the use of grain size trend analysis in macrotidal areas with breakwaters: implications of settling...

Marine Geology 253 (2008) 132–148

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The use of grain size trend analysis in macrotidal areas with breakwaters:Implications of settling velocity and spatial sampling density

T.A. Plomaritis a,⁎, D. Paphitis a, M. Collins a,b

a School of Ocean and Earth Science, National Oceanography Centre, Southampton University of Southampton, European Way, Southampton, SO14 3ZH, UKb Marine Research Division, AZTI-Tecnalia, Herrera Kaia, Portualdea z/g, 20110 Pasaia, Spain

⁎ Corresponding author. Tel.: +30 6944530129; fax: +E-mail address: [email protected] (T.A. Plomarit

0025-3227/$ – see front matter © 2008 Elsevier B.V. Adoi:10.1016/j.margeo.2008.05.003

A B S T R A C T
A R T I C L E I N F O
Article history:
In a macrotidal environme Received 19 June 2007Received in revised form 2 May 2008Accepted 11 May 2008
Keywords:sediment transportsettling velocitygrid spacinggrain size trendsbreakwatersElmer

nt with offshore breakwaters (Elmer, West Sussex) a new approach for theidentification of the sediment transport pathways with grain size trend analysis (GSTA) was undertakenusing statistical parameters (mean, sorting and skewness) directly derived from settling velocitiesdistributions. The same samples were analysed with sieving (quarter- and half-phi resolution) and GSTAwas performed again in order to directly compare the resultant sediment transport directions derived withthe two analytical techniques. Furthermore, both regular and irregular sampling distributions were used torecalculate GSTA. Hydrodynamic data were collected in different locations around the breakwaters and netsediment transport directions were calculated in order to assess the accuracy of the sediment transportpathway directions derived with the different analytical techniques.The accuracy of settling velocity in determining the statistical parameters of the grain size distribution isidentified, especially for the fine-medium sand sediments. Settling velocities produced better results than thesieving; the quarter-phi resolution producing the poorer results in comparison with the coarser half-phiresolution. The results for the different spatial sampling strategies are found to depend upon the number ofsamples utilised; that shows that the accuracy of the GSTA is based upon the ability of representing,adequately, the spatial distribution of the sediment parameters.

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1. Introduction

Spatial variation in grain size parameters (i.e. mean, sorting andskewness) in a sedimentary environment are mainly in response tosediment transport processes. Such variations are known as grain sizetrends (McLaren, 1981). For the extraction of information from suchdata and their translation into sediment transport pathways, anumber of approaches have been proposed by various authors (Folkand Ward, 1957; Pettijohn et al., 1972; McCave, 1978). Relationshipbetween sediment grain size parameters have revealed the possibilityof using them to infer transport patterns (McLaren and Bowles, 1985).

The interpretation of relative grain distribution changes is basedupon the assumption that the probability of fine-grains sedimentbeing transported is greater than that of coarser grains (McLaren andBowles, 1985). A corollary of the above assumption is that there is agreater probability of coarser grains being deposited, prior to finergrains. Although the above assumption does not highlight thecomplexity of the transport processes (McLaren and Beveridge,2006) it is reasonable for determining the net transport pathways inmarine and coastal environment (Gao and Collins, 1994a,b).

44 23 80593052.is).

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On this basis, sediments in the direction of transport must beeither: (a) finer, better sorted andmore negatively skewed (FB-); or (b)coarser, better sorted and more positively skewed (CB+). These twopatterns of sediment transport were described byMcLaren and Bowles(1985), as low- and high-energy respectively. Gao and Collins (1991)adopted those assumptions and transport trends, but proposed certainmodifications and improvements to the ‘McLaren approach’. Theirarguments were focused upon problems concerning both mathema-tical and sedimentological considerations. As a result, two-dimen-sional treatment of the data was proposed, together with a differentstatistical test for the determination of ‘no transport conditions’.

This 2D grain size trend analysis (GSTA) has been applied widely toa variety of environments, such as: closed embayments (Gao andCollins, 1992); sandbanks (Gao et al., 1994); the inner continental shelf(Gao and Collins, 1994a,b); river floodplains (Asselman, 1999);estuaries (Mallet et al., 2000); tidal inlets (Friend et al., 2006); aridge and runnel system (Pedreros et al., 1996) and sea straits (Chenget al., 2004). Most of these studies applied GSTA on a regional scale,with only rare application of the method to smaller-scale environ-ments (Pedreros et al., 1996). Lastly, it should be noted that it has beencommon practice to compute the necessary GSTA statistical para-meters on the basis of mechanical sieving.

The present investigation assesses the benefits in using settlingvelocity determinations for the computation of statistical parameters,

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133T.A. Plomaritis et al. / Marine Geology 253 (2008) 132–148

rather than mechanical sieving; in addition the sensitivity of the GSTAmethod to the sieving resolution (quarter-phi and half-phi distribu-tions) will be tested. Likewise, to study the influence of grid spacing onthe resultant transport pathways comparison of regular square grids(a present pre-requisite of the method), with irregular and randomsampling grids (which need to be transformed into a regular grid, toform the input file for the method) was undertaken. Interestingly, theuse of settling velocity in sedimentary investigations provides theimplicit inclusion of any grain shape and density effects (Collins andRigler, 1982; Komar and Clemens, 1986; Paphitis et al., 2002), whichinfluence the sediment transport direction, in relation to the principalassumption required in the technique (McLaren and Bowles, 1985).Finally, the overall method has not been tested at such a fine-detail,within an environment showing high spatial hydrodynamic varia-bility. Towards the above objectives seabed samples collected in thevicinity of the offshore breakwater scheme at Elmer, south coast of UK(Fig. 1), were selected for study.

2. Study area

Elmer is located on the West Sussex coastline (southern England)(Fig. 1). The coast here is protected by a segmented offshore breakwaterscheme, constructed in 1993, located within the intertidal zone. Themorphology of the beach has undergone changes in response to theconstruction of the offshore breakwaters; these form salients duringhigh water and tombolos at lower stages of the tidal cycle. The tide issemi-diurnal and progressive, with a mean spring tidal range of approx.6m (macrotidal). Themean neap tidal range is not exceeding 2.9m. Thepeak tidal currents flow in a west-southwest direction during high

Fig. 1. Map of the study area, showing its regional setting (a), together with a sector of the c

water, entering the landward area of the structures through the gapbetween breakwaters 6 and 7 (Fig. 1c); they accelerate over the salientfeatures, causing local increases in sediment transport and interact withthe diffracted waves (Plomaritis, 2006).

The area under investigation is covered essentially with sand-sizedsediments (115 μm median grain size), whilst the berm has beenreplenished with shingle (of about 20 cm mean grain size). This latterdeposit follows the general shape of the coastline and forms, onaverage, a 1 m deep layer. The seabed on the immediate landward sideof the breakwaters is covered by coarse-grained material (pebble tocobble size). These coarser-grained sediments are considered to betransported either from the berm, or from offshore sources, i.e. a chalkoutcrop offshore of the scheme (Bray et al., 1995), during high-energyconditions. Further transport of such coarse material is unlikely, sinceit is deposited in the most protected area of the scheme. Recentmeasurement shows that, even during storm conditions, shingle sizematerial remains immobile (King et al., 2000). Algal growth on thismaterial verifies this conclusion.

The dominant wave direction is south westerly, with 65% of thewaves approaching from within the segment of 180° to 220° (Fig. 2).These directions correspond also to the greater waves, with significantwave heights of up to 5.5m andwave period of around 7.5 s (HydraulicResearch, 1994). Some 15% of the waves approach from the 100° to160° (southeast). The waves that reach the Elmer coastline, fromwesterly to southwesterly directions, are associated with somewhatsmaller wave heights than might be anticipated for areas with such afetch length, i.e. open to waves from the Atlantic Ocean, this is due tothe sheltering effect of the Isle of Wight (Fig. 1(a)). In response to thegently sloping bathymetry at Elmer, the waves reach the coastline at

oastline (b) and the breakwater scheme (c), together with the responsible Authorities.

Fig. 2. Annual distribution (in percentage) of the incoming wave directions at Elmer(Hydraulic Research, 1994).

134 T.A. Plomaritis et al. / Marine Geology 253 (2008) 132–148

very small angles. The area is wave dominated with the eastwardlongshore drift (Motyka and Brampton, 1993).

3. Methodology

3.1. Field methods

Sediment sampling was undertaken in the embayment formed byBreakwaters 3 and 4 (Fig. 1(c)) on the 24/06/02; it was confined to the

Fig. 3. Bathymetry (in metres above OD) of the study site, with the sediment sampling locatioin position D assuming symmetrical wave diffraction (see text for details).

intertidal zone, during low water on spring tides. The sampling areaextended over 255m, in a longshore direction, and 180m in the cross-shore direction. A total of 158 samples were collected and samplingfollowed a regular 15×15 m grid (Fig. 3); of these, 146 samples wereused for the GSTA. The remaining 12 samples were located at theextremities of the sampling area or very close to the structures andwere mainly immobile pebble and cobble-size shingle and chalk (seeabove). Moderate weather conditions preceded the sampling period;as such, the transport was likely to be restricted to the surficial layers,sampling being restricted to the upper 3 cm of the bed (Pedreros et al.,1996).

Hydrodynamic data were collected using three AutonomousBenthic Landers (ABLs), combining a pressure sensor and an Electro-Magnetic Current Meter (EMCM) measuring the horizontal velocityfield. Data were collected over tidal cycles; however the weatherconditions prior to the sampling were constant for a period of a fewdays. The three ABLs were positioned as follows (Fig. 3): (i) offshore ofthe west breakwater (A); (ii) within the gap between the twobreakwaters (B); and (iii) on the landward side of the westernbreakwater (C). The sediment transport direction was computed atposition D (landward side of the western breakwater) as described inthe following section. The pressure sensor and the ECM werepositioned at a height 0.5 m and 0.3 m above the bed, respectively,at all of the stations. Data were collected at a frequency of 4 Hz, for4 min and 16 s. The three instruments collected data in burst mode,every 10 min. Weather conditions during the field work were mildwith typical wave height of around 0.5m, approaching from the south-southwest direction (220°).

3.2. Methods of analysis

The mean settling velocity of each sample was determined using asettling tower, 2 m long and with an internal diameter of 0.2 m (forgeneral details, see Rigler et al., 1981). Triplicate measurements wereundertaken on each sample, for the accurate determination of thestatistical parameters. The water temperature during the settling

n (●). The ABL were positioned in stations A, B and C. Sediment transport was estimated


experiments was maintained at approx. 19 °C (±2 °C). The loggingfacility (triggered automatically upon the introduction of thesediment at the water surface) is based upon a balance accumulationsystem, which logs onto a computer at 6 Hz; this provided acontinuous settling velocity distribution that was binned in 1 sclasses. The distributions of the main statistical parameters of thesand-sized surficial sediments are presented as psi (ψ) values, which isdefined as:

W ¼ −log2ws

where ws is the settling velocity (in m/s) (Gibbs et al., 1971). Thenegative logarithm to the base of 2 was used for the settling velocity,analogous to the phi (φ) value used commonly instead of the graindiameter. The logarithmic scaling was introduced originally toenhance the small, but important, differences in the settling velocitiesbetween the coarse and fine sand-size sediments. Furthermore, thisform of representation potentially simplifies the data interpretationand analytical procedure, as it produces large ψ values for fine-grainedsediments and smaller values for coarser sediment (similar to thesieving results, expressed in φ). In addition, all the sediment sampleswere dry sieved, for the determination of grain size distributions. Inthis case, three replicates for each sample were analysed, using a stackof standard quarter-phi interval screens (Folk, 1980).

From the resulting distributions, the mean (μ), sorting (σ) andskewness (Sk) were calculated, using the moments formulae(McManus, 1988).

μ ¼ ∑ fm�=100 σ ¼ ∑ f m�−μ� �2

=100� �1=2

Sk ¼ ∑f m�−μ� �3

=100� �1=3

:

The use of continuous settling velocity distributions, for thecalculation of statistical parameters, offers considerable advantages(over sieving), especially in the determination of the higher-ordermoment; they provide very detailed information on the shape of thedistribution. In contrast, sieving can provide only distributioncharacteristics of the curve greater than differences between twosuccessive meshes. Statistical parameters derived from the sievinganalysis were obtained on the basis of quarter-phi resolution and half-phi resolution, as used commonly by researchers in GSTA. For both theregular and irregular sampling grids, data were interpolated usingkriging method (Asselman, 1999) and the grid was resampled at theoriginal sample locations; this was done in order to obtain sedimentparameters and the subsequent transport pathways. As such, anyangle differences are not due to scaling.

Hydrodynamic data were collected when the sensors wheresubmerged; thesewere calibrated and despiked. Only complete burstswhere utilised, those containing ‘dry’ and ‘wet’ data were discarded.The velocity time-series were detrended using a highpass filter, with a‘cut-off’ frequency of 0.033 Hz (~30 s). The resultant orbital velocitieswere calculated above the wave boundary layer, assuming: linearwave theory in the estimation of the wavelength; and a waveboundary layer of limited thickness in comparison with the totalwater depth. For the steady currents (the low-frequency part of thesignal) a logarithmic profile was assumed to establish the velocity atthe bed (Collins et al., 1998). Wave-induced sediment transport wasbased on the ‘wave to wave’ analysis of the high-frequency velocityrecord. This approach takes into account any asymmetries of thewaves, which could be important in the nearshore environment(Russell and Huntley, 1999). From the high-frequency signal, the wavecrests and troughs were determined. The half-cycle periods for eachwave were determined for both the crests and the troughs, whilstmaximum orbital velocities were identified for each. The combinedshear stresses (τmax and τmean) were calculated for each half period,using the algebraic approximation of the parameterised wave–currentinteraction models (Soulsby et al., 1993), based, in turn, upon theGrant and Madsen (1979) model. Sediment transport calculated over

the tidal cycle was combined to produce a net sediment transportdirection, for comparisonwith the GSTA results. Because of the nearlyperpendicular (to the breakwaters) incident wave direction during thefield measurements and assuming symmetrical wave propagationconditions and constant tidal currents (Plomaritis, 2006), transportrates were estimated for the landward side of the eastern breakwater(position D in Fig. 3) using the same method but for opposing wave–current directions.

3.3. Theoretical considerations of grain size trend analysis

The two-dimensional GSTA for the determination of sedimenttrends, as proposed by Gao and Collins (1991, 2001), was used on thedata collected. Mean grain size, sorting, and skewness were used toidentify the two trends (out of the 8 possible), with the higherprobability of occurrence under transport conditions; this has beenconfirmed by field observations (Gao and Collins, 1992; Gao et al.,1994).

Type-A: σ2≤σ1, µ2Nµ1, and Sk2≤Sk1Type-B: σ2≤σ1, µ2Nµ1, and Sk2≥Sk1

For each sampling station, the grain size parameters werecompared with those of the neighbouring stations. If either Type-Aor Type-B trends were identified between the central and aneighbouring station, a dimensionless trend vector was defined. Thetrend vectors identified for each station were summed, to produce asingle vector. Filtering was applied, to reduce the noise using a simplevector-averaging of the central point vector, with its neighbouringvectors. Finally, a significance test was applied, to estimate thebackground values of the probability of Type-A and/or -B to exist bychance. A random redistribution of the samples, together withcalculation of the vectors for both types, represents the probabilisticoccurrence of this trend under ‘no transport’ conditions (Gao andCollins, 1991).

The above method for the determination of sediment transportpathways has been applied to variousmarine environments. However,some limitations and practical considerations should be noted, for thecorrect interpretation of the results. Sediment trends can predict thedirection of transport, but not the magnitude. Gao and Collins (1994b)indicated that assigning a vector length other than unity will createbias towards one of the grain size parameters. Unlike internalsampling points, those at the boundaries of the sampling grid havefewer samples available for determining the trend vectors; this resultsin a biased vector that needs to be excluded from the finalinterpretation. This phenomenon is known as the ‘edge effect’. Theuse of bi- or multimodal sediment samples is a point of controversyregarding the determination of the correct grain size trends because oftheir abundance in the natural environment. McLaren and Beveridge(2006) argued that the use of multimodal sediment samples is notintroducing any error in the resultant trends; on the other hand, Gaoand Collins (1994a), LeRoux and Rojas, (2007) suggest that the use ofsuch sediments is introducing errors in the determination of thetransport direction. A detailed analysis on the impact of bimodalsediment on grain size trends (Flemming, 2007) showed that the useof such sediment samples produce results which are unrelated to thetransport processes and sample decomposition into individualpopulations must be undertaken to such distributions.

Sampling depth is another important factor that influences thetime-scale that the derived trends represent (2001). McLaren andBeveridge (2006) support that the sediment sampling depth has nosignificance in the determination of sediment transport trends andhence no temporal fluctuations can be identified. On the other handGao and Collins (2001) and LeRoux and Rojas (2007) state that thesampling depth has to be in accordance with the physical processesscale. Temporal variations of sediment transport trends have beenidentified with the above method over the coastal area with great


success (Pedreros et al., 1996). However, the temporal–spatial-scaleanalogy identified in coastal processes (Larson and Kraus, 1995) mustalso be applied to the case of grain size trend analysis. The

Fig. 4. Spatial distribution of (a) mean, (b) sorting and (c)

methodology followed in the STA (McLaren method) has indeed nobenefit in the selection of sediment sample depth, because the use ofall possible pairs in identifying the transport vector is creating a

skewness, based upon settling velocity distributions.

Fig. 5. Differences between the values of a) sorting and b) skewness calculated on thebasis of quarter- and half-phi sieving versus the mean grain size.


preference for the large scale processes that are not influenced by thetemporal changes of sediment transport. However, for small areastemporal fluctuations are possible to be determined by using thecorrect sampling depth. The selection of the sampling depth is sitespecific since similar sampling depths can be related to differenttime-scales, in environments with different sedimentation rates orenergy inputs. Analogous to the sampling depth, grid spacinggoverns the spatial scale of the transport processes that can beidentified by GSTA. All the above requirements were fulfilled in thepresent study, whilst conclusions are drawn (see below) consideringthe limitations of the method. A discussion related to the practicalconsiderations can be found in numerous up-to-date reviews of thegrain size trend analysis (Gao and Collins, 2001; McLaren andBeveridge, 2006; LeRoux and Rojas, 2007; McLaren et al., 2007;Poizot et al., 2008).

4. Results and discussion

4.1. Surficial sediments

The seafloor of the study area consists mainly of medium- to fine-grained sands, moderately well- to well-sorted and positive, to nearlysymmetrically, skewed (Fig. 4). The sediment appears to be finer andless well-sorted over the central part of the area. The spatialdistribution of the mean settling velocity (Fig. 4a) shows that thefine and very fine sand (settling velocities ranging from 1.4 cm/s to1.2 cm/s, equivalent to 6.16 and 6.38 psi) are located offshore of thebreakwater and in the embayment behind the gap (between the twobreakwaters). The coarser material (medium to coarse sand; settlingvelocity ranging from 2.2 cm/s to 1.5 cm/s, equivalent to 5.50 and6.06 psi values) is present mainly on the salient features and close tothe gap. The salients are more protected than the area in theimmediate vicinity of the gap; however, they experience strongertidal currents, due to locally accelerated flow (Plomaritis, 2006) thatresults in the removal of the finer sediment material. Sorting is betterover the salients, decreasing monotonically towards the gap (Fig. 4b).Positively skewed sediments tend to dominate the area, with highervalues over the central and western parts. Negative values aregenerally located at the extremities and close to the gap (Fig. 4c).

Sediment distribution characteristics obtained from the sievinganalysis (not included here) show similar patterns to those of thesettling velocity; however, the sorting is decreased i.e. improved.Skewness differences between the settling and sieving (quarter-phi)approaches have differences ranging between −1 and 1 with positivedifferences located to landward of the breakwaters and negative toseaward. Skewness derived on the basis of half-phi results wasalways more positive than that of the quarter-phi one: differences aremore pronounced over the areas of the finer sediments. Differencesbetween the estimated quarter- and half-phi sorting and skewnessvalues are dependent on the mean grain size and they increaselinearly when the mean grain size becomes larger than 2.92 phi(smaller than 0.132 mm) (Fig. 5). Such differences relate to the natureof the sieving analysis; this provides reduced resolution for thecoarser grains, in comparison with the finer, for the specific sand size.Sensitivity to sorting and skewness constitutes one of the mainreasons for adopting settling analysis as an alternative method ofobtaining sediment distribution characteristics (towards the calcula-tion of sediment transport pathways using GSTA). An intercompar-ison will be undertaken (see below) on the results of GSTA. In turn,these will be compared with net sediment transport directions,derived on the basis of field measurements.

4.2. Transport pathways inferred from GSTA

Sediment transport pathways, derived on the basis of settlingvelocity distributions, are presented in Fig. 6a. The vectors indicate

onshore sediment movement deflected, behind the breakwaters,towards the salient features. These transport directions are consistentwith the morphological characteristics (salient development behindthe breakwaters) of the area and the calm weather conditions thatprevailed prior and during the sampling period. Wave diffractiondirections are dissimilar for the two sides of the gap. The amount ofdeflection is greater over thewest part than over the east part (Table 1,Fig. 6a).

The sediment transport pathways obtained using the dry sievingquarter-phi sediment distributions (Fig. 6b) show the same transportpattern, as obtained from the settling velocity analysis (Fig. 6a), butwith different deflection angles (Table 1). In the central part of thestudy the transport is onshore, but not deflected. Close to high waterthe trends appear to reverse, indicating different directions than thoseobtained previously. The half-phi resolution provides once again the

Fig. 6. Sediment trend vectors, calculated using the results from: (a) the settling velocity analysis; (b) quarter-phi resolution sieve analysis; (c) half-phi resolution sieve analysis.



same general sediment transport pattern (Fig. 6c), as those of settlingvelocity and quarter-phi results.

4.3. Comparison between settling and sieving results

Comparison between the derived grain size trends has beenundertaken on the basis of the absolute difference between thederived sediment transport directions. For the comparison of thetransport vectors, a set of arbitrary criteria was established basedupon practical considerations. Angle deviations b10° are characterisedas areas of ‘zero difference’ since they are insignificant within thecontext of sediment transport. Differences of between 10° and 45° arecharacterised as ‘small’, since the general direction is being main-tained. Finally, differences larger than 45° are characterised as being‘significant’.

Small differences occur over the majority of the sampling area,with significant differences in the transport direction present close tothe gap and at the extremities of the sampling area, for all of the cases(Fig. 7). In more detail, comparison between the settling velocities andquarter-phi sieving directions (Fig. 7a) produce large absolutedifferences, of between 50° and 100°, over the aforementionedareas. Large differences are observed also over the eastern half ofthe embayment, where the transport directions produced by thesettling velocities (Fig. 6a) and the quarter-phi sieving results (Fig. 6b)have different deflection angles (Table 1). The greatest differencesbetween the settling velocity and half-phi sieving results are locatedover the same areas (Fig. 7b); however, they appear to be less intenseandmore evenly distributed, in comparisonwith the quarter-phi case.Large differences are produced to seaward of the eastern breakwaterand the gap; however, such angle differences at the boundary of thesampling area are not always significant.

The differences in transport direction between the quarter- andhalf-phi sieving results (Fig. 7c) produce larger areas of negligibleangle differences (b10°). Areas of significant angle differences arelimited and located over the central part of the area. Further, these are,as well, the same areas over which the half-phi skewness values havemore pronounced differences, in comparison with the quarter-phi.Such differences are related to the fact that the resolution betweentwo adjacent sieves is larger for coarser material, than for finer grainsize. Angle differences are apparent also in other areas, highlightingthe fact that even small differences in the mean, sorting and skewnesscan be important in the determination of sediment transport path-ways, using GSTA. Transport is inferred from the combination of allthree parameters (McLaren, 1981; Gao and Collins, 1994a).

4.4. Computed bedload transport

The currents measured around the breakwaters (Fig. 8) representspring tidal conditions. The superimposed wind conditions (withspeeds of around 3 m/s and an approach direction of 220°) havecreated a wind-driven current, with a northerly component. Such apattern is evident at both the seaward and landward locations, aroundhigh water. Flow conditions within the gap do not reveal anysignificant northerly components; this is because of the dominanteffect of water flushing out, during the ebb. The flow pattern over the

Table 1The mean sediment transport direction (in degrees, related to the North) obtained fromthe field data (and computations) together with the GSTA, based upon the results ofsettling velocities and sieving

Station locations a A B C D

Field data 33.4 2.0 303.4 349.4Settling velocities 23.5 17.1 309.1 357.5Quarter-phi 55.1 334.5 274.9 30.7Half-phi 353.7 347.4 293.9 17.2

a For station locations, see Fig. 3.

landward station (Fig. 8c) does not show any gyre-type circulationpattern (typical behind offshore breakwater), except during the veryearly and late stages of the tidal cycle, suggesting that the wave-induced water circulation is not dominant over the area for theduration of the study. Over the seaward (Fig. 8a) areas, waves breakand reflect on the structure producing a southerly component at theseaward station.

The magnitude and direction of net sediment transport underwave–current interaction, is presented in Fig. 9. The transport directionis influenced significantly by the tidal current direction (Fig. 8);especially around high water, i.e. peak currents. This pattern is morepronounced at the seaward (A) and landward (C) stations (Fig. 9 a andc). Here, sediment transport directions are influenced by thewestward tidal currents around high water; and by the directionof the incident and diffracted waves, during the early and latestages of the tidal cycle. Within the gap between the breakwaterssediment transport is persistently onshore despite the strongoffshore flow (Fig. 8b). This suggests that the sediment transport isdominated by the oscillatory flow over the area that presents largeasymmetries under all stages of the tidal cycle (Plomaritis, 2006).Because of the nearly perpendicular (to the breakwaters) incidentwave direction during the field measurements and assumingsimilar wave propagation conditions and tidal currents, wave–current interaction transport rates were estimated for the land-ward side of the eastern breakwater. Here, the wave propagationand the tidal current directions are opposed (Fig. 9d). In terms oftransport rates no important differences are observed in compar-ison with the western breakwater landward area (Fig. 9c).However, especially at high water, the transport direction wasmodified, producing more northerly transport directions (Table 1).

4.5. Comparison between transport directions, based upon GSTA andfield observations

The mean transport direction calculated using settling velocity,quarter- and half-phi sieving, at the different stations, together with thesediment transport vectors calculated using the field data, aresummarised in Table 1. Throughout the area, the results based uponthe settling analysis lie closer to the calculation based upon fieldmeasurements. Half-phi sieving produces also good estimates (differ-ences b45°) with the calculated transport, whereas the quarter-phisieving results show larger deviations. The non-parametric analysis ofvariance by rank (Kruskal–Wallis) and a multiple comparison test (leastsignificant difference, with 95% confidence interval) were used to checkif the differences between the transport directions obtained fromsieving and settling are significant. For this analysis the 9 stations closestto the ABLs were used. For all of the stations, apart from the easternsalient, the settling and the half-phi results show no significantdifference whilst differences with the quarter-phi resolution weresignificant. Over the eastern salient (station D) quarter- and half-phitransport directions are in agreement with the settling velocity resultsbeing significantly different. The latter are also producing a sedimenttransport direction closer to the one computed based on the field dataresults (Table 1). Poor GSTA results obtained with higher sievingresolution have been reported previously (McLaren and Bowles, 1991);this was attributed to an increase in the ‘distribution noise’ for thesmaller class intervals. However, the settling velocity method does notreveal such aproblemdespite the large numberof classes (i.e. small classinterval) used for the distribution.

Settling velocity distributions result from sediment characteristicsand the hydraulic behaviour of the sediments. This observation isparticularly important, since the assumption of the GSTA imply,strongly, processes that sort the sediment in response to hydraulictransport. During all of the phases of transport (i.e. initiation ofmovement, transport and deposition) various properties of thesediment, other than the grain diameter may influence the mobility;

Fig. 7. Contourmaps showing the absolute difference (degrees) in derived GSTA transport vectors, between: (a) the settling and the quarter-phi sieving results; (b) the settling and thehalf-phi sieving results; and (c) the quarter-phi and half-phi sieving results.


the most important of these are particle density (Collins and Rigler,1982) and shape (Paphitis et al., 2002). Furthermore, finer- andcoarser-grained sediments are represented by a large number ofclasses; this is in contrast with the sieving analysis, where fine sandsare better resolved than the coarser sand fraction. This imbalance canbe important in the case of GSTA; because of the systematicdifferences between the quarter- and half-phi results for sorting andskewness (see Section 4.1). Based upon the above results, the settling

velocity approach appears to produce more accurate transportpathways, throughout the area under investigation.

4.6. Sampling density and regularity

On the basis of the above results, considering the assumptions ofthe GSTA, the settling velocity analysis was selected as being the moreappropriate method to be used, for testing the influence of spatial

Fig. 8. Measured currents, at locations around the breakwater: (a) seaward of the structure; (b) at the gap between the structures; and (c) landward of the structures (for stationlocations, see Fig. 3).

Fig. 9. Mean sediment transport rates and directions for wave–current interaction, for the prevailing conditions, at locations around the breakwater: (a) seaward of the structure;(b) at the gap between the structures; (c) landward of the structures (for station locations see Fig. 3); and (d) the landward area of the east structure, where wave and currentdirections are opposing, assuming symmetrical wave diffraction and the same current. Note: the sediment size used was 130 μm.



sampling density and regularity, on the GSTA results. Two regular and3 irregular sub-sampling datasets were tested against the results ofthe original 15×15 m grid obtained from the settling velocityinformation. For the regular sampling strategy, 2 spatial resolutionswere selected, with grid spacing of 30×30 m and 45×45 m; theseprovided 43 and 20 sediment samples, respectively. For the case of theirregular sampling strategy, the original sediment samples were sub-sampled randomly; this produced 3 datasets that contained 75%, 50%and 25% of the original sediment samples. The spatial density for the 3irregular sub-sampled datasets was constant, throughout the studyarea. These resolutions provided a sampling strategy, with lesssampling stations that provided complete cover for the originalsampling. For all of the datasets, the mean, sorting and skewnessvalues were interpolated. Values were extracted on a 15×15 m grid,for calculating the trend vectors at the same station as in the originalgrid. Using the above procedure all the resultant differences are due tochanges in spatial information and not to inaccuracies caused bysampling irregularities (Poizot et al., 2006).

Sampling density is a parameter defined commonly by the studyarea and the processes under investigation (Gao and Collins, 2001). It isregarded widely that the more samples and the greater the samplingdensity, the more accurate the results. However, the optimum sample

Fig. 10. Regular 30×30 m sampling grid: (a) sediment trend vectors, derived using the settlibetween the original grid (Fig. 6(a)) and the above vectors (a).

density for the establishment of sediment transport pathways isunclear. High density sampling can result in an insignificant improve-ment in the transport pathways, or even introduce noise; this is whenthe analytical error exceeds the natural spatial variation (Gao andCollins, 2001).

4.6.1. Regular sub-samplingThe GSTA directions of the 30×30 m grid are presented in Fig. 10(a).

The general patternofmean, sorting and skewness, producedby the twogrids, is similar; however, some detail has been lost, for all of theparameters. Differences in the spatial distribution of μ are located only atthe extremities of the area. Conversely, differences in σ and Sk areobserved throughout the area. The above deviations influence theabsolute direction differences between the two grids (Fig. 10(b)).Differences can be identified throughout the area sampled, the‘minimum difference’ areas (b10°) are present, but scattered. ‘Smalldeviations’ (b45°) arewidespread in the offshore areas and in the centralpart of the bay. ‘Significant differences’ (N45°) are present mainly tolandward of the structures and throughout the eastern salient features,where the newgridproduces amore intense diffractionpattern than theoriginal grid (Table 2); similarly offshore of the western structure, closeto the gap.

ng velocity analysis; and (b) contour maps showing the absolute difference in degrees,

Table 2The mean sediment transport direction (in degrees, related to the North) obtained fromsettling velocity GSTA, for the different spatial sampling configurations

Station locations a A B C D

15×15 m 23.5 17.1 309.1 357.530×30 m 8.0 32.5 322.7 36.645×45 m – – 339.9 117.5Irregular1 (75%) 8.0 13.0 331.2 18.1Irregular2 (50%) 357.1 9.4 335.9 32.4Irregular3 (25%) 178.0 351.0 339.9 342.9

a For station locations, see Fig. 3.


Comparison between the results of the 45×45 m and the originalgrid (Fig. 11) was undertaken only landwards of the breakwaters; thisis because the grid spacing did not result in an adequate number ofsamples being available to seaward of the breakwaters. Differences inthe transport pathways are increased, in comparison with the30×30 m case (Fig. 10); areas of ‘minimum differences’ have beenreduced. Certain features of the sediment parameters have been lost,due to the sparse sampling. However, once again the general onshoresediment transport of the original grid is maintained over themajorityof the area. Greater deviations are observed throughout the landward

Fig.11. Regular 45×45m sampling grid: (a) sediment trend vectors, derived using the settlingthe original grid (Fig. 6(a)) and the above vectors (a).

area where all transport directions present a stronger westwardcomponent (Fig. 11) in comparison with the original grid that is, mostprobably, indicate the influence of the peak tidal currents (Fig. 8). As aresult, over the eastern salient the diffraction pattern was notreproduced (Table 2).

Transport pathways have been established not only between the15 m neighbouring samples, but also between those at 30 m and the45 m. The main characteristics of the vector field (i.e. onshoresediment transport and vector deflection towards the salients) arereproduced; this indicates that the transport trends reveal a strongsignature in the sediment parameters. Any observed differences are inresponse to the altered spatial sediment distribution information.Samples located farther away within the systemmay be influenced bylarger spatial-scale processes; these are masked on a finer samplinggrid. The angle differences produced are not due to scaling, becausethe grid was resampled on the 15×15 m basis, for all of the sedimentparameters. The absence of any angle differences less than 10°, in bothcases, shows that the interpolation procedure did not estimate themissing sediment parameters at a satisfactory level. As a result, thederived transport vectors differed from those produced using theentire dataset. In both cases, greater differences were observed overthe eastern part of the sampling area; this suggests that, even in such

velocity analysis; (b) contourmaps showing the absolute difference in degrees, between


small sampling area sediment transport processes can be associatedwith different spatial scales.

4.6.2. Irregular sub-samplingFor the irregular sub-sampling of the sample locations, the transport

vectors of the 75% sampling grid, together with the absolute angle

Fig. 12. Irregular sampling grid, using 75% of the total sample stations: (a) the sampled st(c) contour maps showing the absolute difference in degrees, between the original grid (Fig

differences with the original 15×15 m grid, are presented in Fig. 12. The110 samples reproduce all the patterns of the original vectorfield (Fig. 6a),these show a clear onshore sediment transport and different diffractiondirections (Table 2). Small angle differences between the twogrids extendovermost of the study area, together with some scattered patches of zeroangle difference. Larger differences are limited to isolated points only.

ations; (b) sediment trend vectors, calculated using the settling velocity analysis; and. 6(a)) and the above vectors (b).


As the number of sampling points decreases, the areas ofsignificant angle difference increase becoming more pronouncedwithin the overall study area. The 50% irregular grid (Fig. 13) produces


a field of vectors similar to the 30×30 m regular grid (Fig. 10).Transport pathways have a stronger deflection towards the salient andsimilar angle differences (Table 2). Note that the irregular grid was



created taking into account 73 sediment samples, instead of the 43samples that were used in the regular grid.

For the random distribution of 25% of the samples, the GSTAproduces different patterns; this is related particularly to the offshore


areas, with a complete reversal of the transport vector, over some ofthe areas (Fig. 14). In this case, the samples selected are too limited, fora successful interpolation of the original sediment parameters.Landward of the breakwaters, the angle differences increase, in



comparison with those of the other irregular grid, especially over thearea of the gap; this is due to an increase in the westward componentof the sediment transport pathways, over the landward area. Theresultant sediment transport pathways, with large differencescompared with the net sediment transport calculated based uponthe wave and current field data, may be influenced by the largerspatial-scale sediment transport processes (induced by the peak tidalcurrents that flow westwards over the area).

The net transport directions, for both the regular and irregularsampling, are summarised in Table 2. The same ‘analysis of variance’and ‘multiple comparison test’, as above, were used to examine thesignificant differences in sediment transport directions obtained usingGSTA, on the basis of the various sampling strategies. Within the gapand the area to seaward, no significant differences were identifiedbetween the original grid (15×15 m regular sampling) and the rest ofthe grid sampling strategies. An exception was the irregular samplingwhich utilised 25% of the original data; here, significant differenceswere identified. In the areas in the vicinity of the western salient, theoriginal directions were significantly different from those produced byall the other grids (apart from the 75% irregular). As the number ofsamples decreased, the transport directions deviated more from theones obtained using the hydrodynamic data. At the same time, theeastern salient showed significant differences with the regular grids;these differences were non-significant for the irregular ones. The goodagreement of the 50% and 25% results, with the original, over thissensitive area of the eastern salient, could be that processes withsmaller spatial scales can be better resolved with random sampling.

5. Conclusions

The results of the present study demonstrate that the GSTAproduces meaningful sediment transport pathways. The sedimenttrends inferred by the method follow a diffraction pattern; this is aprocess representative of the landward side of the breakwaters. Thelocalised morphological characteristics of the coast (i.e. the presenceof salient features) support the above results.

Settling velocities derived sediment distribution parameters thatproduced net transport pathways directions with differences of lessthan ±15°; these compare with those calculated (empirically) on thebasis offieldmeasurements. Sediment transport directions establishedon the basis of half-phi parameters produce improved results, over thatof the quarter-phi. The settling half-phi differences were notsignificant, statistically, for all of the stations; in contrast, thequarter-phi produced significant differences. For the landwardstations, in particular, the sediment trends established on the basisof settling velocities produced improved estimations, for the case ofopposing (eastern breakwater) and coinciding (western breakwater)wave and current directions. The poor performance of the quarter-phiresolutions, in comparison with those of the half-phi, is not consideredto be due to the increase in noise related to the smaller class intervalsbetween the sieves; but rather to the imbalance between the resolutionof the coarse and the fine fractions of the sediment samples (especiallyfor the fine sands). For the coarser sand sizes, the predicted transportvectors revealed by the twomethods do not differ substantially. Such animbalance produces errors in the calculation of sorting and skewnesswhich, in turn, influence the accuracy of the GSTA. The accuratecalculation of the higher-order sediment parameters (i.e. skewness andsorting) depends upon the resolution of the grain size distribution. Therelative benefits in using settling velocity is that it results in a practicallycontinuous distribution of the grain population within the sample incontrast to sieving that provides discrete forms of grain size distribu-tions. The sediment transport pathways inferred from the trend analysisare sensitive to the methodology and the accuracy on which thestatistical parameters were calculated.

Furthermore, the utilisation of settling velocities could be ofconsiderable importance for GSTA, especially in the case of sediment

grains with different densities and shapes, e.g. sediments with highpercentages of calcareous material; such materials produce a grainsize distribution curve that is the result, not only of the grain diameter,but also of the shape, density and hydraulic behaviour of the grains.These characteristics are important, since they provide the implicitinclusion of any grain shape and density effects, which influenceincipient motion (Collins and Rigler, 1982; Komar and Clemens, 1986;Paphitis et al., 2002) and subsequent sediment transport.

Sampling density has been shown to be an important factor in thecorrect estimation of grain size trends; especially in limited areas withhigh spatial hydrodynamic variability, such as a coastal area protectedwith structures. The sampling spacing selected must be capable ofrepresenting all of the different sedimentary patterns. For all of themethods used in the present investigation dominant transportdirection was onshore. The results of utilising most of the gridsprovided the same onshore component and diffraction patterns,supporting the calculated sediment transport pathways. This conclu-sion proves that the computed directions were not dependent uponparticular samples; rather, they were governed by the general spatialvariation in the sediment parameters. Hence, sub-sampling usingdifferent grid spacing, can be used to validate the original results;likewise, as a method of evaluating the spatial scales of the sedi-ment transport processes. However, such a test can only assess thegeneral direction of sediment since localised differences could bepresent.

Any directional differences, between the various sampling den-sities, could be due to processes with different spatial scales which arenot sampled adequately, or to noise introduced by the dense sampling(Gao and Collins, 2001). In order to distinguish between thesecontrolling factors, an independent method for the estimation ofsediment transport directions (such as the field measurements anduse of empirical formulae, as used in the present study) should beadopted as a means of verification.

Acknowledgements

The authors wish to thank Alex Bastos, Melinda Engleton, AndrewSymonds and Tim Poate for their help in some parts of the field andlaboratory work. Thanks are also due to Roger Spenser (Arun DistrictCouncil) for providing bathymetric data and background informationfor Elmer. This study was performed within the framework of theEuropean Union project EVK3-CT-2000-41, Environmental DEsign ofLOw-crested coastal defence Structures (DELOS). The contribution ofthe two anonymous referees is greatly acknowledged.

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