. The sediment transport shape func-tions required to quantitatively model this berm behaviorhave been defined.While the model presented is based onmeasurements of berm behavior fronting a coastal lagoon,it is expected to be also applicable to themore general caseof beaches without a lagoon.

Acknowledgments

Offshorewave data were collected and provided by theManly Hydraulics Laboratory. Permission from the De-partment of Infrastructure, Planning and Natural Re-sources for the use of these data is appreciated. AdrienneMoseley provided the groundwater exit point measure-ments. The authors greatly appreciate the assistance ofDave Mitchell, Andrew Aouad, Adrienne Moseley (Uni-versity of Sydney), Diane Horn (Birkbeck College) andJose Alsina (Universitat Politècnica de Catalunya) inconducting the field experiments. The paper benefitedfrom comments by Gerd Masselink and an anonymousreviewer.

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Documents

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