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Application of the equilibrium planform concept to natural beaches in Northern Ireland
Coastal Engineering 57 (2010) 112–123
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Coastal Engineering j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c o a s t a l e n g
Application of the equilibrium planform concept to natural beaches in Northern Ireland Derek W.T. Jackson ⁎, J. Andrew G. Cooper Centre for Coastal and Marine Research, School of Environmental Sciences, University of Ulster, Londonderry, BT52 1SA, Northern Ireland, UK
a r t i c l e
i n f o
Available online 31 October 2009 Keywords: Equilibrium planform concept Embayed beaches Beach stability Wave diffraction point North Ireland
a b s t r a c t The equilibrium planform concept (EPC) for bayed beaches has achieved wide currency in coastal morphodynamics. The north coast of Ireland comprises a series of discrete headland-embayment beaches within which waves and currents recycle a finite sediment volume. It is therefore an ideal setting in which to explore the applicability of the concept. Application of the approach to 9 embayment beaches on the north coast of Ireland provides some insights into the application of the concept. The planform of some beaches does correspond to that predicted while others do not. Those whose measured planform does not correspond to the predicted planform can be interpreted through, (a) difficulty in identifying the wave diffraction point, (b) disequilibrium on the beach (sediment scarcity or excess), (c) geological control of beach morphology. The subjectivity in selecting the diffraction point renders alternative explanations difficult and reduces the utility of the approach on natural shorelines, where significant irregularities render identification of such points difficult. © 2009 Elsevier B.V. All rights reserved.
1. Introduction The concept of equilibrium shoreline planform has achieved wide currency in coastal morphodynamics (Bremner, 1983, LeBlond, 1979; Klein and Menezes, 2001) and coastal engineering (Silvester, 1960; Moreno and Kraus, 1999). The concept makes a number of assumptions and a number of formulations have been presented (Yasso, 1965; Silvester, 1974; Hsu and Evans, 1989; Hsu et al., 1987; Hsu et al., 1989a,b; Hsu et al., 2000) that relate shoreline position to distance from an origin related to a physical or dynamic location. Various types of equilibrium are represented in examining planforms of bay shaped beaches ranging from ‘dynamic’ where there is a constant throughput of sediment maintaining beach stability to ‘static’ in cases where updrift sediment supply may cease/reduce and shorelines are restricted to a static position. Static equilibrium models are deemed useful in that they represent a convenient yardstick with which to ascertain a particular shoreline's current stability status. An assessment of the static model most suitable in real world conditions has been examined by Hsu et al. (1987) and Hsu and Evans (1989) where a model based on spiral logarithm (Yasso, 1965; Silvester, 1970a,b and others) was tested. The log-spiral model was shown to have limitations in terms of its reach to the outer margin of the equilibrium bay and as a result an alternative parabolic model was suggested (Hsu and Evans, 1989). The parabolic bay shaped model is now the most widely adopted approach to understanding the stability of headland bay beaches with Hsu et al. (2004) eventually defining a methodology for stability. Detailed assessment of its usefulness and applicability can be found in Gonzalez and Medina (2001) and Klein et al. (2003a,b).
⁎ Corresponding author. Tel.: +44 28 70323083; fax: +44 28 70324911. E-mail address: [email protected] (D.W.T. Jackson). 0378-3839/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.coastaleng.2009.09.007
Some limitations in the model have, however, been highlighted by Gonzalez (1995) including: prediction inaccuracies close to an estuary mouth (from dominant tidal dynamics); inability to predict effect of nearshore islands as well as uncertainties in defining downcoast limits and end points. Gonzalez (1995) does attempt to remedy some of these by proposing a semi-empirical model. Even with the additional proposed model, limitations were still evident with the beach systems having to conform to the following criteria: • Assumption that wave height gradients are controlled only by the diffraction point of the control point. Other diffraction from local islands and bathymetric anomalies cannot be represented. • Non-wave induced currents (tidal) cannot be taken account of and therefore are assumed not to exist. • A single point of diffraction should exist in the bay. Other diffraction points (control points) are assumed not to exist and therefore are not interacting with the beach sediments. • Intuitively, the availability of sediment and local geological framework over which the sediment lie must also be important factors. In this paper we apply the Hsu and Evans (1989) approach to 9 embayment systems on the north coast of Ireland in order to investigate its utility and interpretation. The north coast of Northern Ireland is an ideal location in which to test the approach on natural beaches given its strongly embayed beach systems and finite sediment volume. 2. Environmental setting Ireland has a 6500 km-long, bedrock-framed coast located between 52 and 55oN (Fig. 1). Large-scale coastal plains are not present and coastal sediments usually occur as a series of headland-embayment beaches or occasionally as barriers at estuary mouths (Jackson et al.,
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Irish seaboard (Devoy, 2000). Through its northern positioning the study site still experiences a high-energy wave climate regime with large-scale refraction taking place around the northwest peripheries of Ireland's open Atlantic coast. More specifically, wave energy varies from high (mean significant breaking wave height Hb, 2.18–2.52 m: Magilligan to Whitepark Bay) to moderate (1.8–1.36 m: Ballycastle to Redbay), as seen in Table 1. The beach systems examined are situated around the northern coastline of Northern Ireland over a distance of approximately 100 km. Tidal range along this total stretch of coast falls into the microtidal category, ranging from 0.9 m in the southeast to 1.6 m in the northwest.
3. Beach morphology
Fig. 1. Location map of embayment beach systems around the NE coast of Northern Ireland.
2005). The distribution and variable sediment composition of beaches and barriers in paraglacial settings may be explained in large part by glacial inheritance (FitzGerald and Rosen, 1987). Ice limits in Ireland during deglaciation have largely constrained contemporary coastal geomorphology and dynamics in that they are associated with major sediment sources. Areas positioned close to ice limits tend to possess sandy barriers, the sand having been deposited initially by outwash and subsequently reworked by marine processes (Cooper, 2007). Sediment supply on the Northern Ireland coast occurs predominantly from reworking of shelf sands (themselves of glacial origin) (Cooper et al., 2002), and locally from erosion of bluffs of glacial sediments (Carter, 1991). Coastal sediment supply is therefore strongly related to patterns of ice movement, stabilisation and decay during the last glacial cycle. Sediment has been driven into embayments that are now separated by a sediment-deficient seabed such that each headland-embayment cell contains a finite sediment volume. Longshore sediment exchange between cells is minimal and contemporary sediment supply from other sources (rivers and primary productivity) is similarly low. Only along the northeast Antrim coast is there much sediment yield from river sources. Ireland intersects the main conduit of North Atlantic cyclones, experiencing the maximum impact of Atlantic swell waves and storm activity on its western rim. Significant deep-water wave heights (Hs) off this portion of coast can reach 15–20 m. The wave energy regime around Ireland (Fig. 2) diminishes eastwards into the Irish Sea region where Hs modal values of between 1.6 and 2 m occur and a reduction in overall wave energy by a factor of 5 take places along the eastern
The majority of the beaches are backed by significant vegetated sand dunes. The morphology of the beaches on this coast was recently categorised by Jackson et al. (2005) who compared the observed beach state with predicted states using the Wright and Short (1984) model. The main geomorphological attributes of each beach are described below and morphometric and dynamic details are also listed in Table 1. Magilligan: This 16 km embayment incorporates several major intermediate-dissipative beach complexes including Magilligan– Benone which is backed by an extensive beach ridge plain (Lynch et al., 2009), and Castlerock and Portstewart both of which are backed by extensive dunes. The beach system is confined between the rocky Inishowen peninsula in the west and basalt cliffs at Portstewart in the east. The inlet and ebb delta of the Foyle estuary are located adjacent to the Inishowen peninsula. Waves predominantly travel from the NNW and large-scale wave refraction occurs around the Inishowen peninsula. Wave diffraction may be occurring from a headland in the NW or from the offshore, submerged delta. Jetties are present at the Bann river mouth separating Portstewart and Castlerock and a natural rock outcrop separates Castlerock from Benone to Magilligan. The beach system as a whole is largely stable with no significant erosion or accretion in the historical period. Portrush west: This narrow, intermediate-type beach was formerly backed by dunes that have been heavily modified. Bounded by two rocky headlands in the east and west of the site and is supplied by mainly N/NW wave approaches. A seawall is present along the entire length of the beach (0.9 km) and a harbour was built in the east in the 1800s. Beach lowering and narrowing since the seawall emplacement in the 1960s have been observed (Carter, 1991) and peat is periodically exposed on the foreshore during beach lowering. Portrush east: This 2.8 km-long intermediate-dissipative beach fronts a cuspate dune system and is bounded by two rocky headlands, Ramore Headland in the NW and Whiterocks in the east. The shoreline position is relatively stable in the historical period. The beach is located in the lee of a series of offshore rocky islands, which, together with a prominent headland to the west, affect wave approach. Geophysical investigations have shown there to be a limited sediment supply in the offshore zone at the site (Kelley et al., 2006; Backstrom et al., 2009). Portballintrae: This is a horseshoe-shaped bay located between prominent but low rocky headlands. An existing narrow beach (0.4 km wide) is backed by bluffs of glacial and glacio/marine sediment. Human influence at the site is evident in the form of a pier in the north and a harbour in the SE section of the bay. Extensive beach narrowing has been attributed to alteration of wave patterns by emplacement of a pier in the north (Carter, 1991). Runkerry: This 1.0 km-long beach is underlain by a boulder frame and glacial sediments. It is bounded by two high rocky headlands and the river Bush discharges along the western headland. Sand dunes backing the beach are located on top of glacial till. The beach switches beach state on a seasonal basis (intermediate to dissipative) but on
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Fig. 2. Main wave energy regime around Ireland along with tidal range zones. Note the rapid decline in 50 y wave heights around the north of the island from 30 m in the NW to around 15 m in the NE. Based on Carter (1990) and Orford (1989).
the whole can be viewed as having a stable shoreline position (Shaw, 1985). Whitepark Bay: This 2.2 km-long beach is located between high rocky cliffs and is backed by a dunefield climbing on relict landslides.
The eastern end of the bay is underlain by bedrock at shallow depth and it is periodically exposed on the beach after storms. Semipermanent crescentic bars occur in the nearshore (Carter, 1991). The coastline has been relatively stable historically.
Table 1 Main attributes of selected embayments around NE of Ireland. Site name
Location (Lat. and Long.): centre of beach
Sand grain size (mm)
Beach slope
Length (km)
Tidal range (m)
H0 (mean Hs) m
Beach type
Local geomorphology
Magilligan
55o 10′ 01.94” N 6o 50′ 49.66” W 55o 12′ 08.63” N 6o 39′ 20.16” W 55o 12′ 24.74” N 6o 38′ 04.95” W 55o 12′ 57.03” N 6o 32′ 48.11” W 55o 13′ 20.90” N 6o 310′ 51.36” W 55o 14′ 02.45” N 6o 23′ 41.63” W 55o 12′ 17.78” N 6o 13′ 44.09” W 55o 07′ 38.45” N 6o 02′ 29.11” W 55o 04′ 59.75” N 6o 03′ 19.44” W
0.17
0.0375
16.0
1.6
2.18
Intermediate to dissipative
0.186
0.0320
0.9
1.5
2.34
Dissipative
0.197
0.0352
2.8
1.5
2.34
Intermediate
0.25
0.03
0.3
1.5
2.18
Intermediate
0.28
0.0329
1.0
1.5
2.18
Intermediate
Extensive dune systems, tidal inlet, sand ridge plain Modified dunes, human modification along coastline Convex, extensive dune system, offshore islands Beach backed by glacial unconsolidated sediments, human modification Large sand dunes, rive mouth
0.229
0.0350
2.2
1.2
2.41
Intermediate
Sand dunes
0.634
0.0823
1.2
0.9
2.52
Intermediate
0.397
0.1037
1.0
1.6
1.28
Reflective–intermediate
River mouth, large dunes, human modification Small dunes, river mouth
0.198
0.104
0.4
1.6
1.28
Reflective–intermediate
Portrush west Portrush east Portballintrae Runkerry Whitepark Bay Ballycastle Cushendun Cushendall
Small dunes, river mouth, human modification
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Fig. 3. Static shoreline prediction for Magilligan embayment after diffraction point selected from headland location (image source: NASA images). Note the suggested instability of the coastline in the western section of the site.
Fig. 4. Static shoreline represented after the diffraction point is chosen at the submerged delta in the Magilligan embayment (image source: NASA images). Note close agreement with actual shoreline for the entire length of the embayment.
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Ballycastle: This 1.2 km-long beach is composed of coarse, poorly sorted sand and fine gravel sourced primarily from rivers that dissect relict fluvio-glacial deltas. The beach is confined between high cliffs at each end and is backed by a sand dune system. The close proximity of an amphidromic point results in a low tidal range and this area is transitional between remnants of high-energy Atlantic waves and directly approaching Irish Sea waves (lower energy) originating from the east. Dominant longshore drift to the west results in coastal recession in the east and accumulation in the west at the river mouth (Carter, 1991). Harbour construction (in several phases) in the north of the embayment, channelisation of the Margy River, beach sediment removal and small-scale coastal reclamation adjacent to the harbour have all affected the shoreline morphodynamics. Cushendun: This 1 km-long beach is located in a glaciated valley flanked by bedrock outcrop at both margins. The Glendun River, which enters the sea on the southern margin of the beach supplies the coarse sand and fine gravel that dominate the beach and nearshore. Longshore transport is in a southerly direction toward the river outlet (Carter, 1991). Human interference has manifest itself in the form of dredging and river channelisation in the past, effectively cutting off the linkage between longshore transport of beach material and the Glendun River. Sediment removal from the beach has also occurred in the past with an estimated
30,000 m3 removed over a 30-year period (1960–1990) (Carter, 1991). Historically, this coastline appears to be in a retreating phase. Cushendall: This 0.4 km-long beach is intersected at its southern section by the River Dall. It is located in a glaciated valley and is bounded by high bedrock cliffs. This site had a serious problem of coastal retreat over the period 1903 to 1963 when a 45m shoreline recession was recorded (Carter, 1991) due to sediment removal, resulting in a beach sediment volume deficit. A sea wall installed in 1963 has left a much narrower and lower beach. Wave energy levels in the area are moderate mostly originating from the Irish Sea (East).
4. Application of the planform equilibrium concept The MEPBAY software (Klein et al., 2003b) derived from the EPC for bay beach in static equilibrium (Hsu and Evans, 1989) was used to identify diffraction points on rectified orthophotographs (2004) of beaches along the north coast. In the case of the largest embayment beach (Magilligan), satellite imagery from Google Earth is employed. All images are in a north (top of image) to south alignment. The MEPBAY software (http://siaiacad05.univali.br/~meppe) is used to predict the shoreline position in static equilibrium at each site and the results are discussed below.
Fig. 5. Portrush West Strand and the predicted static shorelines showing close agreement to the existing beach after two diffraction points were selected from a promontory to the west and a harbour end point in the east.
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Fig. 6. Portrush East site showing the multiple diffraction points and corresponding static shoreline positions. Note the presence of the nearby Skerries islands. Close agreement can be seen between predicted and actual shorelines in the western part of the site using part of the western headland while the eastern and western edges of the offshore Skerries islands diffraction points predicts quite close agreement follow an approximate path of the existing salient. Less agreement is evident between actual and predicted shoreline towards the tip of the salient.
Magilligan: At this site, the dominant wave approach is from the northwest and diffraction is therefore likely to be centred on the headland north of the beach. The tidal inlet of the Foyle, however, also provides a potential second diffraction point on the shallowest sections of the ebb tide delta. Consequently both points are selected for simulation of shoreline position. The downdrift end of this 16 km embayment is selected at the eastern edge of Portstewart beach. Fig. 3 shows the result of choosing the main headland as the diffraction point source. The predicted static shoreline is positioned offshore of the actual shoreline, suggesting the coast is an unstable coast, particularly in the western section of the site towards the distal end of the cuspate foreland. Fig. 4 shows the static shoreline prediction when the western edge of the submerged Tunns Bank is selected as a diffraction point. At the resolution of the satellite imagery (15 m pixel size) there is quite close agreement between actual shoreline and predicted static shoreline. East of the River Bann the actual beach is rather landward of that predicted. This can be attributed to the presence of the training walls, which produced some accretion on beaches the west and erosion in the east soon after their emplacement but which now appear to be stable. Portrush west: This embayment has distinctive promontories on both sides of the bay. Selection of both these as diffraction points (Fig. 5) produces a simulated shoreline that is in close agreement with actual shoreline configuration at the present time. Previous work (Carter, 1991) however, has shown historical shoreline changes in response to construction of the harbour (1825), sand removal and seawall construction (1940–1960). The southwest section of the bay retreated by around 80 m between 1825 and 1950 while the northeast sector accreted 80 m during the same period. Thus, while the modern shoreline agrees with the MEPBAY model, the natural shoreline in the southwest part of the bay was 80 m seaward of contemporary shoreline.
Portrush east: The major influence on this beach planform is the presence of a chain of offshore islands (Skerries) and a distinctive promontory (Ramore Head) identification of three diffraction points (Fig. 6) produces a simulated shoreline that matches the actual shoreline in the east and west margins of the beach. The central section comprises a salient that is landward of the predicted shoreline. This is easily explained by the lack of available sediment to attain the predicted morphology. What is more difficult to explain is the fact that the entire western section has retreated by over 100 m since 1834 (Carter, 1991) without having been affected by any engineering works that would have altered the diffraction points. Portballintrae: The eastern side of the bay contains a prominent harbour wall which is an obvious diffraction point. The western headland of this bay comprises a wide, gently sloping, intertidal to subtidal rock platform on which a jetty (Leslie's Pier) was constructed around 1895 (Carter, 1991). Selection of diffraction points on this margin is more problematic since the diffraction point likely migrates across the platform as the tide fluctuates. Selection of three diffraction points (Fig. 7) produces a simulated shoreline that matches quite well the contemporary shoreline in the west; only minor differences in shoreline position are produced by selection of diffraction point on Leslie's Pier and the adjacent rock headland. The eastern part of the bay is quite different in that the predicted shoreline is up to 50 m seaward of the actual position. Interestingly, this bay has shown dramatic shoreline change in the recent past: between 1930 and 1980 more than 100 m of shoreline recession occurred (Carter, 1991). The attribution of this erosion to construction of Leslie's Pier (Carter and Shaw, 1983) is at odds with the simulated shorelines from the MEPBAY model (Note the similarity in the simulated shorelines associated with Leslie's Pier and the natural headland). Runkerry: A variety of diffraction points exist in this bay. Fig. 8 illustrates the shoreline oppositions obtained using three of these. The predicted static planform of the beach matches quite well with the
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Fig. 7. Portballintrae site showing the result of selection of three diffraction points where a simulated shorelines matches quite well the contemporary shoreline in the west while only minor differences in shoreline position are produced by selection of diffraction point on Leslie's Pier and the adjacent rock headland. The eastern part of the bay is quite different in that the predicted shoreline is up to 50 m seaward of the actual position.
actual low water position on the beach (Fig. 8). Interestingly, both of the westerly diffraction points are associated with almost identical simulated shorelines. Whitepark Bay: Several diffraction points were selected either side of the bay, two on the west and one on the eastern sectors. A fairly good agreement is found between the predicted static shoreline and actual low water beach planform (Fig. 9). The predicted static shoreline in the western section of the beach is in better agreement with the actual shoreline when the more landward diffraction point is used. Ballycastle: Ballycastle embayment contains a major harbour (constructed in two phases) and offers the opportunity to test predictions of the shoreline position based on a changing diffraction point. Selecting the diffraction point in Fig. 10(i), at the end of the harbour wall after the first phase of construction, predicts a shoreline broadly similar to the present except in the western margin. Fig. 10(ii) shows the shoreline predicted by a subsequent diffraction point located at the modern outer edge of the existing harbour. Remarkably good agreement between actual and predicted shorelines is clear along the entire beach. The predicted accretion at the western end of the beach is matched by the actual changes recorded by sequential aerial photography. Cushendun: At this site there are two potential diffraction points, one on the natural rock headland to the south of the bay (Fig. 11(i)) and a second at the tip of a jetty at the river mouth (Fig. 11(ii)). The predicted shoreline associated with a diffraction point to the south of the beach displays quite good agreement with the actual shoreline position in the northern section of the beach (Fig. 9). However, in the southern zone where the Glendun River emerges, the actual shoreline
(which rests on exposed bedrock) is seaward of that predicted. When the diffraction point on the end of the jetty is considered the predicted shoreline is even further landward. Cushendall: The southeasterly approach of the dominant wave field prompted selection of a headland diffraction point in the SE of the Cushendall embayment. Quite close agreement is found between the predicted and actual shoreline positions (Fig. 12) with the exception of the southern section of the beach where a river enters the system and the actual shoreline is located seaward of that predicted. This finding was unexpected since the coastline has been retreating at a rapid rate throughout this embayment over the past 100 years (Carter, 1991) and there has been no change in the location of the diffraction point. 5. Discussions The northeast coast of Northern Ireland is a locality in which the historical behaviour of its headland-embayment beaches is well documented (Carter, 1991). The high degree of indentation and isolation of the beaches in distinct embayments reduces longshore influences on beach behaviour and means that each has a wellconstrained sediment circulation operating within fixed boundaries. It therefore offers an ideal location in which to test the applicability of the headland-embayment equilibrium planform concept (EPC) on natural beaches. The results presented here show considerable variability. In several instances quite close agreement was observed between predicted and actual shoreline planform while in others, there was little or no
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Fig. 8. Runkerry embayment which displays a good agreement with predicted static and actual planforms.
agreement. This approach has been used in the past to predict the impact of engineering structures (Hsu and Silvester, 1990; Hsu et al., 1993) and to assess the status of the coastline (Klein et al., 2003a). On the north coast
of Ireland the well documented historical shoreline changes offer the opportunity to set modern and predicted shorelines in their historical context.
Fig. 9. Whitepark Bay site where several diffraction points were selected either side of the bay, two on the west and one on the eastern sectors. A reasonably good agreement is found between the predicted static shoreline and actual low water beach planform. Note that the predicted static shoreline in the western section of the beach is in better agreement with the actual shoreline when the more landward diffraction point is used.
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Fig. 10. Ballycastle embayment where the diffraction point in (i), at the end of the harbour wall after an initial phase of harbour construction, predicts a shoreline broadly similar to the present except in the western margin. Selection of another diffraction point (ii) shows the shoreline predicted by a subsequent diffraction point located at the modern outer edge of the existing harbour. Remarkably good agreement between actual and predicted shorelines is clear along the entire beach. The predicted accretion at the western end of the beach is matched by the actual changes recorded by sequential aerial photography.
At Magilligan, there is an abundant sediment supply which is reflected in the long-term stability of the site. Armed with this knowledge, selection of the ebb delta as an alternative diffraction point provided a simulated coastline that was closer to reality than that associated with diffraction on the adjacent Inishowen headland. It does point to the importance of the ebb delta as a control on the long-term planform stability of the site and therefore enhances the understanding of the coastal form. Conducting the simulation blind (with no prior knowledge of the ebb delta) would however, not have allowed such a proposition to be tested. An alternative approach might have been to fit the curve to the observed shoreline as a means of identifying alternative diffraction points. Selecting the exact position of a diffraction point on a submerged delta is however very subjective. The leading edge of the delta is gently sloping and therefore diffraction may take place in a broad zone dependent on tidal and wave conditions. In this situation where the coast was known to be stable, the shoreline predicted by the equilibrium planform concept (EPC) was similar to that observed. This drew attention to the previously undocumented role of the ebb delta in wave transformation. Previous work confirmed the role of the ebb delta in wave refraction (Carter et al., 1982) but not diffraction. At Portrush west strand the predicted static shoreline using two diffraction points (the headland to the west and harbour to the east) is in close agreement with the contemporary situation. This seems to confirm the role of the harbour in prompting accretion in the east as evidenced by historical shoreline change. In the west however, where the diffraction point has remained fixed, the actual coastline has, however, retreated by 80 m in the past century. The apparent agreement with the contemporary shoreline is most likely due to the need to identify a downcoast limit in MEPBAY which tend to promote agreement. At Portrush east, a convex beach planform generally matches that predicted by selection of multiple diffraction points. The planforms coalesce to form the cuspate feature observed. The eastern shoreline is somewhat landward of that predicted at the confluence of the two
planforms. This could be interpreted as the result of an inadequate sediment supply; the adjacent sea bed is largely sediment poor (Lawlor, 2000; Kelley et al., 2006; Backstrom et al., 2009). The shoreline is known to have been historically stable, suggesting that it is in static equilibrium. This further suggests that the lack of sediment prevents attainment of the theoretical shoreline. At Portballintrae, there is considerable difficulty in selecting a diffraction point on the western side of the bay as the headland is broad and gently sloping in the intertidal and subtidal zone. Sensitivity of predicted shoreline position to the diffraction point location is marked but neither is coincident with the contemporary shoreline. The actual shoreline at Cushendun matches that predicted except in the south where the shoreline is seaward of that predicted regardless of whether the natural rock headland or the river mouth jetty is selected as a diffraction point. This might be due to the effect of the underlying geology (Fig. 11), which if elevated, would cause the sand on top of it to extend further seaward (Jackson and Cooper, 2009). An alternative explanation may be that the river mouth alters the local wave patterns and promotes sediment accumulation. The same is true at Cushendall in the vicinity of its river mouth. While these shorelines appear to be in equilibrium, both beaches are known to have receded in historical times whereas the diffraction point will not have changed. This knowledge of the recorded shoreline changes urges rejection of the conclusion that the beach is in equilibrium as implied by application of the static shoreline concept. 6. Final remarks The EPC provides an explanation of shoreline planform on linear coasts with prominent headlands. It has been used in the past to assess the erosional status of various headland-embayment beaches (Hsu et al., 1993; Klein and Menezes, 2001) through comparison of predicted and actual shorelines. Klein and Menezes (2001) for
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shorelines do not coincide which prompts questions regarding such discrepancy—do they reflect disequilibrium, do they reflect some natural constraint on achievement of idealised equilibrium, or do they reflect inherent subjectivities involved in application of the model? In applying the concept to a range of natural beaches in Northern Ireland we present some observations regarding the practical application of the EPC as a prediction tool for beach planform equilibrium. These observations relate to the following practical aspects of applying the EPC: • Subjectivity in selection of the diffraction point • Temporal variability in location of diffraction point as a result of changing tidal and wave conditions • Subjectivity in selection of downdrift control point (and consequently wave approach angle)
Fig. 11. Cushendun beach where two potential diffraction points are chosen, one on the natural rock headland to the south (i) and a second at the tip of a jetty (ii). The predicted shoreline associated with a diffraction point to the south of the beach displays quite good agreement with the actual shoreline position in the northern section of the beach. However, in the southern zone where the Glendun River emerges, the actual shoreline is seaward of that predicted. When the diffraction point (ii) is considered the predicted shoreline is even further landward.
example identified equilibrium and disequilibrium bays along the south Brazilian coast. The examples described in this paper show various levels of agreement between predicted and actual shorelines on the Northern Ireland coast for which the historic coastal behaviour is well known. This allows the predictive ability of the EPC to be tested. The results presented above show various levels of agreement between shorelines predicted using the MEPBAY software and actual shorelines. In some cases modern shorelines closely match predicted shorelines suggesting them to be in static equilibrium. Several of these, however, (e.g. Portrush west) are known to be experiencing long-term coastal recession which points toward disequilibrium. In some cases, the approach has been a useful tool in identifying unexpected potential influences on shoreline planform (e.g. the ebb delta at Magilligan Point). In other instances the predicted and actual
The subjectivity of the selection of the diffraction point has also been addressed by Lausman et al. (2010-this issue) who demonstrated through blind testing that the operator is strongly influenced by sight of the actual shoreline position. When this was not visible the coincidence of predicted and actual shorelines decreased significantly. The natural variability of coastal systems means that many potential sites could be selected as the diffraction point. This is evident at Magilligan where a better shoreline fit was achieved by selection of the ebb tide delta as a diffraction point rather than the adjacent rocky headland. While this in itself is a useful finding pointing to a previously unexpected role for the ebb delta, it hinders use of the approach in assessing the equilibrium nature of the coast. The coast is known to have been historically stable and consequently our provisional interpretation is that the ebb delta plays a more significant role in wave diffraction than the adjacent headland. Without this local knowledge a different conclusion might have been drawn. In addition, several diffraction points on this coast probably change with the tide, with wave direction and with wave height. The flat, gently sloping rocky headland at Portballintrae is a case in point. Here, the diffraction point at low tide must be several tens of metres distant from that at high tide. A similar scale of displacement is likely associated with differences in wave height. These constraints do not exist in the laboratory or computer models with a vertical headland defining the diffraction point, a monochromatic wave field and uniform sediment size in an unconstrained setting. On a natural beach there may also be more than one diffraction point at any given time. This is evident at Portrush West Strand, Portrush East Strand and Portballintrae where it is clear that diffraction points exist on both sides of the bay. In these cases the full equilibrium planform is not developed and identification of the downdrift control point is therefore inhibited. This is important because of the fixed relationship in the EPC between wave approach angle and the downcoast tangent line (Hsu et al., 1987); misidentification of this downdrift point changes the wave approach angle and vice versa, with consequent implications for the predicted shoreline position. There are also a number of conceptual aspects of beach behaviour that influence the relationship between MEPBAY-predicted and actual shorelines and which influence the utility of the approach in identifying equilibrium and non-equilibrium shorelines. These include: • Reliance on contemporary beach morphometrics as an input • Omission of other dynamic variables (secondary wave motions, tidal and river currents) • Role of underlying geologic framework in shaping seabed (Jackson and Cooper, 2009) • Variability in grain size characteristics On several beaches that are known to be in long-term recession (e.g. Portrush west), the coincidence between predicted and actual shorelines seems puzzling. However, when it is realised that the actual shoreline (i.e. the downdrift control point) forms part of the
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Fig. 12. Cushendall embayment and the predicted static shoreline position using MEPBAY software. Note that overall prediction is good with the exception of the southern section where the River Dall emerges and the actual shoreline is located seaward of that predicted. The coastline at the Cushendall embayment has been retreating at a rapid rate throughout this embayment over the past 100 years (Carter, 1991) whilst the location of the diffraction point is presumed to have remained fixed.
prediction, this coincidence is less surprising. This acts to force agreement between predicted and actual shorelines and limits its predictive capacity. In theory this can be avoided if one has knowledge of the deep-water wave approach direction, but in practice data on wave height, much less direction are rather rare for most of the world's coasts. The equilibrium planform concept assumes that no other processes than wave diffraction influence the coastal planform. Clearly this is not a valid assumption on many natural coasts but from the perspective of interpreting the predicted static shorelines it is an important consideration. On some beaches where the predicted shoreline closely matches the actual shoreline, thereby implying stability, there are known to be large-scale secondary wave motions (viz the crescentic bars at Whitepark Bay). Assuming that the diffraction point has been selected correctly and that the wave approach angle is correct (see above) there are two possible interpretations: a) that the shoreline is stable and secondary wave motions
do not influence it; and b) that the coast is unstable and that its coincidence with the predicted shoreline is caused by circulations that the model does not consider. A similar line of argument applied to situations where the coastline does not match the predicted static shoreline must conclude that the deviation may be due to either a) the operation of dynamics that are excluded by the model, b) shoreline instability through lack of sediment or geological control. As in many conceptual models, no account is taken in the ECP of geological variables (seabed topography and material, sediment supply and type) as a constraint on the dynamic processes (Cooper and Pilkey, 2004; Jackson et al., 2005). In the ECP, coastal behaviour is considered to be unconstrained by geological factors other than the headlands bounding the embayment. This is clearly an invalid assumption on many natural beaches where there may be shallowly buried bedrock or semi-consolidated sediments. In theory, the model may be useful in identifying geological control as a factor causing
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deviation from the predicted static shoreline, as implied at Cushendun and Cushendall where shallow outcrop of glacial till is invoked to explain deviation from the idealised shoreline morphology. Application of the ECP to several beaches along the Northern Ireland coast has been a useful exercise. It has prompted questions regarding the stability of the coast and prompted insights into coastal behaviour that were otherwise unexpected. It has also revealed some natural constraints on achievement of equilibrium through geological factors. Most importantly, it urges caution in the simple use of the ECP to determine whether a shoreline is in equilibrium and prompts users to consider not only the already documented issues concerning the subjectivity of input selection but also the potential for geological, dynamic and sedimentological constraints on shoreline planform development. Acknowledgements Reproduction from the Ordnance Survey Northern Ireland (OSNI) map with the permission of the controller of HSMO© 2006, permit no. 60089. We would also like to thank Kilian McDaid, Drawing Office (University of Ulster) and Euan Dawson (University of Ulster) for help with some of the figures. Thanks are also due to Robert Stewart and Sam Smyth (CCMR, University of Ulster) who helped carry out DGPS surveys and sediment sampling. Helpful and detailed discussion with John Hsu helped improve the paper. References Backstrom, J., Jackson, D.W.T., Cooper, J.A.G., 2009. Shoreface morphodynamics of a high-energy, steep and geologically constrained shoreline segment in Northern Ireland. Marine Geology 257, 94–106. Bremner, J.M., 1983. Properties of logarithmic spiral beaches with particular reference to Algoa Bay. In: McLachlan, A., Erasmus, T. (Eds.), Sandy Beaches as Ecosystems. Proc. 1st Inter. Sym. Sandy Beaches, Port Elizabeth, South Africa, pp. 97–113. Carter, R.W.G., 1990. The Impact on Ireland of Changes in Mean Sea Level. Programme of Expert Studies, Number 2. Department of the Environment, Dublin. pp. 128. Carter, R.W.G., 1991. Shifting Sands: A Study of the Coast of Northern Ireland from Magilligan to Larne. HMSO, Belfast. Carter, R.W.G., Shaw, J., 1983. An eighty year history of shoreline erosion in a small Irish Bay. Shore and Beach 51, 34–37. Carter, R.W.G., Lowry, P., Stone, G.W., 1982. Sub-tidal ebb shoal control of shoreline erosion via wave refraction, Magilligan Foreland, Northern Ireland. Marine Geology 48, 17–25. Cooper, J.A.G., 2007. Geomorphology of Irish estuaries: inherited and dynamic controls. Journal of Coastal Research SI 39, 176–180. Cooper, J.A.G., Pilkey, O.H., 2004. Sea-level rise and shoreline retreat: time to abandon the Brunn Rule. Global and Planetary Change 43, 157–171. Cooper, J.A.G., Kelley, J.T., Belknap, D.F., Quinn, R., McKenna, J., 2002. Inner shelf seismic stratigraphy off the north coast of Northern Ireland: new data on the depth of the Holocene lowstand. Marine Geology 186, 369–387. Devoy, R.J.N., 2000. Implications of accelerated sea-level rise (ASLR) for Ireland. Proc. SURVAS Expert Workshop on European Vulnerability and Adaptation to impacts of Accelerated Sea-Level Rise (ASLR), Hamburg, pp. 52–66. Fitzgerald, D.M., Rosen, P.S. (Eds.), 1987. Glaciated Coasts. Academic Press, San Diego, CA.
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Gonzalez, M., 1995. Morfologia de playas en equilibrio: planta y perfil. PhD Thesis, Departamento de Ciencias y Tecnicas del Agua y del Medio Ambiente, Universidad de Cantabria. Santander, Spain. Gonzalez, M., Medina, R., 2001. On the application of static equilibrium bay formations to natural and man-made beaches. Coastal Engineering 43 (3–4), 209–225. Hsu, J.R.C., Evans, C., 1989. Parabolic bay shapes and applications. Proceedings Institution Civil Engineers Part 2 87, 557–570. Hsu, J.R.C., Silvester, R., 1990. Accretion behind single offshore breakwater. Journal of Waterway, Port, Coastal and Ocean Engineering, ASCE 116 (3), 362–380. Hsu, J.R.C., Klein, A.H.F., Benedet, L., 2004. Geomorphic approach for mitigation beach erosion downdrift of littoral barrier. Proceedings 29th International Conference Coastal Engineering: ASCE, vol. 2, pp. 2022–2034. Hsu, J.R.C., Silvester, R., Xia, Y.M., 1987. New characteristics of equilibrium shape bays. Proceedings 8th Australasian Conference on Coastal and Ocean Engineering, pp. 140–144. Hsu, J.R.C., Silvester, R., Xia, Y.M., 1989a. Static equilibrium bays: new relationships. Journal of Waterway, Port, Coastal Ocean Engineers, ASCE 115 (3), 285–298. Hsu, J.R.C., Silvester, R., Xia, Y.M., 1989b. Generality on static equilibrium bays. Coastal Engineering 12, 353–369. Hsu, J.R.C., Uda, T., Silvester, R., 1993. Beaches downcoast of harbours in bays. Coastal Engineering 19, 163–181. Hsu, J.R.C., Uda, T., Silvester, R., 2000. Shoreline protection methods—Japanese experience. In: Herbich, J.B. (Ed.), Handbook of Coastal Engineering. McGrawHill, New York, pp. 9.1–9.7. Jackson, D.W.T., Cooper, J.A.G., 2009. Geological control on beach form: accommodation space and contemporary dynamics. Journal of Coastal Research SI56, 69–72. Jackson, D.W.T., Cooper, J.A.G., del Rio, L., 2005. Geological control of beach morphodynamic state. Marine Geology 216, 297–314. Kelley, J., Cooper, J.A.G., Jackson, D.W.T., Belknap, D., Quinn, R.J., 2006. Sea-level change and inner shelf stratigraphy off Norhern Ireland. Marine Geology 232, 1–15. Klein, A.H.F., Menezes, J.T., 2001. Beach morphodynamics and profile sequence for a headland bay coast. Journal of Coastal Research 17 (4), 812–835. Klein, A.H.F., Benedet, L., Hsu, J.R.C., 2003a. Stability of headland-bay beaches in Santa Catarina: a case study. Journal of Coastal Research SI 35, 151–166. Klein, A.H.F., Vargas, A., Raabe, A.L.A., Hsu, J.R.C., 2003b. Visual assessment of bayed beach stability using computer software. Computers and Geosciences 29, 1249–1257. Lawlor, D.P., 2000. Inner shelf sedimentology off the North Coast of Northern Ireland. Unpublished PhD thesis, University of Ulster. Lausman, R., Klein, A.H.F., Stive, M.J.F., 2010. Uncertainty in the application of the parabolic bay shape equation: Part 1. Coastal Engineering 57, 132–141 (this issue). LeBlond, P.H., 1979. An example of the logarithmic spiral plan of headland bay beaches. Journal of Sedimentary Petrology 49, 1093–1100. Lynch, K., Jackson, D.W.T., Cooper, J.A.G., 2009. Foredune accretion under offshore winds. Geomorphology 105, 139–146. Moreno, L.J., Kraus, N.C., 1999. Equilibrium shape of headland-bay beaches for engineering design. Proc. Coastal Sediments '99, ASCE, v. 1, pp. 860–875. Orford, J.D., 1989. A review of tides, currents and waves in the Irish Sea. In: Sweeney, J. (Ed.), The Irish Sea: A Resource at Risk, Special Publication Number 3. Geogr. Soc. Ireland, Dublin, pp. 18–46. Shaw, J., 1985. Beach morphodynamics of an Atlantic coastal embayment: Runkerry strand, Co. Antrim. Irish Geography 18, 51–58. Silvester, R., 1960. Stabilization of sedimentary coastlines. Nature 188, 467–469. Silvester, R., 1970a. Coastal defense. Proceedins Institution Civil Engineers, London 45, 677–682. Silvester, R., 1970b. Growth of crenulate shaped bays to equilibrium. Journal of the Waterways and Harbors Division 96, 275–287. Silvester, R., 1974. Coastal Engineering, Vol. 2. Elsevier, Amsterdam. Wright, L.D., Short, A.D., 1984. Morphodynamic variability of surf zones and beaches: a synthesis. Marine Geology 56, 93–118. Yasso, W.E., 1965. Plan geometry of headland bay beaches. Journal of Geology 73, 702–714.
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Coastal Engineering j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c o a s t a l e n g
Application of the equilibrium planform concept to natural beaches in Northern Ireland Derek W.T. Jackson ⁎, J. Andrew G. Cooper Centre for Coastal and Marine Research, School of Environmental Sciences, University of Ulster, Londonderry, BT52 1SA, Northern Ireland, UK
a r t i c l e
i n f o
Available online 31 October 2009 Keywords: Equilibrium planform concept Embayed beaches Beach stability Wave diffraction point North Ireland
a b s t r a c t The equilibrium planform concept (EPC) for bayed beaches has achieved wide currency in coastal morphodynamics. The north coast of Ireland comprises a series of discrete headland-embayment beaches within which waves and currents recycle a finite sediment volume. It is therefore an ideal setting in which to explore the applicability of the concept. Application of the approach to 9 embayment beaches on the north coast of Ireland provides some insights into the application of the concept. The planform of some beaches does correspond to that predicted while others do not. Those whose measured planform does not correspond to the predicted planform can be interpreted through, (a) difficulty in identifying the wave diffraction point, (b) disequilibrium on the beach (sediment scarcity or excess), (c) geological control of beach morphology. The subjectivity in selecting the diffraction point renders alternative explanations difficult and reduces the utility of the approach on natural shorelines, where significant irregularities render identification of such points difficult. © 2009 Elsevier B.V. All rights reserved.
1. Introduction The concept of equilibrium shoreline planform has achieved wide currency in coastal morphodynamics (Bremner, 1983, LeBlond, 1979; Klein and Menezes, 2001) and coastal engineering (Silvester, 1960; Moreno and Kraus, 1999). The concept makes a number of assumptions and a number of formulations have been presented (Yasso, 1965; Silvester, 1974; Hsu and Evans, 1989; Hsu et al., 1987; Hsu et al., 1989a,b; Hsu et al., 2000) that relate shoreline position to distance from an origin related to a physical or dynamic location. Various types of equilibrium are represented in examining planforms of bay shaped beaches ranging from ‘dynamic’ where there is a constant throughput of sediment maintaining beach stability to ‘static’ in cases where updrift sediment supply may cease/reduce and shorelines are restricted to a static position. Static equilibrium models are deemed useful in that they represent a convenient yardstick with which to ascertain a particular shoreline's current stability status. An assessment of the static model most suitable in real world conditions has been examined by Hsu et al. (1987) and Hsu and Evans (1989) where a model based on spiral logarithm (Yasso, 1965; Silvester, 1970a,b and others) was tested. The log-spiral model was shown to have limitations in terms of its reach to the outer margin of the equilibrium bay and as a result an alternative parabolic model was suggested (Hsu and Evans, 1989). The parabolic bay shaped model is now the most widely adopted approach to understanding the stability of headland bay beaches with Hsu et al. (2004) eventually defining a methodology for stability. Detailed assessment of its usefulness and applicability can be found in Gonzalez and Medina (2001) and Klein et al. (2003a,b).
⁎ Corresponding author. Tel.: +44 28 70323083; fax: +44 28 70324911. E-mail address: [email protected] (D.W.T. Jackson). 0378-3839/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.coastaleng.2009.09.007
Some limitations in the model have, however, been highlighted by Gonzalez (1995) including: prediction inaccuracies close to an estuary mouth (from dominant tidal dynamics); inability to predict effect of nearshore islands as well as uncertainties in defining downcoast limits and end points. Gonzalez (1995) does attempt to remedy some of these by proposing a semi-empirical model. Even with the additional proposed model, limitations were still evident with the beach systems having to conform to the following criteria: • Assumption that wave height gradients are controlled only by the diffraction point of the control point. Other diffraction from local islands and bathymetric anomalies cannot be represented. • Non-wave induced currents (tidal) cannot be taken account of and therefore are assumed not to exist. • A single point of diffraction should exist in the bay. Other diffraction points (control points) are assumed not to exist and therefore are not interacting with the beach sediments. • Intuitively, the availability of sediment and local geological framework over which the sediment lie must also be important factors. In this paper we apply the Hsu and Evans (1989) approach to 9 embayment systems on the north coast of Ireland in order to investigate its utility and interpretation. The north coast of Northern Ireland is an ideal location in which to test the approach on natural beaches given its strongly embayed beach systems and finite sediment volume. 2. Environmental setting Ireland has a 6500 km-long, bedrock-framed coast located between 52 and 55oN (Fig. 1). Large-scale coastal plains are not present and coastal sediments usually occur as a series of headland-embayment beaches or occasionally as barriers at estuary mouths (Jackson et al.,
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Irish seaboard (Devoy, 2000). Through its northern positioning the study site still experiences a high-energy wave climate regime with large-scale refraction taking place around the northwest peripheries of Ireland's open Atlantic coast. More specifically, wave energy varies from high (mean significant breaking wave height Hb, 2.18–2.52 m: Magilligan to Whitepark Bay) to moderate (1.8–1.36 m: Ballycastle to Redbay), as seen in Table 1. The beach systems examined are situated around the northern coastline of Northern Ireland over a distance of approximately 100 km. Tidal range along this total stretch of coast falls into the microtidal category, ranging from 0.9 m in the southeast to 1.6 m in the northwest.
3. Beach morphology
Fig. 1. Location map of embayment beach systems around the NE coast of Northern Ireland.
2005). The distribution and variable sediment composition of beaches and barriers in paraglacial settings may be explained in large part by glacial inheritance (FitzGerald and Rosen, 1987). Ice limits in Ireland during deglaciation have largely constrained contemporary coastal geomorphology and dynamics in that they are associated with major sediment sources. Areas positioned close to ice limits tend to possess sandy barriers, the sand having been deposited initially by outwash and subsequently reworked by marine processes (Cooper, 2007). Sediment supply on the Northern Ireland coast occurs predominantly from reworking of shelf sands (themselves of glacial origin) (Cooper et al., 2002), and locally from erosion of bluffs of glacial sediments (Carter, 1991). Coastal sediment supply is therefore strongly related to patterns of ice movement, stabilisation and decay during the last glacial cycle. Sediment has been driven into embayments that are now separated by a sediment-deficient seabed such that each headland-embayment cell contains a finite sediment volume. Longshore sediment exchange between cells is minimal and contemporary sediment supply from other sources (rivers and primary productivity) is similarly low. Only along the northeast Antrim coast is there much sediment yield from river sources. Ireland intersects the main conduit of North Atlantic cyclones, experiencing the maximum impact of Atlantic swell waves and storm activity on its western rim. Significant deep-water wave heights (Hs) off this portion of coast can reach 15–20 m. The wave energy regime around Ireland (Fig. 2) diminishes eastwards into the Irish Sea region where Hs modal values of between 1.6 and 2 m occur and a reduction in overall wave energy by a factor of 5 take places along the eastern
The majority of the beaches are backed by significant vegetated sand dunes. The morphology of the beaches on this coast was recently categorised by Jackson et al. (2005) who compared the observed beach state with predicted states using the Wright and Short (1984) model. The main geomorphological attributes of each beach are described below and morphometric and dynamic details are also listed in Table 1. Magilligan: This 16 km embayment incorporates several major intermediate-dissipative beach complexes including Magilligan– Benone which is backed by an extensive beach ridge plain (Lynch et al., 2009), and Castlerock and Portstewart both of which are backed by extensive dunes. The beach system is confined between the rocky Inishowen peninsula in the west and basalt cliffs at Portstewart in the east. The inlet and ebb delta of the Foyle estuary are located adjacent to the Inishowen peninsula. Waves predominantly travel from the NNW and large-scale wave refraction occurs around the Inishowen peninsula. Wave diffraction may be occurring from a headland in the NW or from the offshore, submerged delta. Jetties are present at the Bann river mouth separating Portstewart and Castlerock and a natural rock outcrop separates Castlerock from Benone to Magilligan. The beach system as a whole is largely stable with no significant erosion or accretion in the historical period. Portrush west: This narrow, intermediate-type beach was formerly backed by dunes that have been heavily modified. Bounded by two rocky headlands in the east and west of the site and is supplied by mainly N/NW wave approaches. A seawall is present along the entire length of the beach (0.9 km) and a harbour was built in the east in the 1800s. Beach lowering and narrowing since the seawall emplacement in the 1960s have been observed (Carter, 1991) and peat is periodically exposed on the foreshore during beach lowering. Portrush east: This 2.8 km-long intermediate-dissipative beach fronts a cuspate dune system and is bounded by two rocky headlands, Ramore Headland in the NW and Whiterocks in the east. The shoreline position is relatively stable in the historical period. The beach is located in the lee of a series of offshore rocky islands, which, together with a prominent headland to the west, affect wave approach. Geophysical investigations have shown there to be a limited sediment supply in the offshore zone at the site (Kelley et al., 2006; Backstrom et al., 2009). Portballintrae: This is a horseshoe-shaped bay located between prominent but low rocky headlands. An existing narrow beach (0.4 km wide) is backed by bluffs of glacial and glacio/marine sediment. Human influence at the site is evident in the form of a pier in the north and a harbour in the SE section of the bay. Extensive beach narrowing has been attributed to alteration of wave patterns by emplacement of a pier in the north (Carter, 1991). Runkerry: This 1.0 km-long beach is underlain by a boulder frame and glacial sediments. It is bounded by two high rocky headlands and the river Bush discharges along the western headland. Sand dunes backing the beach are located on top of glacial till. The beach switches beach state on a seasonal basis (intermediate to dissipative) but on
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Fig. 2. Main wave energy regime around Ireland along with tidal range zones. Note the rapid decline in 50 y wave heights around the north of the island from 30 m in the NW to around 15 m in the NE. Based on Carter (1990) and Orford (1989).
the whole can be viewed as having a stable shoreline position (Shaw, 1985). Whitepark Bay: This 2.2 km-long beach is located between high rocky cliffs and is backed by a dunefield climbing on relict landslides.
The eastern end of the bay is underlain by bedrock at shallow depth and it is periodically exposed on the beach after storms. Semipermanent crescentic bars occur in the nearshore (Carter, 1991). The coastline has been relatively stable historically.
Table 1 Main attributes of selected embayments around NE of Ireland. Site name
Location (Lat. and Long.): centre of beach
Sand grain size (mm)
Beach slope
Length (km)
Tidal range (m)
H0 (mean Hs) m
Beach type
Local geomorphology
Magilligan
55o 10′ 01.94” N 6o 50′ 49.66” W 55o 12′ 08.63” N 6o 39′ 20.16” W 55o 12′ 24.74” N 6o 38′ 04.95” W 55o 12′ 57.03” N 6o 32′ 48.11” W 55o 13′ 20.90” N 6o 310′ 51.36” W 55o 14′ 02.45” N 6o 23′ 41.63” W 55o 12′ 17.78” N 6o 13′ 44.09” W 55o 07′ 38.45” N 6o 02′ 29.11” W 55o 04′ 59.75” N 6o 03′ 19.44” W
0.17
0.0375
16.0
1.6
2.18
Intermediate to dissipative
0.186
0.0320
0.9
1.5
2.34
Dissipative
0.197
0.0352
2.8
1.5
2.34
Intermediate
0.25
0.03
0.3
1.5
2.18
Intermediate
0.28
0.0329
1.0
1.5
2.18
Intermediate
Extensive dune systems, tidal inlet, sand ridge plain Modified dunes, human modification along coastline Convex, extensive dune system, offshore islands Beach backed by glacial unconsolidated sediments, human modification Large sand dunes, rive mouth
0.229
0.0350
2.2
1.2
2.41
Intermediate
Sand dunes
0.634
0.0823
1.2
0.9
2.52
Intermediate
0.397
0.1037
1.0
1.6
1.28
Reflective–intermediate
River mouth, large dunes, human modification Small dunes, river mouth
0.198
0.104
0.4
1.6
1.28
Reflective–intermediate
Portrush west Portrush east Portballintrae Runkerry Whitepark Bay Ballycastle Cushendun Cushendall
Small dunes, river mouth, human modification
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Fig. 3. Static shoreline prediction for Magilligan embayment after diffraction point selected from headland location (image source: NASA images). Note the suggested instability of the coastline in the western section of the site.
Fig. 4. Static shoreline represented after the diffraction point is chosen at the submerged delta in the Magilligan embayment (image source: NASA images). Note close agreement with actual shoreline for the entire length of the embayment.
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Ballycastle: This 1.2 km-long beach is composed of coarse, poorly sorted sand and fine gravel sourced primarily from rivers that dissect relict fluvio-glacial deltas. The beach is confined between high cliffs at each end and is backed by a sand dune system. The close proximity of an amphidromic point results in a low tidal range and this area is transitional between remnants of high-energy Atlantic waves and directly approaching Irish Sea waves (lower energy) originating from the east. Dominant longshore drift to the west results in coastal recession in the east and accumulation in the west at the river mouth (Carter, 1991). Harbour construction (in several phases) in the north of the embayment, channelisation of the Margy River, beach sediment removal and small-scale coastal reclamation adjacent to the harbour have all affected the shoreline morphodynamics. Cushendun: This 1 km-long beach is located in a glaciated valley flanked by bedrock outcrop at both margins. The Glendun River, which enters the sea on the southern margin of the beach supplies the coarse sand and fine gravel that dominate the beach and nearshore. Longshore transport is in a southerly direction toward the river outlet (Carter, 1991). Human interference has manifest itself in the form of dredging and river channelisation in the past, effectively cutting off the linkage between longshore transport of beach material and the Glendun River. Sediment removal from the beach has also occurred in the past with an estimated
30,000 m3 removed over a 30-year period (1960–1990) (Carter, 1991). Historically, this coastline appears to be in a retreating phase. Cushendall: This 0.4 km-long beach is intersected at its southern section by the River Dall. It is located in a glaciated valley and is bounded by high bedrock cliffs. This site had a serious problem of coastal retreat over the period 1903 to 1963 when a 45m shoreline recession was recorded (Carter, 1991) due to sediment removal, resulting in a beach sediment volume deficit. A sea wall installed in 1963 has left a much narrower and lower beach. Wave energy levels in the area are moderate mostly originating from the Irish Sea (East).
4. Application of the planform equilibrium concept The MEPBAY software (Klein et al., 2003b) derived from the EPC for bay beach in static equilibrium (Hsu and Evans, 1989) was used to identify diffraction points on rectified orthophotographs (2004) of beaches along the north coast. In the case of the largest embayment beach (Magilligan), satellite imagery from Google Earth is employed. All images are in a north (top of image) to south alignment. The MEPBAY software (http://siaiacad05.univali.br/~meppe) is used to predict the shoreline position in static equilibrium at each site and the results are discussed below.
Fig. 5. Portrush West Strand and the predicted static shorelines showing close agreement to the existing beach after two diffraction points were selected from a promontory to the west and a harbour end point in the east.
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Fig. 6. Portrush East site showing the multiple diffraction points and corresponding static shoreline positions. Note the presence of the nearby Skerries islands. Close agreement can be seen between predicted and actual shorelines in the western part of the site using part of the western headland while the eastern and western edges of the offshore Skerries islands diffraction points predicts quite close agreement follow an approximate path of the existing salient. Less agreement is evident between actual and predicted shoreline towards the tip of the salient.
Magilligan: At this site, the dominant wave approach is from the northwest and diffraction is therefore likely to be centred on the headland north of the beach. The tidal inlet of the Foyle, however, also provides a potential second diffraction point on the shallowest sections of the ebb tide delta. Consequently both points are selected for simulation of shoreline position. The downdrift end of this 16 km embayment is selected at the eastern edge of Portstewart beach. Fig. 3 shows the result of choosing the main headland as the diffraction point source. The predicted static shoreline is positioned offshore of the actual shoreline, suggesting the coast is an unstable coast, particularly in the western section of the site towards the distal end of the cuspate foreland. Fig. 4 shows the static shoreline prediction when the western edge of the submerged Tunns Bank is selected as a diffraction point. At the resolution of the satellite imagery (15 m pixel size) there is quite close agreement between actual shoreline and predicted static shoreline. East of the River Bann the actual beach is rather landward of that predicted. This can be attributed to the presence of the training walls, which produced some accretion on beaches the west and erosion in the east soon after their emplacement but which now appear to be stable. Portrush west: This embayment has distinctive promontories on both sides of the bay. Selection of both these as diffraction points (Fig. 5) produces a simulated shoreline that is in close agreement with actual shoreline configuration at the present time. Previous work (Carter, 1991) however, has shown historical shoreline changes in response to construction of the harbour (1825), sand removal and seawall construction (1940–1960). The southwest section of the bay retreated by around 80 m between 1825 and 1950 while the northeast sector accreted 80 m during the same period. Thus, while the modern shoreline agrees with the MEPBAY model, the natural shoreline in the southwest part of the bay was 80 m seaward of contemporary shoreline.
Portrush east: The major influence on this beach planform is the presence of a chain of offshore islands (Skerries) and a distinctive promontory (Ramore Head) identification of three diffraction points (Fig. 6) produces a simulated shoreline that matches the actual shoreline in the east and west margins of the beach. The central section comprises a salient that is landward of the predicted shoreline. This is easily explained by the lack of available sediment to attain the predicted morphology. What is more difficult to explain is the fact that the entire western section has retreated by over 100 m since 1834 (Carter, 1991) without having been affected by any engineering works that would have altered the diffraction points. Portballintrae: The eastern side of the bay contains a prominent harbour wall which is an obvious diffraction point. The western headland of this bay comprises a wide, gently sloping, intertidal to subtidal rock platform on which a jetty (Leslie's Pier) was constructed around 1895 (Carter, 1991). Selection of diffraction points on this margin is more problematic since the diffraction point likely migrates across the platform as the tide fluctuates. Selection of three diffraction points (Fig. 7) produces a simulated shoreline that matches quite well the contemporary shoreline in the west; only minor differences in shoreline position are produced by selection of diffraction point on Leslie's Pier and the adjacent rock headland. The eastern part of the bay is quite different in that the predicted shoreline is up to 50 m seaward of the actual position. Interestingly, this bay has shown dramatic shoreline change in the recent past: between 1930 and 1980 more than 100 m of shoreline recession occurred (Carter, 1991). The attribution of this erosion to construction of Leslie's Pier (Carter and Shaw, 1983) is at odds with the simulated shorelines from the MEPBAY model (Note the similarity in the simulated shorelines associated with Leslie's Pier and the natural headland). Runkerry: A variety of diffraction points exist in this bay. Fig. 8 illustrates the shoreline oppositions obtained using three of these. The predicted static planform of the beach matches quite well with the
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Fig. 7. Portballintrae site showing the result of selection of three diffraction points where a simulated shorelines matches quite well the contemporary shoreline in the west while only minor differences in shoreline position are produced by selection of diffraction point on Leslie's Pier and the adjacent rock headland. The eastern part of the bay is quite different in that the predicted shoreline is up to 50 m seaward of the actual position.
actual low water position on the beach (Fig. 8). Interestingly, both of the westerly diffraction points are associated with almost identical simulated shorelines. Whitepark Bay: Several diffraction points were selected either side of the bay, two on the west and one on the eastern sectors. A fairly good agreement is found between the predicted static shoreline and actual low water beach planform (Fig. 9). The predicted static shoreline in the western section of the beach is in better agreement with the actual shoreline when the more landward diffraction point is used. Ballycastle: Ballycastle embayment contains a major harbour (constructed in two phases) and offers the opportunity to test predictions of the shoreline position based on a changing diffraction point. Selecting the diffraction point in Fig. 10(i), at the end of the harbour wall after the first phase of construction, predicts a shoreline broadly similar to the present except in the western margin. Fig. 10(ii) shows the shoreline predicted by a subsequent diffraction point located at the modern outer edge of the existing harbour. Remarkably good agreement between actual and predicted shorelines is clear along the entire beach. The predicted accretion at the western end of the beach is matched by the actual changes recorded by sequential aerial photography. Cushendun: At this site there are two potential diffraction points, one on the natural rock headland to the south of the bay (Fig. 11(i)) and a second at the tip of a jetty at the river mouth (Fig. 11(ii)). The predicted shoreline associated with a diffraction point to the south of the beach displays quite good agreement with the actual shoreline position in the northern section of the beach (Fig. 9). However, in the southern zone where the Glendun River emerges, the actual shoreline
(which rests on exposed bedrock) is seaward of that predicted. When the diffraction point on the end of the jetty is considered the predicted shoreline is even further landward. Cushendall: The southeasterly approach of the dominant wave field prompted selection of a headland diffraction point in the SE of the Cushendall embayment. Quite close agreement is found between the predicted and actual shoreline positions (Fig. 12) with the exception of the southern section of the beach where a river enters the system and the actual shoreline is located seaward of that predicted. This finding was unexpected since the coastline has been retreating at a rapid rate throughout this embayment over the past 100 years (Carter, 1991) and there has been no change in the location of the diffraction point. 5. Discussions The northeast coast of Northern Ireland is a locality in which the historical behaviour of its headland-embayment beaches is well documented (Carter, 1991). The high degree of indentation and isolation of the beaches in distinct embayments reduces longshore influences on beach behaviour and means that each has a wellconstrained sediment circulation operating within fixed boundaries. It therefore offers an ideal location in which to test the applicability of the headland-embayment equilibrium planform concept (EPC) on natural beaches. The results presented here show considerable variability. In several instances quite close agreement was observed between predicted and actual shoreline planform while in others, there was little or no
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Fig. 8. Runkerry embayment which displays a good agreement with predicted static and actual planforms.
agreement. This approach has been used in the past to predict the impact of engineering structures (Hsu and Silvester, 1990; Hsu et al., 1993) and to assess the status of the coastline (Klein et al., 2003a). On the north coast
of Ireland the well documented historical shoreline changes offer the opportunity to set modern and predicted shorelines in their historical context.
Fig. 9. Whitepark Bay site where several diffraction points were selected either side of the bay, two on the west and one on the eastern sectors. A reasonably good agreement is found between the predicted static shoreline and actual low water beach planform. Note that the predicted static shoreline in the western section of the beach is in better agreement with the actual shoreline when the more landward diffraction point is used.
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Fig. 10. Ballycastle embayment where the diffraction point in (i), at the end of the harbour wall after an initial phase of harbour construction, predicts a shoreline broadly similar to the present except in the western margin. Selection of another diffraction point (ii) shows the shoreline predicted by a subsequent diffraction point located at the modern outer edge of the existing harbour. Remarkably good agreement between actual and predicted shorelines is clear along the entire beach. The predicted accretion at the western end of the beach is matched by the actual changes recorded by sequential aerial photography.
At Magilligan, there is an abundant sediment supply which is reflected in the long-term stability of the site. Armed with this knowledge, selection of the ebb delta as an alternative diffraction point provided a simulated coastline that was closer to reality than that associated with diffraction on the adjacent Inishowen headland. It does point to the importance of the ebb delta as a control on the long-term planform stability of the site and therefore enhances the understanding of the coastal form. Conducting the simulation blind (with no prior knowledge of the ebb delta) would however, not have allowed such a proposition to be tested. An alternative approach might have been to fit the curve to the observed shoreline as a means of identifying alternative diffraction points. Selecting the exact position of a diffraction point on a submerged delta is however very subjective. The leading edge of the delta is gently sloping and therefore diffraction may take place in a broad zone dependent on tidal and wave conditions. In this situation where the coast was known to be stable, the shoreline predicted by the equilibrium planform concept (EPC) was similar to that observed. This drew attention to the previously undocumented role of the ebb delta in wave transformation. Previous work confirmed the role of the ebb delta in wave refraction (Carter et al., 1982) but not diffraction. At Portrush west strand the predicted static shoreline using two diffraction points (the headland to the west and harbour to the east) is in close agreement with the contemporary situation. This seems to confirm the role of the harbour in prompting accretion in the east as evidenced by historical shoreline change. In the west however, where the diffraction point has remained fixed, the actual coastline has, however, retreated by 80 m in the past century. The apparent agreement with the contemporary shoreline is most likely due to the need to identify a downcoast limit in MEPBAY which tend to promote agreement. At Portrush east, a convex beach planform generally matches that predicted by selection of multiple diffraction points. The planforms coalesce to form the cuspate feature observed. The eastern shoreline is somewhat landward of that predicted at the confluence of the two
planforms. This could be interpreted as the result of an inadequate sediment supply; the adjacent sea bed is largely sediment poor (Lawlor, 2000; Kelley et al., 2006; Backstrom et al., 2009). The shoreline is known to have been historically stable, suggesting that it is in static equilibrium. This further suggests that the lack of sediment prevents attainment of the theoretical shoreline. At Portballintrae, there is considerable difficulty in selecting a diffraction point on the western side of the bay as the headland is broad and gently sloping in the intertidal and subtidal zone. Sensitivity of predicted shoreline position to the diffraction point location is marked but neither is coincident with the contemporary shoreline. The actual shoreline at Cushendun matches that predicted except in the south where the shoreline is seaward of that predicted regardless of whether the natural rock headland or the river mouth jetty is selected as a diffraction point. This might be due to the effect of the underlying geology (Fig. 11), which if elevated, would cause the sand on top of it to extend further seaward (Jackson and Cooper, 2009). An alternative explanation may be that the river mouth alters the local wave patterns and promotes sediment accumulation. The same is true at Cushendall in the vicinity of its river mouth. While these shorelines appear to be in equilibrium, both beaches are known to have receded in historical times whereas the diffraction point will not have changed. This knowledge of the recorded shoreline changes urges rejection of the conclusion that the beach is in equilibrium as implied by application of the static shoreline concept. 6. Final remarks The EPC provides an explanation of shoreline planform on linear coasts with prominent headlands. It has been used in the past to assess the erosional status of various headland-embayment beaches (Hsu et al., 1993; Klein and Menezes, 2001) through comparison of predicted and actual shorelines. Klein and Menezes (2001) for
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shorelines do not coincide which prompts questions regarding such discrepancy—do they reflect disequilibrium, do they reflect some natural constraint on achievement of idealised equilibrium, or do they reflect inherent subjectivities involved in application of the model? In applying the concept to a range of natural beaches in Northern Ireland we present some observations regarding the practical application of the EPC as a prediction tool for beach planform equilibrium. These observations relate to the following practical aspects of applying the EPC: • Subjectivity in selection of the diffraction point • Temporal variability in location of diffraction point as a result of changing tidal and wave conditions • Subjectivity in selection of downdrift control point (and consequently wave approach angle)
Fig. 11. Cushendun beach where two potential diffraction points are chosen, one on the natural rock headland to the south (i) and a second at the tip of a jetty (ii). The predicted shoreline associated with a diffraction point to the south of the beach displays quite good agreement with the actual shoreline position in the northern section of the beach. However, in the southern zone where the Glendun River emerges, the actual shoreline is seaward of that predicted. When the diffraction point (ii) is considered the predicted shoreline is even further landward.
example identified equilibrium and disequilibrium bays along the south Brazilian coast. The examples described in this paper show various levels of agreement between predicted and actual shorelines on the Northern Ireland coast for which the historic coastal behaviour is well known. This allows the predictive ability of the EPC to be tested. The results presented above show various levels of agreement between shorelines predicted using the MEPBAY software and actual shorelines. In some cases modern shorelines closely match predicted shorelines suggesting them to be in static equilibrium. Several of these, however, (e.g. Portrush west) are known to be experiencing long-term coastal recession which points toward disequilibrium. In some cases, the approach has been a useful tool in identifying unexpected potential influences on shoreline planform (e.g. the ebb delta at Magilligan Point). In other instances the predicted and actual
The subjectivity of the selection of the diffraction point has also been addressed by Lausman et al. (2010-this issue) who demonstrated through blind testing that the operator is strongly influenced by sight of the actual shoreline position. When this was not visible the coincidence of predicted and actual shorelines decreased significantly. The natural variability of coastal systems means that many potential sites could be selected as the diffraction point. This is evident at Magilligan where a better shoreline fit was achieved by selection of the ebb tide delta as a diffraction point rather than the adjacent rocky headland. While this in itself is a useful finding pointing to a previously unexpected role for the ebb delta, it hinders use of the approach in assessing the equilibrium nature of the coast. The coast is known to have been historically stable and consequently our provisional interpretation is that the ebb delta plays a more significant role in wave diffraction than the adjacent headland. Without this local knowledge a different conclusion might have been drawn. In addition, several diffraction points on this coast probably change with the tide, with wave direction and with wave height. The flat, gently sloping rocky headland at Portballintrae is a case in point. Here, the diffraction point at low tide must be several tens of metres distant from that at high tide. A similar scale of displacement is likely associated with differences in wave height. These constraints do not exist in the laboratory or computer models with a vertical headland defining the diffraction point, a monochromatic wave field and uniform sediment size in an unconstrained setting. On a natural beach there may also be more than one diffraction point at any given time. This is evident at Portrush West Strand, Portrush East Strand and Portballintrae where it is clear that diffraction points exist on both sides of the bay. In these cases the full equilibrium planform is not developed and identification of the downdrift control point is therefore inhibited. This is important because of the fixed relationship in the EPC between wave approach angle and the downcoast tangent line (Hsu et al., 1987); misidentification of this downdrift point changes the wave approach angle and vice versa, with consequent implications for the predicted shoreline position. There are also a number of conceptual aspects of beach behaviour that influence the relationship between MEPBAY-predicted and actual shorelines and which influence the utility of the approach in identifying equilibrium and non-equilibrium shorelines. These include: • Reliance on contemporary beach morphometrics as an input • Omission of other dynamic variables (secondary wave motions, tidal and river currents) • Role of underlying geologic framework in shaping seabed (Jackson and Cooper, 2009) • Variability in grain size characteristics On several beaches that are known to be in long-term recession (e.g. Portrush west), the coincidence between predicted and actual shorelines seems puzzling. However, when it is realised that the actual shoreline (i.e. the downdrift control point) forms part of the
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Fig. 12. Cushendall embayment and the predicted static shoreline position using MEPBAY software. Note that overall prediction is good with the exception of the southern section where the River Dall emerges and the actual shoreline is located seaward of that predicted. The coastline at the Cushendall embayment has been retreating at a rapid rate throughout this embayment over the past 100 years (Carter, 1991) whilst the location of the diffraction point is presumed to have remained fixed.
prediction, this coincidence is less surprising. This acts to force agreement between predicted and actual shorelines and limits its predictive capacity. In theory this can be avoided if one has knowledge of the deep-water wave approach direction, but in practice data on wave height, much less direction are rather rare for most of the world's coasts. The equilibrium planform concept assumes that no other processes than wave diffraction influence the coastal planform. Clearly this is not a valid assumption on many natural coasts but from the perspective of interpreting the predicted static shorelines it is an important consideration. On some beaches where the predicted shoreline closely matches the actual shoreline, thereby implying stability, there are known to be large-scale secondary wave motions (viz the crescentic bars at Whitepark Bay). Assuming that the diffraction point has been selected correctly and that the wave approach angle is correct (see above) there are two possible interpretations: a) that the shoreline is stable and secondary wave motions
do not influence it; and b) that the coast is unstable and that its coincidence with the predicted shoreline is caused by circulations that the model does not consider. A similar line of argument applied to situations where the coastline does not match the predicted static shoreline must conclude that the deviation may be due to either a) the operation of dynamics that are excluded by the model, b) shoreline instability through lack of sediment or geological control. As in many conceptual models, no account is taken in the ECP of geological variables (seabed topography and material, sediment supply and type) as a constraint on the dynamic processes (Cooper and Pilkey, 2004; Jackson et al., 2005). In the ECP, coastal behaviour is considered to be unconstrained by geological factors other than the headlands bounding the embayment. This is clearly an invalid assumption on many natural beaches where there may be shallowly buried bedrock or semi-consolidated sediments. In theory, the model may be useful in identifying geological control as a factor causing
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deviation from the predicted static shoreline, as implied at Cushendun and Cushendall where shallow outcrop of glacial till is invoked to explain deviation from the idealised shoreline morphology. Application of the ECP to several beaches along the Northern Ireland coast has been a useful exercise. It has prompted questions regarding the stability of the coast and prompted insights into coastal behaviour that were otherwise unexpected. It has also revealed some natural constraints on achievement of equilibrium through geological factors. Most importantly, it urges caution in the simple use of the ECP to determine whether a shoreline is in equilibrium and prompts users to consider not only the already documented issues concerning the subjectivity of input selection but also the potential for geological, dynamic and sedimentological constraints on shoreline planform development. Acknowledgements Reproduction from the Ordnance Survey Northern Ireland (OSNI) map with the permission of the controller of HSMO© 2006, permit no. 60089. We would also like to thank Kilian McDaid, Drawing Office (University of Ulster) and Euan Dawson (University of Ulster) for help with some of the figures. Thanks are also due to Robert Stewart and Sam Smyth (CCMR, University of Ulster) who helped carry out DGPS surveys and sediment sampling. Helpful and detailed discussion with John Hsu helped improve the paper. References Backstrom, J., Jackson, D.W.T., Cooper, J.A.G., 2009. Shoreface morphodynamics of a high-energy, steep and geologically constrained shoreline segment in Northern Ireland. Marine Geology 257, 94–106. Bremner, J.M., 1983. Properties of logarithmic spiral beaches with particular reference to Algoa Bay. In: McLachlan, A., Erasmus, T. (Eds.), Sandy Beaches as Ecosystems. Proc. 1st Inter. Sym. Sandy Beaches, Port Elizabeth, South Africa, pp. 97–113. Carter, R.W.G., 1990. The Impact on Ireland of Changes in Mean Sea Level. Programme of Expert Studies, Number 2. Department of the Environment, Dublin. pp. 128. Carter, R.W.G., 1991. Shifting Sands: A Study of the Coast of Northern Ireland from Magilligan to Larne. HMSO, Belfast. Carter, R.W.G., Shaw, J., 1983. An eighty year history of shoreline erosion in a small Irish Bay. Shore and Beach 51, 34–37. Carter, R.W.G., Lowry, P., Stone, G.W., 1982. Sub-tidal ebb shoal control of shoreline erosion via wave refraction, Magilligan Foreland, Northern Ireland. Marine Geology 48, 17–25. Cooper, J.A.G., 2007. Geomorphology of Irish estuaries: inherited and dynamic controls. Journal of Coastal Research SI 39, 176–180. Cooper, J.A.G., Pilkey, O.H., 2004. Sea-level rise and shoreline retreat: time to abandon the Brunn Rule. Global and Planetary Change 43, 157–171. Cooper, J.A.G., Kelley, J.T., Belknap, D.F., Quinn, R., McKenna, J., 2002. Inner shelf seismic stratigraphy off the north coast of Northern Ireland: new data on the depth of the Holocene lowstand. Marine Geology 186, 369–387. Devoy, R.J.N., 2000. Implications of accelerated sea-level rise (ASLR) for Ireland. Proc. SURVAS Expert Workshop on European Vulnerability and Adaptation to impacts of Accelerated Sea-Level Rise (ASLR), Hamburg, pp. 52–66. Fitzgerald, D.M., Rosen, P.S. (Eds.), 1987. Glaciated Coasts. Academic Press, San Diego, CA.
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