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Marine Geology 299–302 (2012) 33–42
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Marine Geology
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An analysis of the cross-shore beach morphodynamics of a sandy and a compositegravel beach
Harshinie Karunarathna a,⁎, Jose M. Horrillo-Caraballo d, Roshanka Ranasinghe b,c,Andrew D. Short e, Dominic E. Reeve f
a School of Engineering, University of Glasgow, Glasgow, G12 8LT, UKb Department of Civil Engineering and Geosciences, Delft University of Technology, PO Box 5048, 2600 GA Delft, The Netherlandsc Department of Water Engineering, UNESCO-IHE, PO Box 3015, 2601 DA Delft, The Netherlandsd Coastal Engineering Research Group, School of Marine Science and Engineering, University of Plymouth, Plymouth, PL4 8AA, UKe School of Geosciences, University of Sydney, NSW 2006, Australiaf College of Engineering, Swansea University, Singleton Park, Swansea, SW2 8PP, UK
⁎ Corresponding author. Tel.: +44 141 330 5209; faxE-mail addresses: [email protected]
[email protected] (J.M. [email protected] (R. Ranasinghe), andrew.(A.D. Short), [email protected] (D.E. Reeve).
0025-3227/$ – see front matter © 2012 Elsevier B.V. Alldoi:10.1016/j.margeo.2011.12.011
a b s t r a c t
a r t i c l e i n f oArticle history:Received 26 May 2011Received in revised form 12 December 2011Accepted 26 December 2011Available online 21 January 2012
Communicated by J.T. Wells
Keywords:sand and composite sand–gravel beachescross-shore beach profilebeach morphodynamicsOrthogonal Eigenfunction AnalysisCanonical Correlation Analysis
In this paper, beach profile surveys acquired over more than a decade at a sandy beach (Narrabeen Beach,New South Wales, Australia) and a composite sand–gravel beach (Milford-on-Sea, Christchurch Bay, UK)are analysed to compare and contrast cross-shore morphodynamics of the two beach types. The differentbehavioural characteristics of the two beach types at decadal, inter-annual and intra-annual time scales areinvestigated. Comparisons of beach profiles with Dean's equilibrium profile and Vellinga's erosion profileshow that the Dean's profile satisfactorily represents the time mean profiles of both beach types. Statisticaland Empirical Orthogonal Function (EOF) analyses confirm the generally accepted model that the inter-tidal zone is the most morphodynamically active region on a sandy beach whereas the swash zone is themost dynamic region on a mixed sand–gravel beach. The results also imply that during storms compositesand–gravel beaches may become unstable due to cutback of the upper beach while sandy beaches aremore likely to be unstable as a result of beach lowering due to sediment transport from the inter-tidalzone to the sub-tidal zone during storms. EOF results also show that Milford-on-Sea beach is in a state ofsteady recession while the Narrabeen Beach shows a cyclic erosion–accretion variability. A multivariate tech-nique (Canonical Correlation Analysis, CCA) shows that on the composite beach a strong correlation existsbetween incident wave steepness and profile response, which could be attributed to the unsaturated surfzone, whereas on the sandy beach any correlation is much less evident.
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
Composite sand–gravel beaches are composed of a gravel inter tosupra-tidal swash zone and sand lower to sub-tidal surf zone and area common feature along many higher latitude coastlines around theworld. The importance of such beaches as a part of natural coastalsystems and as a form of coastal defence is well recognised in the lit-erature (Carr, 1983; Bradbury and Powell, 1992). There are a growingnumber of reports and studies of their degradation, and in some in-stances severe cutback (e.g. Chadwick et al., 2005) and breaching(Carter and Orford, 1993).
Morphological evolution of a beach is characterised by cross-shoreand long-shore morphodynamic changes. Long-shore coastal evolution
: +44 141 330 4557.(H. Karunarathna),raballo),[email protected]
rights reserved.
is mainly characterised by varying coastal forms such as changingshoreline position, beach rotation and development of rhythmic fea-tures. Cross-shore beach change is associated with changes to theshape of cross-shore profile in time and space. Our focus here is themorphodynamic changes in the cross-shore direction.
Changes in cross-shore beach profiles are controlled by many fac-tors including waves, tidal flows and sediment characteristics. How-ever, these changes can also depend on the beach type. It has beenreported that the cross-shore variability of composite sand–gravelbeaches is distinctly different to that of sand beaches (Larson andKraus, 1994; Pontee et al., 2004). It is also different to the otherforms of coarse-grain beaches (mixed beaches and pure gravel bea-ches) in terms of profile shape, profile response to hydrodynamicforcing, sediment characteristics and sediment distribution (Ponteeet al., 2004). The composition and cross-shore distribution of beachsediment plays a major role in determining the morphodynamicresponse of a beach profile to environmental forcing (Pontee et al.,2004). Sand beaches have gentler cross-shore slopes and wide butshallow surf and swash zones while composite sand–gravel beaches
34 H. Karunarathna et al. / Marine Geology 299–302 (2012) 33–42
in contrast have a coarse steep swash zone that grades abruptly into alow gradient sandy lower inter-tidal to sub-tidal (Carter and Orford,1993; Jennings and Shulmeister, 2002). Gravel has a tendency fornet onshore transport due to the more energetic wave uprush fol-lowed by less energetic back-wash (Carr, 1983; Carter and Orford,1984; Pedrozo-Acuña et al., 2007). As a result, sediment sortingtakes place across the profile where gravel accumulates at thesupra-tidal and upper inter-tidal region of the profile while sand ac-cumulates at the lower inter-tidal and sub-tidal regions thus formingcomposite beaches (McLean and Kirk, 1969). Due to the presence of asteep gravel upper shoreface and a gentler sand lower beach, com-posite beaches show characteristics of both reflective and dissipativebeaches at different times of a tidal cycle.
Morphodynamic evolution of cross-shore beach profiles take placeat a range of time scales: millennial scale evolution as a result ofQuaternary sea level changes; long term variability in the time scalesof several decades to a century associated with climate changeimpacts; medium-term evolution in the time scales of several yearsto a decade, associated with engineering intervention and prevailingsedimentary processes; and short term variability in the time scales ofdays to a year as a result of weather conditions (storms) and seasonalchanges.
Millennial and long term adjustment of beach changes associatedwith Quaternary sea level changes and climate change impacts havebeen extensively studied by various researchers (Carter et al., 1989;Carter and Orford, 1993). In an attempt to understand medium termbeach change, a number of studies have been reported discussingthe relationship between medium term changes to incident wave cli-mate and beach response (e.g. Horrillo-Caraballo and Reeve, 2008;Ranasinghe et al., 2004; Larson et al., 2003, and many others).
Cross-shore variability of beach systems has been studied by var-ious researchers in the past. Early studies on beach profiles dateback to the 1950's when Brunn (1954)) developed the concept ofan equilibrium beach profile shape on sandy beaches and found asimple empirical relationship between cross-shore profile depth anddistance measured offshore from the shoreline. Dean (1977) provid-ed the physical argument for the shape of Brunn's profile. Larson etal. (1999) provided physical reasoning for a linearly sloping upperbeach but this result was independent of grain size. Later Dean(1991) included gravity effects to the Bruun's profile to get the linearupper beach and also retain the dependence on grain size.
Swart (1974) and Sunamura and Horikawa (1974) examinedcharacteristics of beach profiles through laboratory investigationsand identified erosive and accretive profiles, relating profile geometryto incident wave conditions and sediment characteristics. Vellinga(1983, 1984) developed a relationship between cross-shore distanceand profile depth for erosive beach profiles, which was a function ofgrain size.
There were several attempts to understand cross-shore morpho-dynamic variability through statistical analysis of waves and beachprofiles. Larson and Kraus (1994) used Empirical Orthogonal Eigen-function Analysis (EOF) to examine spatial and temporal variabilityof alongshore bars at Duck, North Carolina. They observed that aver-age profile elevation change is symmetric around the mean sea leveland that typical storms transported sand to nearshore. Larson et al.(2000) used a large number of beach profiles at Duck and related pro-file evolution to incident waves using Canonical Correlation Analysis(CCA). They found a strong correlation between profile shape vari-ability and nerashore waves. Horrillo-Caraballo and Reeve (2010) ex-tended this correlation to predict future beach profiles and foundgood agreement between measured and predicted profiles.
Research on coarse grain beaches is scarce, with existing studieseither limited to geological time scales (Kirk, 1980; Carter andOrford, 1984; Carter, 1986) or short-term scales (Jennings andShulmeister, 2002; Pontee et al., 2004; Ivamy and Kench, 2006; Ruizde Alegria-Arzaburu et al., 2010; Masselink et al., 2010). Besides,
these studies were done on either pure gravel or mixed sand–gravelbeaches. Composite sand–gravel beaches differ significantly frompure gravel or mixed sand–gravel beaches where sand and gravelare spatially separated in their cross-shore profile (Pontee et al.,2004). Morphodynamic variability of composite sand–gravel beachesat a full range of time scales is not well understood.
Understanding the response of a composite sand–gravel beach tomorphodynamic drivers at various time scales is extremely impor-tant for developing methodologies to predict their behaviour,which is essential to inform effective management decisions. In theabsence of systematic investigations and with limited available mor-phodynamic process knowledge, the appropriate methodologies donot yet exist.
This study focuses on comparing and contrasting cross-shore mor-phodynamic variability of a composite sand–gravel beach with acharacteristic sandy beach, at a range of time scales, using historicmeasurements of beach profiles and wave data. The aim is to system-atically investigate the similarities and differences of the two beachesin detail and establish their morphodynamic response characteristics.The outcome of the research will contribute to better understandingof morphodynamic behaviour of composite beaches.
2. Field sites and historic data
The beaches considered here are the composite sand–gravelbeach, Milford-on-Sea, located in Christchurch Bay, United Kingdom(Fig. 1) and the sandy Narrabeen Beach, located in New SouthWales (NSW), Australia (Fig. 2). Both sites have been extensivelymonitored over several decades and therefore, rich in cross-shoreprofile surveys and wave measurements.
2.1. Milford-on-Sea beach
Milford-on-Sea is a composite sand–gravel beach that forms a partof the Christchurch Bay beach system facing the English Channel, UK.The beach extends about 3 km to the west from the Hurst Castle Spit(see Fig. 1). It is narrowand steep at thewestern side andhas a landwardmargin of receding cliffs, which becomes wide and less steep at theeastern end.
The Milford-on-Sea beach has a steep upper beach face with a gra-dient between 1:5 and 1:7 and a moderate inter-tidal beach with agradient between 1:10 and 1:20. The gentler sub-tidal beach is char-acterised by highly mobile and segmented multiple alongshore bars.Cross-shore gradients on the western part of Milford-on-Sea beachare significantly steeper than those on the eastern part. The sedimentgrain size at Milford-on-Sea beach varies significantly along the crossshore profile. Coarse shingles and pebbles with a median grain diam-eter (D50) around 16 mm dominate the upper beach. A sand–gravelmix which has D50-gravel=10 mm and D50-sand=1 mm with only62% sand fraction, dominates the upper inter-tidal areas. (Martìn-Grandes et al., 2009). No quantitative measurement on sedimentsizes at the lower inter-tidal area is available but visual inspectionshows sediment is predominantly sand. Sediment grain sizes on thewestern beach are slightly coarser than those on the eastern end,which contributes to the alongshore variation of the beach slope.Small scale beach nourishment had taken place between 1996 and1999, to stabilise the Milford-on-Sea beach.
Christchurch Bay receives semi-diurnal tides with a moderatemean spring tidal range of 2.0 m OD, reducing to 0.8 m OD duringneap tidal cycle. Mean high water spring (MHWS), mean low waterspring (MLWS) and mean water level (MWL) are 0.87 m, −1.13 mand 0.14 m above OD. Tidal currents as high as 3.0 m/s are observedin close proximity to the Milford-on-Sea beach (SCOPAC, 2003).Waves are incident predominantly from the SSW direction with occa-sional SSE waves. Waves at the eastern end of Christchurch Bay aremore energetic than those incident on the western end due to the
b
Christchurch Bay 5f00107
Milford-on-Sea
Wave recorder
a
Fig. 1. (a) Milford-on-Sea beach and its location in the UK and (b) a view of the beach and a typical cross shore profile.
a
b
Fig. 2. (a) Narrabeen Beach and its location in New South Wales, Australia (Callaghan et al., 2008) and (b) a view of the beach and a typical cross shore profile.
35H. Karunarathna et al. / Marine Geology 299–302 (2012) 33–42
-4.0
-2.0
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2.0
4.0
6.0
0.0 10.0 20.0 30.0 40.0 50.0 60.0
Cross-shore Distance (m)
Prof
ile E
leva
tion
(m)
Fig. 4.Measured cross-shore beach profiles at transect 5f00107 at Milford-on-Sea from1987 to 2005. Profiles extend from the top of the dune to the mean low water level.
36 H. Karunarathna et al. / Marine Geology 299–302 (2012) 33–42
sheltering effect of Hengistbury Head. SCOPAC (2003) quote typical(1 year return period) and extreme (1 in 100 year) significant waveheights for Milford-on-Sea as 2.5 m and 3.4 m respectively. Fig. 3shows near-shore significant wave height measured at a depth of12 m offshore of the Christchurch Bay Beach from 1986 to 1994.The wave climate is seasonal with calmer summer months (March–September) and stormy winter months (October–February).
Beach profiles have been surveyed at 45 cross-shore beach tran-sects along Christchurch Bay. Inter-tidal beach was measured usingRTK-GPS, using the UK South-East Regional Coastal MonitoringProgramme's ground control network. This is tied into OrdnanceSurvey (OS) Active Network in the UK. Measurements along the pro-file are deemed accurate to ±30 mm (vertical and horizontal). GPSwas used for all profiles from 1994. Prior to that, profiles were mea-sured by line and level from a fixed marker at the back of the beach(the markers were tied into OS by theodolite height transfer). Allheights are relative to Ordnance Datum Newlyn (ODN), the standardUK reference level. The zero chainage position is a fixed bench marksome distance from the back of the beach beyond the area whichmight erode in the next 100 years. All surveys use this chainage aszero, so the profiles can be overlain for comparison. Earlier line andlevel survey data was corrected to this start of line position.
Surveys at cross-shore beach transect 5f00107, (see Fig. 1), wherenet long-shore transport is minimal (SCOPAC, 2003), were selectedfor the analysis here. There are 49 profile surveys in total, measuredbetween 1987 and 2005, are available at this transect with an averageof 3 surveys per year. The length of profile measured varied from sur-vey to survey, but always went out at least to MLWS. Thus, all profileswere truncated aroundMLWS to provide a consistent basis for analysis.The shoreline position is defined as the point of intersection betweenthe cross-shore profile and the Mean Water Level (MWL) (Fig. 4).
Milford-on-Sea beach is subjected to typical winter–summer waveconditions approaching from the English Channel. As a result, beachvariability during winter months is considerably higher than thatduring the summer months where few metres of beach lowering isobserved. Overall morphodynamics of the Milford-on-Sea beach isdetermined by its swash dominance.
2.2. Narrabeen Beach
Narrabeen is a wave-dominated embayed beach located 20 kmnorth of Sydney, in NSW, Australia (Short and Wright, 1981). Thebeach that faces east into the Tasman Sea, is 3.6 km long and boundedby two headlands, Narrabeen Head to the north and Long Reef Pointto the south. It is composed of medium to fine quartz and carbonatesands with D50=0.3–0.4 mm and has a relatively steep upper beachand a gentler lower beach in the sub-tidal region.
As a part of a coastal monitoring programme, beach profiles at fivecross-shore locations along the Narrabeen Beach were regularly mea-sured first at bi-weekly intervals and then, at monthly intervals since1976, by the Coastal Studies Unit, University of Sydney. Surveys were
0
1
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4
29/03/86 11/08/87 23/12/88 07/05/90 19/09/91 31/01/93 15/06/94Date
Wav
e H
eigh
t (m
)
Fig. 3. Nearshore wave climate at Christchurch Bay. Waves were measured using awave rider buoy deployed at 12 m water depth.
undertaken at low tide and profiles were recorded at 10 m cross-shore intervals from a fixed bench mark at the landward limit of theactive beach at 10 m elevation. Hourly non-directional (1976–1992)and directional (1992–2005) wave data were also measured at an off-shore wave buoy located at the Long Reef Point, at a depth of 80 m.Cross-shore beach profile surveys carried out at Profile 4 (Fig. 2),which is situated in the central part of the Narrabeen Beach, is usedfor the analysis presented herein. Profile 4 was selected for this anal-ysis as it is the least likely location to be affected by the cyclic beachrotation phenomenon that operates at Narrabeen Beach (Short andTrembanis, 2004; Ranasinghe et al., 2004). Cross-shore profile surveysat Profile 4 from1976 to 1992 are shown in Fig. 5. Shoreline position islocated at MWL.
Narrabeen Beach is exposed to highly variable, moderate- to high-energy wind waves superimposed on long period, moderate- to high-energy south-easterly swell waves (Short and Wright, 1981). Wavesare derived from three cyclonic sources: mid-latitude cyclones thatpass across the southern Tasman Sea all-year-round, generatingsouth-easterly swell; extra-tropical cyclones off NSW coast generat-ing east and south-easterly waves peaking between May and August;and tropical cyclones that generate moderate to high north-easterlyand easterly swell during February and March. In addition, summer(December to March) sea breeze generates low to moderate north-easterly seas. 20% of the waves are found to exceed 2 m. Mean signif-icant wave height and peak period in the study area are 1.6 m and10 sec respectively (Short and Wright, 1981; Short and Trenaman,1992). On average, Narrabeen Beach, is subjected to 12 storms peryear (based on the local definition that Hs>3 m lasting more than1 h represents a storm). Fig. 6 shows typical offshore wave climatemeasured at the wave buoy at Long-reef.
The beach experiences micro-tidal, semi-diurnal tides with meanspring tidal range of 1.6 m and neap tidal range of 1.2 m. MHWSand MLWS are 0.9 m and −0.7 m above Australian Height Datum(AHD) respectively. The effect of tides on the morphology of theNarrabeen Beach is considerably less than waves (Short, 1985; Shortand Trembanis, 2004).
-6.0
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0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0Cross-shore Distance (m)
Prof
ile E
leva
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(m)
Fig. 5. Historic cross-shore profile survey data at Profile 4 at Narrabean Beach, NSW,Australia. Profiles have been measured from 10 m elevation above shoreline.
0
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6
8
28/08/76 28/08/77 28/08/78 28/08/79 27/08/80 27/08/81 27/08/82
Date
H (
m)
Fig. 6. Measured wave height time series at a water depth of 80 m offshore of NarrabeenBeach, NSW, Australia. Waves were measured using a non-directional wave rider buoy.
-2.0
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10 20 30 40 50 60
h (m
)h
(m)
Mean profile
Dean (1991)
Vellinga(1983)
MHWS
MLWS
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8.0
12.0
0 20 40 60 80 100 120 140 160x (m)
x (m)
Mean profile
Dean (1991)
Vellinga (1983)
MHWS
MLWS
Fig. 7. Comparison of Mean beach profile with Dean's equilibrium beach profile (Dean,1991) and Vellinga's erosion profile (Vellinga, 1983, 1984). Top panel—Milford-on-Sea,bottom panel—Narrabeen Beach.
37H. Karunarathna et al. / Marine Geology 299–302 (2012) 33–42
Due to the prevalence of moderate to high wave energy conditionsand the exposed nature of the beach, the morphodynamic response ofNarrabeen Beach is highly variable and extremely rapid where ero-sion and accretion can take place any time of the year. Accordingly,cross-shore beach profile shape varies rapidly with time (Wrightand Short, 1984; Ranasinghe et al., 2004).
3. Analysis and discussion of cross-shore beach variability
3.1. Equilibrium profile
In order to assess the long-term cross-shore morphodynamic var-iability of Milford-on-Sea and Narrabeen Beach and compare and con-trast long-term beach profile shape and its association with beachsediment properties, the time-mean beach profiles at both siteswere first computed using available historic cross-shore profile sur-veys at Profile 5f00107 (Milford-on-Sea) and Profile 4 (NarrabeenBeach). The mean profiles were then compared with Dean's (1991)equilibrium profile and Vellinga's (1983) erosion profile.
D50 for Milford-on-Sea was taken as 10 mm (Martìn-Grandeset al., 2009). D50 for Narrabeen Beach was taken as 0.35 mm (Shortand Trembanis, 2004). The depth of the equilibrium profile is calcu-lated from the mean high water level. The beach profile shape param-eter A in the Dean model is determined from Moore's (1982) curvefor given sediment sizes. The resulting Dean's equilibrium profilesand Vellinga's erosion profile for Milford-on Sea (profile 5f00107)and Narrabeen Beach (Profile 4) are shown in Fig. 7. Both profilescommence from the MHWS.
At Narrabeen Beach, the mean profile is in good agreement withthe Dean's equilibrium profile, with less than 5% root mean squareerror. This could be expected as Narrabeen Beach consists mostly ofuniformly distributed sediment and is similar in type to the beachesused to derive Dean's equilibrium profile. Vellinga's profile agreeswell with the mean profile in the upper inter-tidal region but overes-timates the lower inter-tidal region. This may partly be attributed tothe slightly steeper frequent storm waves (Hs/Ls~0.042) prevailing atNarrabeen than the wave steepness considered for deriving Vellinga'serosion profile (Hs/Ls~0.034).
At Milford-on-Sea beach, Dean's equilibrium profile slightly over-estimates the mean profile in the upper part of the inter-tidal zoneand is in better agreement in the lower inter-tidal zone. This couldmainly be attributed to the fact that Moore's (1982) relationship isbased on a uniform grain size to determine profile scale parameterwhereas the inter-tidal region of the Milford-on-Sea beach consistsof sediment with a bimodal distribution with 88% gravel 12% sand.Pilkey et al. (1993) describes the difficulty in choosing a singleshape parameter for beaches with large cross-shore sediment vari-ability as well as the shortcomings of the Moore's expression for A.Overall, despite possible differences betweenwave energy dissipationon the steep Milford-on-Sea beach and on a gentle slope associatedwith Dean's profile shape parameter, the mean sub-aqueous profileshape of Milford-on-Sea beach agrees well with the concave shape
of the Dean's profile shape with only 11% root mean square error.On the other hand Vellinga's profile significantly overestimates themean profile throughout the inter-tidal region, which could againbe attributed mainly to the bimodal sediment composition atMilford-on-Sea. This shows that the Dean's profile can be taken as asuitable measure to describe long-term averaged profile shape of acomposite beach, if time averaging is taken over a sufficiently longperiod of time.
However, the overall profile shape of a composite sand–gravelbeach cannot simply be determined by wave dissipation and a singlesediment size. Profile response to wave action is complicated by thecomplex mix of sediment and sediment sorting across the profile.
3.2. Bulk statistics
In order to quantify cross-shore variability of beach profiles, bulkstatistics were computed at Milford-on-Sea and Narrabeen Beaches.All available survey data are used to determine statistical parameters.
3.2.1. Milford-on-Sea beachFig. 8 shows mean cross-shore profile, the profile envelopes deter-
mined from the cross-shore profile surveys, and the standard devia-tion of the profile depth. The mean profile is indicative of a highenergy upper beach with a gradient of 1:5 and an inter-tidal beachwith a gradient of 1:10. The mean beach width at the shoreline(mean water level), measured from the shoreward limit of the activeprofile at the benchmark, is 43 m. The envelope of the beach profilesshows that the beach width at the shoreline varies by around 13 mduring the 18 year study period, with a minimum width of 37 mand a maximum of 50 m, i.e. 30% of the mean beach width. The max-imum cross-shore beach movement of 17 m occurs around 2–3 melevation. The envelope shows the upper beach berm development/recession associated with accretion/erosion in the swash region,which is typical of coarse-grain beaches. However, it should benoted that these results may have been slightly affected by thebeach filling that had been carried out at Milford-on-Sea between1996 and 1999 (SCOPAC, 2003). The standard deviation peaks in thesupra-tidal zone, around 2 m elevation above mean water level. Thisis well above the inter-tidal zone and that indicates the swash domi-nance in cross-shore beach morphodynamics of a composite sand–gravel beach. A secondary peak is seen at –1 m water depth, which
0.0
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-2 -1 0 1 2 3 4 5 6
Stan
dard
Dev
iatio
n (m
)
Mean Profile Elevation (m)
6.0
4.0
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-4.0Mea
n Pr
ofile
Ele
vatio
n (m
)
x (m)
0.0 10.0 20.0 30.0 40.0 50.0 60.0
Fig. 8. Mean profile elevation (dark line) and profile envelop (faint lines) (top panel),and standard deviation (bottom panel), of cross shore profiles at survey location5f00107 at Milford-on-Sea beach.
38 H. Karunarathna et al. / Marine Geology 299–302 (2012) 33–42
is the swash region at low tide. Even though the standard deviationsharply drops through the inter-tidal zone, values well above zeroat the MLWS indicate that the active beach profile extends furtherseaward.
3.2.2. Narrabeen BeachFig. 9 shows mean cross-shore profile with profile envelope and
standard deviation at Profile 4. The width of the mean profile at the
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1.0
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-4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0Mean Profile Elevation (m)
Stan
dard
Dev
iatio
n
Fig. 9. Mean profile elevation (dark line) and profile envelop (faint lines) (top panel),and standard deviation (bottom panel), of cross shore profiles at Profile 4, NarrabeenBeach, NSW, Australia.
shoreline (MWL) with respect to the selected bench mark at the topof the dune is 100 m. The envelope of the measured profiles showsthat the beach width at the shoreline fluctuates by 70 m in the on-off-shore direction, which is 70% of the mean beach width. The stan-dard deviation of beach profile depths drawn against profile depthshows three peaks. The largest peak is around 0.8 m above MWL,which is at the upper region of the inter-tidal zone. A secondarypeak with standard deviation that is nearly half that of the primarypeak, is seen around 6 m above mean water level, which may be at-tributed to variability of the upper beach as a result of frequentstorms. The peak at the end of the profile indicates that the surveysdo not extend to the depth of closure.
3.2.3. ComparisonInvestigation of raw data and bulk statistics of cross-shore profiles
at Milford-on-Sea and Narrabeen Beaches show that composite sand–gravel and sandy beaches have distinctly different cross-shore profileshapes, and spatial and temporal variability. At Milford-on-Sea, thehighest beach variability occurred at the supra-tidal level (2–3 mMSL). This is attributed to strong swash movements associated withincident wave groupiness and waves breaking on or at close proxim-ity to the shoreline (Karunarathna et al., 2005; Masselink et al., 2010).The surf similarity parameter at Milford-on-Sea calculated on themean inter-tidal profile gradient with mean wave steepness is 1.4,showing plunging to surging waves near the waterline. Highly dy-namic swash motions enabled by plunging/surging waves then initi-ate the strongest sediment transport at the upper beach face.
At Narrabeen Beach on the other hand, cross-shore variability ishighest in the inter-tidal region. This can be related to the gradualwave dissipation on the gentle sub-tidal beach which results inmore sediment transport in the surf zone than that in the swashzone. The surf similarity parameter determined using the averageinter-tidal beach slope with mean wave steepness on the NarrabeenBeach is approximately 0.24, showing mostly spilling breakers.Swash movements on gentle beaches with spilling breakers are sig-nificantly lower than that on steep beaches due to partial or full satu-ration of the surf zone as a result of incident wave energy dissipationdue to wave breaking (Baldock et al., 1999; Karunarathna et al.,2005).
3.3. Empirical Orthogonal Function Analysis
Empirical Orthogonal Function (EOF) Analysis is widely used toinvestigate patterns in beach variations (e.g. Winant et al., 1975 andWijnberg and Terwindt, 1995) and other coastal features (e.g. Reeveet al., 2001; Kroon et al., 2008; Reeve et al., 2008). The methodmaps the observed coastal morphological data into a set of shapefunctions known as eigenfunctions that are determined from thedata itself. When applied to cross-shore beach profiles, it can revealpatterns of variation about the mean profile shape, such as bars andtroughs (Pruszak, 1993; Larson et al., 2003; Kroon et al., 2008). Thecross-shore profile shape is represented as a linear summation oftime and space varying functions:
hxt ¼ ∑ncn tð Þ⋅en xð Þ ð1Þ
where h=profile depth, x=distance measured offshore. n=nx=thenumber of measurement points in the cross-shore profile and n=nt=number of cross-shore profile surveys. en and cn are spatial orthogonalfunctions and corresponding time coefficients respectively, where
cn tð Þn ¼Xnt
n¼1
hxt ⋅en xð Þ: ð2Þ
39H. Karunarathna et al. / Marine Geology 299–302 (2012) 33–42
Each eigenfunction corresponds to a statistical description of thedata with respect to how the data variance is concentrated in thatfunction. The functions are usually ranked according to the magni-tude of their corresponding eigenvalues which are proportional tothe data variance. Typically, a large proportion of the data varianceis contained within a small number of eigenvalues and hence, only alimited number of eigenfunctions are needed to explain most of thevariation in the measurements (Pruszak, 1993; Reeve et al., 2001;Larson et al., 2003).
EOF analysis was performed on the beach profiles measured atboth study sites. The results at both sites show that more than 93%of the data variation is captured by the first five eigenfunctions.
The first five normalised spatial eigenfunctions for Profile 5f00107at Milford-on-Sea and Profile 4 at Narrabeen Beach are shown inFig. 10. The dark line in the figures gives the first eigenfunction thatclosely corresponds to the mean cross-shore profile. The primary ver-tical axis in the figures corresponds to second and subsequent eigen-functions while secondary vertical axis corresponds to the meanprofile. The second eigenfunction reflects the presence of an upperbeach ridge at Milford-on-Sea and inter-tidal beach trough and ter-race at Narrabeen Beach respectively, which distinctly deform theprofiles from their mean profile shape. The third eigenfunction re-flects the presence of a sub-tidal trough and a bar at both sites. Thefourth eigenfunction implies sediment exchange across the profile,which reflects erosion of the upper beach at Milford-on-Sea andinter-tidal zone at Narrabeen Beach. The fifth eigenfunction and sub-sequent functions (not shown) may be related to other accumula-tive–erosive features in the profiles which contribute to deform theprofile shape in time.
There are distinct differences between the spatial eigenfunctionsat Milford-on-Sea and Narrabeen Beach. At Milford-on-Sea, the spa-tial variability of all eigenfunctions is strongest between 18 m and40 m, which covers the entire swash zone and the upper half of theinter-tidal zone. This confirms that the sub-aerial (above MWL)beach undergoes the strongest morphodynamic variability, asindicated by the bulk statistical analysis of raw profile data.
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0 10 20 30 40 50 60
-2.0
0.0
2.0
4.0
6.0EOF2 EOF3
EOF4 EOF5
-1.2
-0.8
-0.4
0
0.4
0.8
0 20 40 60 80 100 120 140 160
-4.0
0.0
4.0
8.0
12.0
EOF2 EOF3
EOF4 EOF5
Cross-shore Distance
Cross-shore Distance (m)
Eig
enfu
nctio
nE
igen
func
tion
Fig. 10. Spatial orthogonal eigenfunctions for Profile 5f00107 at Milford-on-Sea beach(top panel) and Profile 4 at Narrabeen Beach (bottom panel). Dark line shows themean profile.
Eigenfunctions at the Narrabeen Beach show strongest variability be-yond 60 m, which covers the inter-tidal and sub-tidal zone of the pro-file. Variability of eigenfunctions in the swash region of the NarrabeenBeach is significantly smaller than that of the rest of the profile. Onboth beaches, spatial eigenfunctions do not reach constant values atthe seaward end of the profile, indicating that the depth of closureis located further offshore from the truncation point of the measuredprofiles.
As seen in the third eigenfunction, the bar crest at Milford-on-Seais located in the inter-tidal zone and therefore can be exposed at lowtide. On the other hand, the bar crest on the Narrabeen profile is lo-cated in the sub-tidal zone and is submerged at all times except dur-ing low water spring tide. The fourth eigenfunction which impliessediment exchange cross the profile, shows offshore sediment trans-port, which typically happens during storms. At Milford-on-Sea,sediment moves from beach foreshore to the inter-tidal zone thuseroding the upper beach while at Narrabeen Beach, sediment movesfrom the inter-tidal zone to the sub-tidal zone that lowers the sub-tidal beach. These characteristics show how each beach will respondto erosive events.
To investigate the temporal variability of different cross-shoremorphological features at a range of time scales, temporal eigenfunc-tions were examined. The first temporal eigenfunction (not shown) isapproximately constant at both sites as it corresponds to the time-mean cross-shore beach profile. The second temporal eigenfunctionat Milford-on-Sea, shown in Fig. 11, exhibits a gradual decline overtime, indicating long term beach recession due to degradation of theupper beach ridge. No seasonal signature is evident. The second tem-poral eigenfunction at Narrabeen Beach shows a high frequencysignal with a 3–5 month period as well as a longer-term 3–8 yearcyclic variability. The high frequency variability can be attributed tofrequent storms that govern the NSW wave climate. The lowerfrequency variability is likely to be due to the ENSO driven cyclicbeach rotation signal at Narrabeen Beach as postulated byRanasinghe et al. (2004). Although Profile 4, being approximately atthe centre of the pocket beach, is thought to be least influenced bythe rotation signal, the result in Fig. 11 indicates that at least a smallportion of the rotation signal may still be felt at this location, whichis confirmed by the 3–8 year cyclic variability. Subsequent temporaleigenfunctions did not show any significant long term periodicity ateither beach.
3.4. Canonical Correlation Analysis
To investigate cross-shore profile response to incident wavesCanonical Correlation Analysis (CCA) was performed between cross-shore profiles and corresponding incident waves. CCA, which is atype of multi-variate linear statistical analysis, allows joint patternsof behaviour to be detected in the evolution of the beach profilesand the incident wave conditions.
In the application of CCA here, a regression matrix (ψ), which re-lates the beach profiles to incident wave properties is derived basedon the dominant patterns of these two variables. A detailed descrip-tion of the methodology is given in Clark (1975) and Różyński (2003).
CCA requires two time series (cross-shore profiles and incidentwaves) sampled at the same rate. Therefore, the waves betweenthe dates of each consecutive pair of beach profiles were used tocompile probability density functions (pdf), before using in CCA.Larson et al. (2000) proposed the use of a parametric distributionfor describing the waves. Rihouey (2004) subsequently proposedthe use of an empirical distribution. Horrillo-Caraballo and Reeve(2008) tested both suggestions on data from Duck, North Carolinaand found superior results when using an empirical distribution.The empirical distribution is a cumulative probability distributionfunction that concentrates probability 1/n at each of the n num-bers of a sample. A combined pdf (pn) may then be derived by
Fig. 11. Second Temporal Eigenfunction for Profile 5f00107, Milford-on-Sea (top panel)and Profile 4, Narrabeen Beach (bottom panel).
40 H. Karunarathna et al. / Marine Geology 299–302 (2012) 33–42
superimposing the individual pdfs available for the period betweentwo consecutive profile surveys,
pn að Þ ¼ 1n
Xn
i¼1
I ai≤að Þ ð3Þ
where a is the wave height or steepness, n is the number of individ-ual wave measurements between two consecutive source functionsand i is an index.
0 1 2 3 4 50
0.1
0.2
0.3
0.4
0.5
0.6
of w
ave
heig
ht
a b
0 1 2 3 4 50
0.05
0.1
0.15
0.2
Wave height (m)
of w
ave
heig
ht
Fig. 12. Probability density functions of (a) incident wave height and (b) wave ste
Offshore waves measured at Long Reef Point off the coast ofNarrabeen Beach were first transformed to a nearer location in 20 mwater depth, using the SWAN wave transformation model. In orderto investigate profile response to both wave height and period, CCAwas then performed between sequences of beach profiles and, inturn, wave height and wave steepness probability density functions.Fig. 12a and b show composites of the probability density functionsof wave height and wave steepness respectively for Milford-on-Seaand Narrabeen Beach respectively.
It is evident that the structure of Fig. 12b significantly differs fromthe structure of Fig. 12a at both sites. This indicates that differentrelationships between cross-shore profiles and incident waves maybe expected when wave height alone, and combined wave heightand period, are considered.
The performance of CCA can normally be improved by filtering theinput data time series. Here, we have followed Clark (1975) and ex-panded the data sequence as EOFs. The data sequence is then recon-structed using only a subset of the EOFs in order to filter out noise.The appropriate number of EOFs required for data reconstruction isdetermined using a “rule of thumb” (North et al., 1982).
Table 1 shows the “skill scores” of the CCA method for bothMilford-on-Sea and Narrabeen Beach. The “skill score” is analogousto the correlation coefficient between cross-shore profiles and waveheight or steepness, with a value of 0 corresponding to no correlationand a value of 1 being a perfect correlation. The “skill” is calculatedusing the regression matrix, and the percentage of total variance inthe profiles and the percentage of variance of input predict andEOFs following Różyński (2003).
The results given in Table 1 show that the wave steepness is, ingeneral, better correlated to the cross-shore profile shape, than theincident wave height, at both Milford-on-Sea and Narrabeen Beach.However, it should be noted that the correlation coefficient atMilford-on-Sea is substantially larger than that of Narrabeen Beach,for both wave height and steepness, indicating that beach profiles atMilford-on-Sea are strongly correlated to incident waves while onlya moderate correlation exists at the Narrabeen Beach.
This could be strongly attributed (i) to the saturation of the surfzone when the incident waves break and strongly dissipate in the
0 0.02 0.04 0.060
0.02
0.04
0.06
0.08
0.1
of w
ave
stee
pnes
s
0 0.02 0.04 0.060
0.05
0.1
0.15
0.2
Wave steepness
of w
ave
stee
pnes
s
epness on Milford-on-Sea (top panel) and Narrabeen Beach (bottom panel).
Table 1“Skill” scores between incident waves and cross-shore profiles.
Profile Skill
Hs Hs/Ls
Milford-on-Sea 5f000107 0.88 0.96Narrabeen Beach Profile 4 0.37 0.41
41H. Karunarathna et al. / Marine Geology 299–302 (2012) 33–42
surf zone of a sand beach where an incident wave structure no longerexists. On the other hand individual incident waves dominate the un-saturated surf zone on a steep, coarse-grain beach (Larson and Kraus,1994). (ii) Dominance of waves at infragravity frequencies, drive surfand swash sediment transport at an incident wave group time scaleon a sand beach. On a steep, coarse-grain beach, swash sedimenttransport that dominates beach profile response, is driven primarilyby the individual incident waves (Wright et al., 1982; Karunarathnaet al., 2005; Masselink et al., 2010). As a result, the profile responseof a steep beach is strongly correlated to the cumulative effect of inci-dent waves while that of a sand beach shows less correlation to inci-dent waves.
4. Conclusions
Long term historic beach profile surveys at Milford-on-Sea beach,UK and Narrabeen Beach, Australia, were analysed using a variety oftechniques to compare and contrast the behavioural characteristicsof composite sand–gravel and sandy beaches at various time scales.
The time mean cross-shore profile at Milford-on-Sea beach indi-cates a reflective upper beach and a moderately dissipative lowerbeach. The sub-aqueous mean profile closely resembles Dean's equi-librium profile, with only 11% RMSE, despite the complex spatialvariability of sediment characteristics. The observed differences canbe attributed to the bimodal sediment distribution across the profile.This observation confirms that Dean's equilibrium profile can still beused as a suitable estimate of long-term profile evolution of a com-posite sand–gravel beach. The mean beach profile of the NarrabeenBeach is in close agreement with Dean's equilibrium profile asexpected, with only less than 5% RMSE.
The standard deviation of profile depth shows that the swash zoneis the most morphodynamically active region of the composite sand–gravel beach and the inter-tidal zone on the sandy beach. Both bulkstatistical and EOF analyses confirm this observation and identifiescross-shore beach profile variability at different time scales. In theshort-term, the composite sand–gravel beach responds to differentwave conditions through variability in the upper beach (swashzone) while the sandy beach responds mainly through variability inthe inter-tidal zone. Differences in ground water dynamics and infil-tration–exfiltration of water through the beach face in sand and com-posite gravel beaches can contribute to these differences. Infiltrationand exfiltration across the beach has been known to be an importantfactor for swash zone sediment transport as well as for stability of thebeach face at short term time scales (e.g. Turner and Masselink, 1998;Mason and Coates, 2001) especially on coarse beaches (e.g. Austinand Masselink, 2006; Pedrozo-Acuña et al., 2006, 2007). On a gravelbeach, a significant proportion of the uprush will infiltrate into theswash zone beach and weaken the backwash. Therefore, sedimenttransported onshore barely moves to offshore again resulting indeposition on the upper beach. On a sand beach on the other hand,less infiltration takes place as a result of low permeability. Therefore,the effect of infiltration on sediment transport will be considerablysmaller.
Our results provide a quantitative demonstration that the cross-shore variability of composite sand–gravel beaches can be very differ-ent to that of sand beaches. This specific profile response characteris-tic may lead to distinctly different mechanisms of beach instability; acomposite sand–gravel beach may become unstable due to sub-aerial
profile cutback during storms while sandy beaches destabilise as a re-sult of beach lowering. This same characteristic may make it more dif-ficult for the upper foreshore of a composite sand–gravel beach torecover from an erosive event than for a sandy beach. Also, asPontee et al. (2004) observed, upper beach evolution is governed bythe upper foreshore itself, and therefore recession of the foreshorecontributes to further recession. This is supported by the form ofthe second eigenfunction which reflects the observation of steady re-cession of the beach foreshore at Milford-on-Sea and the mainly cycli-cal beach erosion at Narrabeen.
The CCA shows that beach profile change on Milford-on-Sea beachis more strongly correlated to the incident wave steepness than at theNarrabeen Beach, which signifies the impacts of surf zone saturationand the presence of infragravity waves in the surf and swash oncross-shore profile evolution.
Finally, the impacts of the above observations on current model-ling practises of cross-shore beach profiles should be noted. Mostcross-shore evolution models either use sediment transport routinesapplicable only to sandy beaches (Rolevink et al., 2009), based on sin-gle sediment size (Larson and Kraus, 1989; Larson et al., 1989) or useonly the sub-aqueous profile (Southgate and Nairn, 1993; Reniers etal., 1995). Therefore, development of new routines, such as describedby Jamal et al. (2010), to incorporate profile response of gravel bea-ches will be extremely timely.
It should also be noted the fact that the beach profiles at both sitesselected for the current study do not extend to the depth of closureraise some uncertainties in the analysis as we are not dealing with aclosed sediment system. Under the assumption of no longshore trans-port, sediment volumes in a profile out to the depth of closure shouldbe conserved. In practise, there are gradients in longshore transportwhich mean this is not necessarily the case. Further, the concept ofa depth of closure is very much dependent upon the duration ofchanges under consideration.
Acknowledgements
Beach profile surveys and wave data at Milford-on-Sea are from theChannel Coastal Observatory, UK. HK and DER acknowledge supportfrom EPSRC through Grant EP/C005392/1—RF-PeBLE (“A Risk-basedFramework for Predicting Long-term Beach Erosion”). JMH-C and DERacknowledge the support of the European Commission through FP7,2009-1, Contract 244104—THESEUS (“Innovative technologies for saferEuropean coasts in a changing climate”).
References
Austin, M.J., Masselink, G., 2006. Swash–groundwater interaction on a steep gravelbeach. Continental Shelf Research 26, 2503–2519.
Baldock, T.E., Holmes, P., Horn, D.P., 1999. Low frequency swash motion induced bywave grouping. Coastal Engineering 36, 197–222.
Bradbury, A.P., Powell, K.A., 1992. The short-term profile response of shingle spits tostorm wave action. Proc. 22nd Internaltional Conference in Coastal Engineering.Venice 1, 439–449.
Brunn, P., 1954. Coast erosion and development of beach profiles. TechnicalMemorandumNo. 44, beach Erosion Board.
Callaghan, D., Nielsen, P., Short, A., Ranasinghe, R., 2008. Statistical simulation of waveclimate and extreme beach erosion. Coastal Engineering 55 (5), 375–390.
Carr, A.P., 1983. Shingle beaches: aspects of their structure and stability. Shoreline pro-tection. Proceedings of Shore Protection, A Conference Organised by the Institutionof Civil Engineers. University of Southampton, Thomas Telford, pp. 69–76.
Carter, J.D., 1986. Discussion: gravel beach profile characterisation and discrimination.Journal of Coastal Research 1 (2), 129–139.
Carter, R.W.G., Orford, J.D., 1984. Coarse clastic barrier beaches: a discussion of thedistinctive dynamic and morphosedimentary characteristics. Marine Geology 60,377–389.
Carter, R.W.G., Orford, J.D., 1993. The morphodynamics of coarse clastic barriers andbeaches: a short and long term perspective. Journal of Coastal Research 15,158–179.
Carter, D.L., Forbes, S.C., Jennings, J.D., Orford, J.D., Shaw, J., Taylor, R.B., 1989. Barrierand lagoon coast evolution under deffering relative sea level regimes; Examplesfrom Ireland and Nova Scotia. Marine Geology 88, 221–242.
42 H. Karunarathna et al. / Marine Geology 299–302 (2012) 33–42
Chadwick, A.J., Karunarathna, H., Gehrels, R., Massey, A.C., O'Brien, D., Dales, D., 2005. Anew analysis of the slapton barrier beach system. Maritime Engineering 158 (4),p147–p161.
Clark, D., 1975. Understanding canonical correlation analysis. Concepts and Techniquesin Modern Geography No. 3. Geo Abstracts Ltd, UK, Norwich.
Dean, R.G., 1977. Equilibrium beach profiles, US, Atlantic and Gulf Coasts. Departmentof Civil Engineering Ocean Engineering Report No. 12. University of Delaware,Delaware.
Dean, R.G., 1991. Equilibrium beach profiles: characteristics and applications. Journal ofCoastal Research 7 (1), 53–84.
Horrillo-Caraballo, J.M., Reeve, D.E., 2008. An investigation of the link between beachmorphology and wave climate at Duck, NC, USA. Journal of Flood Risk Management1, 110–122.
Horrillo-Caraballo, J.M., Reeve, D.E., 2010. An investigation of the performance of adata-driven model on sand and shingle beaches. Marine Geology. doi:10.1016/j.margeo.2010.03.010.
Ivamy, M.C., Kench, P.S., 2006. Hydrodynamic and morphological adjustment of amixed sand and gravel beach, Torere, Bay of Plenty, New Zealand. Marine Geology228, 137–152.
Jamal, M.H., Simmonds, D.J., Magar, V., Pan, S., 2010. Modelling infiltration on gravelbeaches with an XBEACH variant, Paper 25. Proceedings of 32nd ICCE, Shanghai,China.
Jennings, R., Shulmeister, J., 2002. A field based classification scheme for gravel beaches.Marine Geology 186, 211–228.
Karunarathna, H., Chadwick, A.J., Lawrence, J., 2005. Numerical experiments of swashoscillations on steep and gentle beaches. Coastal Engineering 52, 497–511.
Kirk, R.M., 1980. Mixed sand and gravel beaches: morphology, processes and sediments.Progress in Physical Geography 4, 189–210.
Kroon, A., Larson,M.,Moller, I., Yokoki, H., Rozynski, G., Cox, J., Larroude, P., 2008. Statisticalanalysis of coastalmorphological data sets over seasonal to decadal time scales. CoastalEngineering 55, 581–600.
Larson, M., Kraus, N.C., 1989. SBEACH: numerical model for simulating storm inducedbeach change. Report 1: Theory and Model Foundation, Tech. Report CERC 89-9.Coastal Engineering Research Centre, U.S. Army Waterway Experiment Station,Vicksburg, MS.
Larson, M., Kraus, N.C., 1994. Temporal and spatial scales of beach profile change, Duck,North Carolina. Marine Geology 117, 75–94.
Larson, M., Kraus, N.C., Byrnes, M.R., 1989. SBEACH: numerical model for simulatingstorm induced beach change. Report 2: Numerical Formulation and Model Tests,Tech. Report CERC 89-9. Coastal Engineering Research Centre, U.S. ArmyWaterwayExperiment Station, Vicksburg, MS.
Larson, M., Kraus, N.C., Wise, R.A., 1999. Equilibrium beach profiles under breaking andnon-breaking waves. Coastal Engineering 36, 59–85.
Larson, M., Capobianco, M., Hanson, H., 2000. Relationship between beach profiles andwaves at Duck, North Carolina, determined by Canonical Correlation Analysis. MarineGeology 163, 275–288.
Larson, M., Capobianco, M., Jensen, H., Rozyanki, G., Southgate, H.N., Stive, M., Wijnberg,K.M., Hulscher, S., 2003. Analysis andmodelling of field data on coastal morphologicalevolution over yearly and decadal time scales, Part 1: Background and linear tech-niques. Journal of Coastal Research 19 (4), 760–775.
Martìn-Grandes, I., Hughes, J., Simmonds, D.J., Chadwick, A.J., Reeve, D.E., 2009. Novelmethodology for one line model calibration using impoundment on mixed beach.Proceedings of Coastal Dynamics 2009, Tokyo. doi:10.1142/9789814282475_0106.
Mason, T., Coates, T.T., 2001. Sediment transport processes on mixed beaches: a reviewfor shoreline management. Journal of Coastal Research 17 (3), 645–657.
Masselink, G., Russell, P., Blenkinsopp, C., Turner, I., 2010. Swash zone sediment transport,step dynamics and morphological response on a gravel beach. Marine Geology 274,50–68.
McLean, R.F., Kirk, R.M., 1969. Relationship between grain size, size-sorting, and fore-shore slope on mixed sand–shingle beaches. New Zealand Journal of Geology andGeophysics 12, 138–155.
Moore, B.D., 1982. Beach profile evolution in response to change in water level and waveheight, Master's Thesis, Department of Civil Engineering, University of Delaware.
North, G.R., Bell, T.L., Cahalan, R.F., Moeng, F.J., 1982. Sampling errors in the estimationof empirical orthogonal functions. Monthly Weather Review 110, 699–706.
Pedrozo-Acuña, A., Simmonds, D.J., Otta, A.K., Chadwick, A.J., 2006. On the cross-shoreprofile change of gravel beaches. Coastal Engineering 53 (4), 335–347.
Pedrozo-Acuña, A., Simmonds, D.J., Chadwick, A.J., Silva, R., 2007. A numerical–empiricalapproach for evaluating morphodynamic processes on gravel and mixed sand–gravelbeaches. Marine Geology 241 (1–4), 1–18.
Pilkey, O.H., Young, R.S., Riggs, S.R., Smith, A.W., Pilkey, W.D., 1993. The concept ofshore profile of equilibrium: a critical review. Journal of Coastal Research 9 (1),255–278.
Pontee, N.I., Pye, K., Blott, S.J., 2004. Morphodynamic behaviour and sedimentary variationof mixed sand and gravel beaches, Suffolk, UK. Journal of Coastal Research 20 (1),256–276.
Pruszak, Z., 1993. The analysis of beach profile changes usingDean'smethod and empiricalorthogonal functions. Coastal Engineering 19, 245–261.
Ranasinghe, R., McLoughlin, R., Short, A., Symonds, G., 2004. The Southern OscillationIndex, wave climate and beach rotation. Marine Geology 204, 273–287.
Reeve, D.E., Li, B., Thurston, N., 2001. Eigenfunction analysis of decadal fluctuations insandbank morphology at Great Yarmouth. Journal of Coastal Research 17 (2),371–382.
Reeve, D.E., Horrillo-Caraballo, J.M., Magar, V., 2008. Statistical analysis and forecasts oflong-term sandbank evolution at Great Yarmouth, UK. Estuarine, Coastal and ShelfScience 79, 387–399.
Reniers, A.J.H.M., Roelvink, J.A., Walstra, D.J.R., 1995. Validation Study of UNIBEST-TCModel. Report H2130. Delft Hydraulics, Delft, The Netherlands.
Rihouey D., 2004. Analyse statistique de l'évolution morphodynamique des plagessableuses — application aux sites d'étude du Programme National d'EnvironnementCôtier et aux plagesd'Anglet. Thèse d'université. Anglet, Université de Pau et desPays de l'Adour (LaSAGeC2), France.
Rolevink, D., Reniers, A., van Dongeren, A., de Vries, J.T., McCall, R., Lescinski, J., 2009.Modelling storm impacts on beaches, dunes and barrier islands. Coastal Engineering56, 1133–1152.
Różyński, G., 2003. Data-driven modelling of multiple longshore bar evolution and in-teractions. Coastal Engineering 48 (3), 151–170.
Ruiz de Alegria-Arzaburu, A.R., Pedrozo-Acuna, A., Horrillo-Caraballo, J.M., Masselink,G., Reeve, D.E., 2010. Determination of wave-shoreline dynamics of a macrotidalgravel beach using Canonical Correlation Analysis. Coastal Engineering 57,290–303.
Short, A.D., 1985. Rip current type, spacing and persistence, Narrabeen beach, Australia.Marine Geology 65, 47–71.
Short, A.D., Trembanis, A.C., 2004. Decadal scale patterns in beach oscillation and rota-tion Narrabeen beach, Australia-Time series, PCA and Wavelet Analysis. Journal ofCoastal Research 20 (2), 523–532.
Short, A.D., Trenaman, N., 1992. Wave climate of the Sydney region. Australian Journalof Marine & Freshwater Research 42, 765–791.
Short, A.D.,Wright, L.D., 1981. Beach systems of the Sydney region. Australian Geographer15, 8–16.
Southgate, H.N., Nairn, R.B., 1993. Deterministic profile modelling of nearshore processes:Part 1. Waves and currents. Coastal Engineering 19, 27–56.
Standing Conference on Problems Associated with the Coastline — SCOPAC, . SedimentTransport Study. Hengistbury Head to Hurst Spithttp://www.Scopac.org.uk/scopac%20sediment%20db/chrst/chrsttxt.pdf[accessed March 2010].
Sunamura, T., Horikawa, K., 1974. Two dimensional beach transformation due towaves. Proceedings of 14th Int. Conference in Coastal Engineering, pp. 920–938.
Swart, D.H., 1974. A schematisation of onshore–offshore transport. Proceedings 14thInt. Conference in Coastal Engineering, pp. 884–900.
Turner, I.L., Masselink, G., 1998. Swash infiltration–exfiltration and sediment transport.Journal of Geophysical Research 103 (C13), 30813–30824.
Vellinga, P., 1983. Predictive computational model for beach and dune erosion duringstorm surges. Proc. Coastal Structures. ASCE, Washington D.C.
Vellinga, P., 1984. A tentative description of a universal erosion profile for sandy beachesand rock beaches. Coastal Engineering 8 (2), 177–188.
Wijnberg, K.M., Terwindt, J.H.J., 1995. Extracting decadal morphological behaviourfrom high-resolution, long-term bathymetric surveys along the Holland coastusing eigenfunction analysis. Marine Geology 126, 301–330.
Winant, C.D., Inman, D., Nordstrom, C.E., 1975. Description of seasonal beach changesusing empirical eigenfunctions. Journal of Geophysical Research 80 (15), 1979–1986.
Wright, L.D., Short, A.D., 1984. Morphodynamic variability of surf zones and beaches: asynthesis. Marine Geology 56, 93–118.
Wright, L.D., Guza, R.T., Short, A.D., 1982. Dynamics of high energy dissipative surfzone. Marine Geology 45, 41–62.
