MESOSCALE BEHAVIOUR OF LONGSHORE BARS – NET ONSHORE OR NET OFFSHORE MIGRATION

Troels Aagaard1 and Aart Kroon2

1. Department of Geography, University of Copenhagen, Oster Voldgade 10,

DK-1350 Copenhagen K., Denmark. taa@geogr.ku.dk 2. Department of Geography, University of Copenhagen, Oster Voldgade 10,

DK-1350 Copenhagen K., Denmark. ak@geogr.ku.dk

Abstract: The aim of this study is to compare long-term (30 yr) bar migration characteristics at two field sites on the Danish North Sea coast. One site displays systematically onshore migrating bars (Skallingen) while the bar migration at the other site (Vejers) is systematically offshore. Using cross-shore profile data and a sediment transport model, the paper discusses the mechanisms that cause divergent longshore bar behaviour at the two sites. The main reason for the difference appears to be larger undertow speeds at Vejers, caused by a steeper outer shoreface and a larger bar relief, leading to breaking wave reformation between bars.

INTRODUCTION With the emergence of data sets on long-term profile change in e.g. the Netherlands and on the East coast of the US, it has been realized that multiple bar systems often display a tendency towards a systematic offshore migration of individual bars. Observations of such systematic seaward bar displacements were reported by Kroon (1990) and Wijnberg and Terwindt (1995) off the Dutch coast. Similar offshore migration tendencies were observed at Duck, N.C. (Plant et al., 1999) and in New Zealand (Shand and Bailey, 1999). The characteristics of the offshore bar migration cycle are similar at most sites. Longshore bars are formed close to the shoreline, they oscillate back and forth in the inner surf zone for a few years and then they begin to migrate consistently offshore. In water depths of 4-7 m, the migration cycle slows down and stops, subsequent to which the bars decay and eventually disappear. The return period for the bar migration cycle ranges between 1-13 years for the different study sites (Ruessink and Terwindt, 2000; Ruessink et al., 2003).

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The onset of offshore bar migration is probably related to the decay of the outermost bar in the system. When the outer bar decays, larger wave heights are allowed further into the surf zone. This causes increased speeds of the undertow under breaking waves across the inner bars and hence increased rates of offshore sediment transport on those bars. However, the reasons for the offshore bar decay are not known and the relationships between the bar migration cycle and coastal sediment budgets are poorly understood. The offshore bar migration cycle should lead to a sediment loss from the beach and an erosion of the shoreline. This does not appear to be the case. Consequently, it has been suggested that there may be a recycling of the sediment within the bar system such that the sand from the outermost decaying bar is transported landward during the decay process (Ruessink and Terwindt, 2000). Alternatively, the bar migration may be only a translation of the form with no sediment transport involved. Not all multiple bar systems display a net offshore migration. Net onshore migrating bars were observed within a multiple-barred system at Skallingen, Denmark (Aagaard et al., 2004a). At this site, longhore bars originate in water depths of 3.5-4 m, migrate onshore through the surf zone and finally weld with the beach face. The onshore bar migration is consistent with measurements of sediment transport which is onshore directed across the bars during storm conditions (Aagaard et al., 2002). A short distance north of Skallingen, at Vejers on the exposed Danish North Sea coast, the longshore bars migrate offshore in the long term. The aim of this paper is to conduct a comparative study of the two sites at Skallingen and Vejers using long-term profile data and a recently proposed sediment transport model (Aagaard et al., 2002) in order to analyze the mechanisms that cause divergent longshore bar behaviour at the two sites. Additionally, the relationships between the bar migration cycles and the sediment budget at the two sites will be addressed. FIELD SITES The two sites are both located on the Danish North Sea coast at either side of the submerged shoal of Horns Rev which is a Saalian terminal moraine and the two sites are separated by a distance of approximately 25 km (Figure 1). Horns Rev is attached to the cuspate foreland of Blaavands Huk which acts as a natural groyne to the southerly littoral drift along the North Sea coast. The Horns Rev shoal significantly affects the two sites. Vejers is located updrift of the shoal and there is a large influx of sand from more northerly sources through the southerly directed littoral drift. According to the Danish Coastal Authority (DCA, 2001), the annual supply of sand to the beaches around Vejers is on the order of 2.3 million cubic meters per year (Table 1) due to a negative littoral drift gradient north of the shoal. Even though there is no doubt that the cuspate foreland at Blaavands Huk has been built up by the littoral drift, the shoreline at Vejers is currently almost stable. In contrast, Skallingen is located to the south of the shoal with a positive littoral drift gradient and the shoreline is receding by about 4-5.5 m/yr on average.

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Figure 1. Map of the study area at the Danish North Sea coast. The two field sites at Vejers and Skallingen are separated by the submerged shoal of Horns Rev.

The annual (southerly directed) net littoral drift at the southern end of Skallingen has been estimated at about 0.6 million cubic meters per year, which is approximately similar to the annual sediment loss from the barrier (Table 1). There is no or very little sediment moving across the Horns Rev (DHI, 2002) because the shoal acts as a wave guide. Because of the shoreline exposure and the location of the shoal, the two sites are also exposed to different hydrodynamic boundary conditions. The mean annual significant offshore wave height is 1.2 m at Vejers, and 1.0 m at Skallingen and the mean spring tidal range is 1.2 and 1.8 m, respectively (Table 1). Low swell frequently occurs at Vejers whereas that is not the case at Skallingen.

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Table 1. Environmental boundary conditions and morphological characteristics at Vejers and Skallingen

Vejers

Skallingen

Mean annual Hs, m

1.2

1.0

Mean spring tidal range, m

1.2

1.8

Net annual littoral drift*, m3 x 106

2.3

0.6

Mean slope, upper shoreface

0.006

0.006

Modal beach state

Intermediate

Dissipative

*The net littoral drift is directed towards the south. Numbers are based on DCA (2001) for Vejers and Aagaard et al. (2004b) for Skallingen.

As Skallingen is located at the head of the bight formed by Horns Rev and the Wadden Sea barriers further south, it often experiences severe storm surges during which the mean water level may reach approximately 4 m DNN (Danish Ordnance Datum). Surges at the more exposed site at Vejers are considerably smaller. Figure 2 illustrates the cross-shore profiles and mean sediment grain sizes at the two sites. Both profiles are typically triple-barred. The mean grain size on the upper shoreface at Vejers is about 180 microns with sediments at bar crests being slightly coarser. The mean grain size is finer at the lower shoreface, about 110 microns. At the crest at the outermost bar, at x ≈ 1200 m, the grain size is much coarser, 520 microns, suggesting a local winnowing of the sediment. Similar grain sizes occur at Skallingen even though bar crest sediments are slightly finer than at Vejers and there is no evidence of winnowing. As a result, the mean upper shoreface slope is similar at both sites, β = 0.006 and the seaward slopes of the bars are also similar, β ≈ 0.025. However, the bars are much larger at Vejers where the bar relief is often up to 3 m whereas it is < 1 m at Skallingen. As a consequence of the deeper troughs at Vejers, waves tend to break through plunging at bars and reform between the bars and the modal beach state is intermediate, while it is dissipative at Skallingen where continuously spilling breakers tend to occur across a wide surf zone. LONGSHORE BAR BEHAVIOUR Figure 3 illustrates the profile evolution at DCA Line 6170 at Vejers during the period 2002-2006. Four bars appear in the profile: A small inner bar very close to the shoreline, a larger middle bar at x = 1400-1500 m, a very large outer bar at x = 1700-1800 m and a broad, low-relief fourth bar in a water depth of about 5 m. In the course of one year (2005-2006), the middle and outer bars both migrated about 60 m offshore and increased in size whereas the fourth bar decreased in size as the crest and landward slope eroded.

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80160240320400480560

mean grain

size (m

m x 10

-3)

Vejers (Line 6170)Skallingen (Line 6420)

Figure 2. Cross-shore profiles at Vejers and at Skallingen. Mean grain sizes across the shoreface are plotted.

It is likely that this bar had entered the state of decay which is consistent with the indication of winnowing of the sediment (Figure 2). A similar plot for DCA Line 6420 at Skallingen is shown in Figure 4 for the years 1994, 1995 and 1996. In 1994, the shoreface was double-barred with longshore bars at x = 150 m and x = 300 m. Within the following year, a trough was eroded at x = 400 m with a new bar forming further seaward. The two existing bars remained stable in position. During the period 1995 to 1996, all three bars migrated between 50-100 m onshore.

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Figure 3. Cross-shore profile evolution 2002-2006 at Line 6170 at Vejers.

To provide a longer-term perspective, bar crest positions in Lines 6200 and 6420 are plotted in Figure 5 for the periods 1969-2002 and 1969-1998, respectively. At Vejers, the bars originate at the shoreline and subsequently migrate offshore at average speeds of 45-55 m/yr and they decay approximately 800-900 m from the shoreline in water depths of 5.5-6 m. In 2006, the outermost bar in the profile (Figure 3) had almost reached this position. The duration of the bar migration cycle is in the order of 15 years. If the

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Figure 4. Cross-shore profile evolution 1994-1996 at Line 6420 at Skallingen. seaward migration of the bars at Vejers involves a net cross-shore transport of sediment, the bar size and the migration speed correspond to a mean annual loss of about 50 m3/m from the beach. However, the surveys indicate that the shoreline and the dunes are weakly accreting by about 6-7 m3/m/yr and the 8 m depth contour, representing the limit of the outer shoreface is moving slightly landward, ≈ 3 m/yr (Figure 5). Thus, there is no evidence for any significant sediment loss from the beach to the shoreface. At Skallingen, longshore bars originate in water depths of 3-4 m and they migrate onshore with speeds of 20-30 m/yr (Figure 5). When the bars enter the intertidal zone, they become dissected by rip channels which initiate cell circulations with onshore directed mean currents across the bars and rip currents in the channels (Aagaard et al., 2004a). This circulation forces the bars further onshore and they finally weld to the beach face. The bar cycle return period is in the order of 8 years, corresponding to a net onshore directed sediment supply of 6-7.5 m3/m/yr. The 5 m depth contour is translating landward at an average rate of 8-17 m/yr, probably in response to a loss of sand from the

1970 1980 1990 2000year

1000

1500

2000

2500

3000

3500

4000

dist

ance

from

bas

elin

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Figure 5. Bar crest positions (dotted lines and crosses) and positions of the shoreline (0 m) and upper/lower shoreface boundary at DCA Lines 6200 and 6420. Distances are given relative to the DCA baseline.

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shoreface, associated with the onshore migrating bar forms. However, there is again a mismatch between the inferred direction of sediment transport and the movement of the shoreline. The mean rate of shoreline recession is 4-5.5 m/yr with brief interruptions to the long-term trend when longshore bars are welding (Figure 5). The main reason for the shoreline recession is the longshore sediment loss which currently far exceeds the onshore supply of sand (Aagaard et al., 2004b). WAVES, CURRENTS AND SEDIMENT TRANSPORT The causes for the different profile response were investigated by running a wave transformation model across representative shoreface profiles at the two sites. The model selected is the well-validated Battjes-Janssen model (Battjes and Janssen, 1978) which was recently assessed in detail for field conditions by Grasmeijer and Ruessink (2003). The selected profiles are depicted in Figure 2: Line 6170 in 2005 at Vejers, and Line 6420 in 1995 at Skallingen. The model is run for two representative (high energy) wave conditions; a westerly storm and a northwesterly gale. The storm event was large but not extreme and it occurred on January 8-9, 2005. The mean significant wave height in deep water was 3.5 m and 3.3 m at Vejers and Skallingen, respectively and zero-crossing wave periods were 7.3 s and 7.6 s. The angle of deep-water wave incidence was 180 and 280, respectively. Mean surge heights were 0.5 m at Vejers and 1.5 m at Skallingen.

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Figure 6. Wave height transformation and undertow speeds across the shoreface at Vejers and Skallingen during storm events..

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Model outputs of rms wave height and undertow speed across the shoreface are plotted in Figure 6. Due to the steeper outer shoreface at Vejers, wave energy dissipation across the bars is more intense, particularly across the large outer bar. The wave transformation model predicts reformation of the breaking waves between bars. At Skallingen, the gently sloping outer shoreface results in much more gradual wave height decay and the waves lose energy across a wide surf zone with no reformation between bars, in accordance with visual observations. The different patterns of wave transformation result in different speeds of the offshore directed mean currents at the two sites. The predicted undertow is up to −0.25 m s-1 on the upper shoreface at Vejers (at the outer bar) whereas maximum undertow speeds on the shoreface at Skallingen are only up to −0.15 m s-1 at the inner (intertidal) bar. In addition, it is unlikely that an undertow does occur at the inner bar at Skallingen as cell circulations tend to dominate in the shallow water depths at this position. Figure 7 depicts the model predictions from more moderate wave conditions. The event selected occurred on November 12-13, 2004. The offshore Hs was 2.1 and 1.6 m at Vejers and Skallingen and wave periods were 5.8 and 5.0 s. The angle of wave incidence was close to zero at Vejers and 440 at Skallingen. Mean surge heights were 0 and 0.5 m.

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)

Vejers Line 6170Skallingen Line 6420

Figure 7. Wave height transformation and undertow speeds across the shoreface at Vejers and Skallingen during gale events.

The predicted wave height and mean current characteristics are qualitatively similar to the storm case. Wave dissipation is strong across the large bars at Vejers and much more gradual at Skallingen. Waves reform between the bars at Vejers whereas that is not the

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case at Skallingen. Maximum undertow speeds are almost identical to those occurring during storms conditions. Most numerical models for cross-shore sediment transport predict net offshore transport under breaking waves (e.g. Gallagher et al., 1998; van Rijn et al., 2003) and therefore they cannot be used to assess the differences in sediment transport characteristics at these two sites, because the transport and the bar movement is onshore under breaking waves at Skallingen. Instead, the empirical sediment transport model proposed by Aagaard et al. (2002) is used to evaluate the processes that result in seaward bar migration at Vejers and landward migration at Skallingen. In this model, a non-dimensional sediment transport index, Qd, takes the values between −1 and +1 such that landward sediment transport occurs for positive values of Qd and seaward transport occurs for negative values. If Qd = +1, the suspended sediment transport is completely dominated by the incident waves and hence directed onshore; if Qd = −1, the transport is accomplished completely by the undertow. Qd does not predict the magnitude of the transport, only the directional tendencies of this transport. Qd depends on the non-dimensional parameter, D:

U

psuD rms= (1)

(Aagaard et al., 2002) where p is the cross correlation between instantaneous (cross-shore) velocity and sediment concentration, s is (cross-shore) velocity skewness, urms is orbital velocity magnitude and U is the mean cross-shore current (undertow) speed. As s and particularly p currently cannot be predicted from any numerical model, D was reformulated in terms of more easily predictable parameters and is denoted Γ:

βγ

θtan

)/(2

max

s

rmsbs uhH=Γ (2)

where θmax is the wave-current Shields parameter, computed according to Soulsby (1997), Hs is the local (significant) wave height, hb is the depth of initial wave breaking, γ is the local relative wave height (Hs/h) and β is the local slope. Based on field observations the empirical relationship 752.0026.0 −Γ=dQ (3) was obtained (Aagaard et al., 2002). Eq.(2) contains parameters which are all predicted from the wave transformation model, or that can be obtained from the beach profile. Consequently, Eqs.(2) and (3) were calculated across the profiles at Vejers and Skallingen. The model is only applicable for locally breaking waves (γs > 0.40) and positive (i.e. seaward facing) slopes. For the computation of the Shields-parameter, a

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grain size of 200 microns has been used for Vejers, which represents the average grain size on the three bar crests, whereas 180 microns has been used at Skallingen. Outputs from the sediment transport model for storm conditions are illustrated in Figure 8. The model predicts Qd < 0 across all bars (except at the outermost decaying bar) and hence offshore migrating bar forms at Vejers, whereas Qd > 0 consistently for Skallingen, except for the innermost intertidal bar where cell circulation tends to replace undertow. Hence, the model is in qualitative agreement with longshore bar migration tendencies at both locations.

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Vejers Line 6170Skallingen Line 6420

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Figure 8. Model predictions of non-dimensional sediment transport (Qd), undertow speed (U) and relative wave height across the shoreface at Vejers and Skallingen during storm events. The model predicts two zones of sediment transport convergence at Vejers (at x ∼ 1500 m and 1730 m), both located 65-70 m seaward of the existing bar crests. These convergence zones correspond to positions towards which bar crests should tend to migrate. No sediment transport convergence zones are predicted for Skallingen (except in the intertidal zone) and the bars are predicted to migrate consistently onshore during storms, in agreement with observations.

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The reason for the different (predicted) behaviour at the two sites during storms is mainly due to larger undertow speeds at Vejers (Figure 8). Model predicted undertow speeds are slightly smaller than predictions from the Battjes-Janssen model (Figure 6), U = −0.21 m s-1 at Vejers and U ∼ −0.10 m s-1 across the bar crests at Skallingen. Undertow speeds are larger at Vejers because of larger relative wave heights across bars, which are caused by 1) the smaller energy dissipation across the relatively steep outer shoreface, and 2) the reformation of breaking waves in troughs between bars. Figure 9 depicts the model predictions for the moderate gale case. The sediment transport tendencies are identical to the storm case, but the zone of active wave breaking has narrowed and the model is applicable only to the inner parts of the profiles. The predicted points of sediment transport convergence on the bars at Vejers have moved slightly onshore because of the smaller wave heights but they are still located on the seaward slopes of the bars and the bars should still tend to migrate offshore at this site.

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Figure 9. Model predictions of non-dimensional sediment transport (Qd), undertow speed (U) and relative wave height across the shoreface at Vejers and Skallingen during gale events. DISCUSSION AND CONCLUSIONS The long-term behaviour of longshore bars is very different at Vejers and Skallingen. At Vejers, longshore bars move offshore in the long term, whereas the opposite is the case

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at Skallingen where longshore bars move onshore under breaking waves. The empirical sediment transport model used here suggests that the main reason for this difference is the larger undertow speeds at Vejers during breaking wave conditions. During storms, the offshore sediment transport caused by the undertow exceeds the onshore sediment transport due to incident wave skewness while the reverse situation occurs at Skallingen. The larger undertow speeds at Vejers occur because a): The lower shoreface is steeper which allows larger waves to reach the upper shoreface and, in particular, b): The bars are much higher and larger at the intermediate beach at Vejers than they are at the dissipative site at Skallingen. This causes significantly larger wave energy and hence radiation stress gradients across the bars at Vejers, as well as larger relative wave heights due to delayed wave breaking. The reasons for the larger bar relief at Vejers so far remain speculative because sediment grain sizes are approximately identical at the two sites. There are two factors that are likely to contribute. One is the difference in tidal range. Tidal ranges are larger at Skallingen and tides tend to smear the morphology, producing smaller bars, because of the divergent sediment transport directions within the surf zone over a tidal cycle (Aagaard, 2002). The other likely explanation is the effect of the littoral drift. Vejers receives a large longshore supply of sediment due to the negative littoral drift gradient updrift of the Horns Rev. Longshore sediment transport occurs primarily on bars which then intuitively should accrete as a consequence of the sediment deposition. At Skallingen, the situation is the opposite. Because of the positive littoral drift gradient south of the Horns Rev, the beach erodes and the bars are starved of sediment, leading to smaller-relief features. The littoral drift gradients are also the likely explanation for the mismatch between the cross-shore sediment transport direction and the long-term profile behaviour at the two sites. The beach at Skallingen recedes even though longshore bar migration (and sediment transport during storms) is landward directed. This is because the longshore loss of sediment far exceeds the onshore supply through the onshore migrating bars (Aagaard et al., 2004b). At Vejers, the beach and dunes are accreting even though bar migration is offshore. It is likely that the longshore supply of sand is an essential factor in this behaviour. The sediment transport model predicts onshore directed transport across the outermost decaying bar at Vejers (Figure 8) and the lower shoreface is not accreting (Figure 5). Hence, it does not appear that the sand supplied through the offshore migrating bar forms is permanently deposited in the profile at Vejers. Research is ongoing in order to close the sediment budget and to ascertain whether the offshore bar migration at Vejers indeed does involve a net transport of sand.

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ACKNOWLEDGEMENTS This work was funded by the Danish Research Council, grant no 272-05-0415. We gratefully acknowledge permission to use the Danish Coastal Authority profile data. REFERENCES Aagaard, T., 2002. Modulation of surf zone processes on a barred beach due to changing

water levels. Journal of Coastal Research, 17, 25-38. Aagaard, T., Black, K.P. and Greenwood, 2002. Cross-shore suspended sediment

transport in the surf zone: a field-based parameterization. Marine Geology, 185, 283-302.

Aagaard, T., Davidson-Arnott, R.G.D., Greenwood, B. and Nielsen, J., 2004a. Sediment supply from shoreface to dunes: linking sediment transport measurements and long- term morphological evolution. Geomorphology, 60, 205-224.

Aagaard, T., Nielsen, J., Jensen, S.G. and Friderichsen, 2004b. Longshore sediment transport and coastal erosion at Skallingen. Danish Journal of Geography, 104, 5-14.

Battjes, J.A. and Janssen, J.P.F.M., 1978. Energy loss and set-up due to breaking of random waves. Proc.16th Int. Conf. on Coastal Eng., ASCE, New York, pp.570-587. DCA, 2001. Sedimentbudget – Vestkysten. Report, Danish Coastal Authority, Lemvig, 54pp. Gallagher, E.L., Elgar, S. and Guza, R.T., 1998. Observations of sand bar evolution on a natural beach. Journal of Geophysical Research, 103, 3203-3215. Grasmeijer, B.T. and Ruessink, B.G., 2003. Modeling of waves and currents in the nearshore parametric vs. probabilistic approach. Coastal Engineering, 49, 185-207. Kroon, A., 1990. Three-dimensional morphological changes of a nearshore bar system

along the Dutch coast near Egmond aan Zee. Journal of Coastal Research Special Issue 9, 430-451.

Plant, N.G., Holman, R.A., Freilich, M.H. and Birkemeier, W.A., 1999. A simple model for interannual sandbar behaviour. Journal of Geophysical Research, 104, 15755-15776.

Ruessink, B.G. and Terwindt, J.H.J., 2000. The behaviour of nearshore bars on the time scale of years: a conceptual model. Marine Geology, 163, 289-301.

Ruessink, B.G., Wijnberg, K.M., Holman, R.A., Kuriyama, Y. and van Enckevort, I.M.J., 2003. Intersite comparison of interannual nearshore bar behaviour. Journal of Geophysical Research, 108(C8), 3249.

Shand, R.D. and Bailey, D.G., 1999. A review of net offshore bar migration with photographic illustrations from Wanganui, New Zealand. Journal of Coastal Research, 15, 365-378.

Soulsby, R., 1997. Dynamics of Marine Sands. Thomas Telford, London, 249pp. Van Rijn, L.C., Walstra, D.J.R., Grasmeijer, B., Sutherland, J., Pan, S. and Sierra, J.P.,

2003. The predictability of cross-shore bed evolution on sandy beaches at the time scale of storms and seasons using process-based profile models. Coastal Engineering, 47, 295-327.

Wijnberg, K.M. and Terwindt, J.H.J., 1995. Extracting decadal morphological behaviour from high-resolution, long-term bathymetric surveys along the Holland

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coast using eigenfunction analysis. Marine Geology, 126, 301-330.

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