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Using Combined Modelling Approaches to Improve Coastal Defence Design

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Using Combined Modelling Approaches to Improve Coastal Defence Design: a case study at Hopton, UK J.J. Williams†, L.S. Esteves‡, T. Conduche†, P. Barber∞, A. Tindle+ † ABPmer, Quayside Suite, Medina Chambers, Town Quay, Southampton, SO14 2AQ, UK. [email protected]

‡ School of Applied Sciences, Bournemouth University, Poole, BH12 5BB, UK [email protected]

∞ Shoreline Management Partnership, Talwryn Green, Townsditch, Wrexham, Clwyd, LL12 0AN, UK [email protected]

www.cerf-jcr.org

+ Rosebay Services, 85 Moor Road North, Gosforth, Newcastle Upon Tyne, NE3 1RJ, UK. [email protected]

ABSTRACT Williams, J.J., Esteves, L.S., Conduche, T., Barber, P., Tindle, A., 2014. Using Combined Modelling Approaches to Improve Coastal Defence Design: a case study at Hopton, UK. In: Green, A.N. and Cooper, J.A.G. (eds.), Proceedings 13th International Coastal Symposium (Durban, South Africa), Journal of Coastal Research, Special Issue No. 70, pp. 018-022, ISSN 0749-0208. www.JCRonline.org

A storm that occurred close to the spring tidal maxima in March 2013 resulted in beach lowering and cliff recession of c. 5 m along a 110 m frontage at Hopton-on-Sea, UK and threatened the static caravan park of Bourne Leisure Ltd. This paper reports a study using XBeach and MIKE21 models to assist with the design of new coastal defences to reduce cliff and beach erosion. Two schemes are examined here: three fishtail rock groynes (Scheme 1); and ten ‘double-head’ curved rock groynes (Scheme 2). The selected design must provide acceptable level of protection and, to be granted consent, no adverse environmental impact must be demonstrated. Current practice using a single numerical model can provide a cost-effective tool for coastal defence assessments. However, the work presented here show that when good agreement between complementary models can be demonstrated, greater confidence can be given to model results. Specifically, refinements to the present scheme design were made possible by the use of the XBeach model, which allowed identification of the cross-shore limits of sediment transport in storm conditions, and by the MIKE21 model which allowed quantification of alongshore scheme impacts. Together, the model results have assisted the development of an improved final scheme design which minimizes potential environmental impacts. ADDITIONAL INDEX WORDS: MIKE21 FM, XBeach, cliff erosion, fishtail breakwater, Hopton-on-Sea.

INTRODUCTION Hopton Holiday Park, owned by Bourne Leisure Ltd. (BLL), is located on an eroding cliff frontage at Hopton-on-Sea, between Great Yarmouth and Lowestoft on the east coast of the UK (Figure 1a). In March 2013, a storm closely coin the spring tidal maxima resulted in beach lowering and cliff retreat (c. 5 m) threatening 110 m of the Park’s frontage (Figure 2a). Temporary emergency works to protect the cliffs from further erosion were carried out by BLL with support from Great Yarmouth Borough Council (GYBC). For business reasons, relocation of the static caravan site is not an option being considered and Shoreline Management Partnership has been appointed to provide specialist advice to assist the design of a coastal defence scheme to prevent further lowering of the beach and to protect the existing defences (Figures 1 and 2). This paper reports results from a study using two complementary models undertaken to inform the design of coastal defences and to assess potential impacts on the adjacent beaches. Local hydrodynamics and sediment transport processes are complex due to the presence of discontinuous offshore sand banks, ____________________ DOI: 10.2112/SI70-004.1 received 8 December 2013; accepted 21 February 2014. © Coastal Education & Research Foundation 2014

the Great Yarmouth Outer Harbour (GYOH) and the tidal/fluvial exchanges of water and sediments with the River Yare. Inshore of the banks tidal flows are parallel to the coast with net tidal residuals directed southwards. At Hopton-on-Sea, peak depthaveraged tidal flow speeds increase from 0.5 m/s at 250 m from the shoreline to 1.0 m/s at 2 km offshore. It is widely reported that alongshore sediment transport is predominantly southwards along this stretch of the coast, with annual average drifts from 10,000 to 40,000 m3a-1 (HR Wallingford, 2002). However, the beach width from Gorleston to Corton gradually declines in a southerly direction (Figure 1). At Hopton-on-Sea variations in alongshore sediment supply and differences in the exposure of the shoreline to waves and tides are complicated by the presence of the offshore sand bank system and coastal defences (SMP, 2013). Numerical modelling (HR Wallingford, 2011a) has indicated that the largest offshore waves originating from the north-east are refracted by the offshore banks to arrive with a low obliquity to the coast. The arrangement of sand banks and channels induce wave energy from the south and south-east sectors to concentrate along the Hopton-on-Sea frontage. Waves from the south-east sector also have greater obliquity providing greater potential for net northerly drift, as is evidenced by the accumulation of sediment south of coastal structures (Figure 1b, c).

Journal of Coastal Research, Special Issue No. 70, 2014


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Figure 2. (a) March 2013 storm impact; and (b) emergency works at Hopton-on-Sea.

Figure 1. (a) Location of study site; (b) detail of GYOH and Gorleston beach; and (c) detail of Hopton-on-Sea.

between structures; (b) on-offshore length of structures to provide sufficient depth of embayment to allow waves to respond to the changed conditions; (c) extent of shore-parallel wave interception to avoid adverse wave interaction along the on-offshore length of the structure and to achieve adequate wave dissipation between structures. Beyond these basic design parameters there are many more detailed considerations of structural form, roughness, stability and hydraulic performance across the structure. While these detailed considerations did not receive direct assistance from the modelling study reported here, the model results have provided specific inputs to the key design parameters set out above.

MODELLING APPROACH HR Wallingford (2011b) and SMP (2013) show that Hopton beach exhibits a trend for beach erosion at its southern end and a trend of overall stability at its northern end derived from analysis of six-monthly beach profiles extending over the period 1991 to 2013. GYOH structures deflect the tidal streams and associated sediments offshore, likely reducing the southward sediment delivery feeding the sand banks system contributing to increased erosion along the Hopton-on-Sea frontage post GYOH construction (SMP, 2013).

COASTAL DEFENCE STRUCTURES The development of larger hydraulic machines over the last 30 years has provided the means to handle, place and profile large rock armour with individual boulder weights of up to 10 tonnes. Increasingly this shore-based construction approach is replacing the traditional steel piling and timber planking. This new construction method has led to the use of larger structures that are more akin to headlands than to traditional groynes. The evolution of more sophisticated models of nearshore coastal processes alongside the new alternative construction has produced a more refined design approach to such works. There are two generic types of coastal defence classified as 'shore-parallel' and 'shore-normal. A combination of these two types leads by logical progression to the 'fishtail' shape of breakwater employed in this study. Shore-normal construction essentially holds longshore currents away from the shoreline whilst allowing waves to advance into the calmer waters between structures where they can generate currents and move sediments during the breaking process. Shore-parallel construction essentially intercepts waves approaching the shoreline and when located offshore can use wave diffraction and refraction around structure extremities to stretch the length of wave crest and thereby reduce the wave energy incident at the shoreline per unit longshore length. Key issues in the design of fishtail breakwaters / groynes are: (a) alongshore spacing of structures to restrict recovery of diverted longshore flows and avoid the generation of strong eddy-fields

The modelling study has examined two coastal defence design options for Hopton-on-Sea: (Scheme 1) three fishtail rock groynes that are partly submerged at high water with alongshore spacing of 300 m and cross-shore extend of 150 m; and (Scheme 2) a linear scheme featuring ten curved rock groynes with a ‘double head’ at the offshore limit, an alongshore spacing of 100 m and a crossshore extent of 55 m. The two schemes selected for test to provide coastal defence at Hopton represent two designs comprising firstly a multiplicity of shorter, closer-spaced structures and secondly fewer, larger structures. These are defined from experience for a specific site from consideration of: (a) inshore wave length, height and direction; (b) nearshore sea bed levels and tide range (including additions due to surge); and (c) the strength of longshore currents and their time of occurrence within the tidal cycle. Information to support the design of the proposed schemes was obtained by coupling the Danish Hydraulic Institute’s (DHI) MIKE21 Flexible Mesh (FM) models: hydrodynamics (HD); spectral wave (SW); and sediment transport (ST). In addition, a 2D XBeach model (Roelvink et al. 2009a,b) was used to provide an improved representation of complex nearshore hydrodynamics and sediment transport of relevance to the design of the proposed schemes. From a scientific point of view the approach would be to run a long series of computer model runs to assess the efficiency of the three key parameters at varied settings against other parameters calculated in the model. In practice the number of model runs is limited due to cost and specific runs are selected from experience once the shoreline exposure settings are known.

MIKE21 FM The MIKE21 FM model domain includes the sand banks systems and the Norfolk and Suffolk coast (from Horsey to Southwold) covering an area of approximately 60 km X 30 km (Figure 3). Fluvial inputs from the River Yare are negligible and are excluded. The north and south domain limits were configured to be perpendicular to the tidal streamlines and the offshore limits were designed to minimise wave obliquity at the open boundary.


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Figure 3. MIKE21 FM bathymetry for the whole domain (left) and detail of bathymetry at Hopton-on-Sea (right) The bathymetry for the model (Figure 3) was derived from three data sources: (1) UKHO survey data; (2) Environment Agency beach profiles; and (3) BLL Hopton-on-Sea frontage survey data. In the offshore area the model resolution was 2 km, gradually reducing to 50 m in the coastal area and to 5 m along the Hoptonon-Sea frontage. Tidal forcing was applied at the northern and southern limits of the domain, and the offshore boundary tidal condition was set as a zero normal velocity. Water levels at the north and south boundaries were derived from harmonic analysis using DHI’s global tidal harmonic database and Lowestoft tidal data from BODC. Wind forcing all over the domain was applied using 3 hourly wind data from the UKMO for the period of study (20-22 April 2008). Overall, the MIKE21 FM model performance agreed well with a Telemac model of the area reported by HR Wallingford (2012a, b; 2013).

Figure 4. XBeach bathymetry: (a) Scheme 1; (b) Scheme 2. Company as part of the monitoring of effects required under the enabling legislation. Figure 5 shows offshore time-series of tidal elevation (h), wind speed (Sw), wind direction ( w), significant wave height (Hs) and peak wave period (Tp) for an interval between successive GY28 profile measurements obtained on 5 October 2010 to 3 December 2010. Using XBeach in 1D mode, GY28 was extended offshore to -10 m ODN and the model was forced using the data shown in Figure. 5.

XBeach Bathymetry for the 2D XBeach model was extracted from the MIKE21 FM model and used to create a non-linear grid with a variable spatial resolution across the model domain. For each scheme the grid mesh over the structures was 1 m and extended approximately three groyne lengths alongshore to the north and south of the schemes and offshore a distance of c. 500 m. The interpolated bathymetry for both schemes is presented in Figure 4. The scheme groynes were defined as ‘hard structures’ in the model (i.e. non-erodible). The model was run assuming that the representative median grain size (D50) for the beach sediments was 0.25 mm and D90 = 0.3 mm (HR Wallingford 2012a). The depth of available sediment at all locations was assumed to be 2 m. Water levels, extracted from the MIKE21 FM-HD model, were applied at the northern and southern boundaries of the XBeach model to generate a shore-parallel tidal flow field with current speed and direction characteristics that agreed closely with the independently verified MIKE21 FM-HD model.

Verification of the XBeach model Beach profile GY28 is located approximately mid-way along the Hopton-on-Sea frontage surveyed by the Great Yarmouth Port

Figure 5. Time-series data used in XBeach model validation.



The measured and predicted GY28 beach profiles at the start (5 October 2010) and end (3 December 2010) of the model run are shown in Figure 6. The model predicts erosion in a cross-shore region spanning approximately 45 m between 2 m and -1 m ODN and accretion in a cross-shore region spanning approximately 25 m between -1 and -5 OND (Figure 6). A Brier Skill Score (BSS) of 0.89 indicates excellent agreement between the observations and the model predictions (Van Rijn et al., 2003). More than 90% of the changes to GY28 during the simulation period occurred during a storm beginning around 8 November 2010 when Hs > 2.5 m (shown by the shaded region in Figure 5). Changes to GY28 during this storm are illustrated in Figure 6 (insert) which shows a surface fitted to a chronological time-stack of predicted beach erosion and accretion spanning a 12 hour period from the start of the storm. XBeach was also verified as being fit-for-purpose at 8 other locations between Hopton-on-Sea and Gorleston. Here it is assumed that the model performs equally well in 2D mode.

Storm scenarios Selecting wave sectors with the highest percentage of occurrence 1:35 year storm wave scenarios from approximately northeast by north (NEbN) and southeast by south (SEbS) directions were obtained from HR Wallingford (2011a) and used to define waves at the northern, southern and offshore boundaries of the MIKE21 FM-SW model (Table 1). Due to the limited fetch in the North Sea, wave directional spreading was set to 30°. The 2D XBeach model runs used wave data extracted from the MIKE21 FM-SW model at the offshore location coincident with the XBeach offshore boundary (i.e. -10m ODN, Table 1). Waves were introduced along the offshore boundary of the XBeach model as JONSWAP spectra and the directional spreading coefficient was set as time invariant.

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Table 1. Offshore and inshore 1:35 year return period waves scenarios applied at the offshore boundaries of the MIKE21 FM-SW and 2D XBeach models. MIKE21 FM-SW 2D XBeach Wave Hs Tp Hs Tp Scenario (m) (s) (m) (s) (oN) (oN) 4.53 10.3 30 1.71 7.0 72 NEbN 4.15 9.4 150 1.75 7.0 90 SEbS has been to assist scheme design and to assess near and far-field impacts. Therefore results presented here focus on the following model outputs over a tidal cycle: (a) average combined wave and tidal current (w-c) flows; (b) critical bed shear stress expressed as the percentage of time w-c flows exceed the critical bed shear stress for sediment entrainment ( crit), hereafter termed %T; (c) percentage change in total load sediment transport magnitude between the baseline condition and the scheme; and (d) changes in beach and nearshore morphology. It is assumed that crit, for D50 = 0.25 mm and ρs = 2650 kg/m3 is 0.19 N/m2 (Soulsby, 1997). Focussing on the nearshore flows for the NEbN baseline case, Figure 7a shows: w-c flow speed in the nearshore region is around 0.3 m/s and tidal currents in excess of 0.4 m/s are located offshore. For Scheme 1, a reduction in w-c flow speed occurs over the length of the scheme, especially between the structures (Figure 7b). Similar flow speed attenuation occurs in Scheme 2 (Figure 7c). Nearshore w-c flows for the SEbS scenario (c. 0.4 m/s) are higher than the NEbN scenario due to differences in the wave incidence angle. Flow attenuation by both schemes is shown in Figure 7e and 7f.

RESULTS As numerical models have a potential to generate extensive data sets, it is important to select the information most relevant to a given study. The primary aim of this numerical modelling study

Figure 6. Beach profiles at the start and end of XBeach model run. Insert shows comparison between measured and predicted storm impacts at GY28.

Figure 7. Tidally averaged w-c flow speeds: (a) baseline NEbN; (b) Scheme 1 NEbN; (c) Scheme 2 NEbN; (d) baseline SEbS; (e) Scheme 1 SEbS; (f) Scheme 2 SEbS.


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If is accepted that scheme impact alongshore is reflected by the distance over which the w-c flow again attains a value above Ucrit (i.e. the value competent to mobilise and transport sediments = 0.41 m/s, Soulsby, 1997), Figure 7 indicates that the scheme impact extends northwards less than one groyne length and two groyne lengths southwards in the NeBN scenario. The reverse is true for the SEbS scenario with impacts extending less than one groyne length southwards and two groyne lengths northwards. In both schemes the attenuation of w-c flows to values < 0.3 m/s in groyne embayments indicates sediment mobility will be reduced compared to the baseline case, thus providing beach protection and possibly accretion by the trapping of some proportion of the sediment moving alongshore. Deflection of flow streamlines around the groyne heads and wave action may also contribute to sedimentation processes within the groyne embayments. The MIKE models showed that in the nearshore region, w-c flows exceed crit for more than 90% of the time. This is primarily attributable to wave-induced flows (radiation stress-driven), as the tidal currents in this region are relatively weak (see Figure 7). Closer inshore, as a result of wave breaking and tidal flow attenuation by bed friction, the %T decreases from a maximum value in the breaker zone to zero at the shoreface. Similarly, the increase in water depth offshore reduces both w-c bed shear stress and %T. The impacts of Scheme 1 are highly localised and principally confined to regions close to the structures. The local reductions in %T reflect wave sheltering and attenuation effects. There is no more than an approximate 10% reduction compared to the baseline to the north and south of Scheme 1. Seaward from the groyne heads, %T values are slightly enhanced compared with the baseline, probably due to the deflection of flow streamlines around the structures. Other than a very slight reduction in %T to the south of Scheme 2, no other impacts are evident. These results imply that waves are able to penetrate into the groyne embayments and generate approximately the same w-c bed shear stress as the baseline case. Percentage changes in total load sediment transport magnitude, Qtot, between the baseline condition and the two schemes are shown in Figure 8 for ebb (tidal flow from south to north) and flood (tidal flow from north to south) flows and for each wave scenario (MIKE21 FM model). It should be noted, that although useful to illustrate differences between baseline and scheme cases, the percentage change can be misleading (e.g. a false impression of large changes when absolute values are small). There are several features common to each sub-plot in Figure 8: (a) a decrease in Qtot of the order of 30% to 40% in inter-groyne embayments; (b) localised increases in Qtot near the base and head of the scheme structures; (c) significant differences between ebb and flood flows especially for Scheme 2 as it is emerged around the time of peak ebb flow. The redistribution of wave energy, combined with a reduction in tidal current speed is shown to be responsible for the decrease in sediment transport at mid-distance between groynes. Changes in bed elevation over a single spring tidal cycle (c. 12.5 hours) predicted by the 2D XBeach model for Schemes 1 and 2 are illustrated in Figure 9 for the NebN and SEbS wave scenarios. Given limitations imposed by the surficial sediment depth defined in the model, the absolute changes in bed elevation may be either: (a) under-estimated due to depth-limited sediment cover; or (b) over-estimated because the depth of available sediment is less than 2 m and thus the patterns of erosion and accretion shown in Figure 9 indicate likely sedimentation patterns and must be interpreted with caution. Further, the 1:35 year wave return period wave events in the model represent an extreme event and thus the predicted beach impacts are correspondingly ‘extreme’.

Figure 8. Percentage change in total load sediment transport magnitude between the baseline condition and schemes: (a) NEbN ebb tide Scheme 1; (b) NEbN flood tide Scheme 1; (c) NEbN ebb tide Scheme 2; (d) NEbN flood tide Scheme 2; (e) SEbS ebb tide Scheme 1; (f) SEbS flood tide Scheme 1; (g) SEbS ebb tide Scheme 2; and (h) SEbS flood tide Scheme 2. Additionally, the initial beach morphology used in the 2D XBeach model is defined by the most recent beach survey data. This may reflect previous unknown and unrecorded erosive and/or accretionary phases and thus may not be representative of the ‘typical’ beach form. The erosion and accretion predicted by the 2D XBeach model is therefore predicated to some degree by the initial beach ‘state’ and should be taken into consideration when interpreting the model results. Irrespective of the scheme or wave scenario Figure 9 exhibits two primary features: (a) a linear, approximately shore parallel, accumulation of sediments (hereafter termed a ‘bar’) that extends across the whole model domain; and (b) a zone of erosion that increases in depth shoreward from -0.5 m to -1.5 m. There is also evidence of erosion in the vicinity of the groyne heads and variable individual patterns of erosion and accretion in the intergroyne embayments. Although exhibiting some spatial variability in accretion depth, the bar is homogeneous and, other than localised interactions with the structures, show no morphological signature that can be easily associated with the scheme. Similarly, the greatest predicted erosion depths are confined to the most shoreward regions and are similar alongshore across the model domain. In this respect the optimised linear scheme appears to have little or no impact on beach erosion compared with locations two or more groyne lengths to the north or south of the scheme.

CONCLUDING REMARKS Coastal defence funded privately (e.g. BLL scheme described here and Bunn Leisure, 2013) or in partnership with local and/or



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incoming waves. However, the alongshore distance of potential impacts tends to be longest lee-ward of the groynes relative to the incoming wave direction. Together, the model results have therefore assisted the development of a cost-effective final scheme design which minimizes potential environmental impacts with respect to coastal and sediment processes. It is acknowledged that the models used here can only look realistically at the two proposed schemes over short periods and thus cannot provide reliable information on the medium- or longterm scheme performance and impacts, where only experience and expert judgment can provide guidance. So that greater confidence can be given to results from similar modelling studies in the future, it is important that the medium- and long-term impacts of the final scheme to be built at Hopton-on-Sea are monitored and disseminated. Finally, looking at the proposed scheme from an ecological perspective, rock structures will change the natural habitat and in turn may lead to unpredictable decreases or enhancements in local biodiversity. Further, depending on a personal viewpoint, the structures might be viewed as being visually intrusive and thus detrimental to environment aesthetics. These aspects of the scheme in the construction and operation phases, and those concerning water quality, fish and fisheries, noise and vibration, recreation, tourism and economics etc. are currently the subject of an independent environmental impact assessment process with key stakeholders. This will be prepared in accordance with the requirements of the EIA Directive (85/337/EEC as amended), the Town and Country (EIA) Regulations 2011 and the Marine Works (EIA) (Amendment) Regulations 2011. Figure 9. Changes in bed elevation predicted by the 2D XBeach model: (a) NEbN Scheme 1; (b) NEbN Scheme 2; (c) SEbS ebb tide Scheme 1; and (d) SEbS ebb tide Scheme 2. national authorities is often undertaken when the value of an asset over a business cycle or the strategic importance of a site makes economic sense. The selected defence design must provide an acceptable level of protection and no adverse environmental impacts must be demonstrated. The work presented here has demonstrated that the use of complementary models that are designed to simulate specific processes and scenarios provide greater confidence in model results when good agreement between models predictions can be demonstrated. Specifically, refinements to the present scheme design were made possible by the use of the XBeach model which provided key information on the cross-shore limits of sediment transport in storm conditions and by the MIKE21 model which provided information on alongshore scheme impacts. MIKE21 FM-HD/SW/ST and XBeach model results have assisted in the design of defence scheme structures (height, profile, length and spacing) and have provided guidance on how the scheme is likely to perform and the impacts it may have on the adjacent shorelines. They have also allowed preliminary material quantities and cost estimates to be confirmed. The XBeach modelling has shown that storm waves with a 1:35 year return period from NebN and SebS directions will result in: (a) a linear alongshore, approximately shore parallel bar 2 m in height; and (b) a zone of erosion that increases in depth shoreward from c. -0.5 m to -1.5 m. Both models show that during a typical spring tidal cycle the maximum potential impacts of the optimised linear schemes extend no more than 150 m and 100 m to the north and south of the groyne field for Scheme 1 and 2, respectively. The exact distance to which these potential impacts extend is determined by the angle of incidence and the energy of the

ACKNOWLEDGEMENT Thanks are extended to Bourne Leisure Ltd. who funded the work described in this paper and granted permission for its publication.

LITERATURE CITED Bunn Leisure, 2013. http://beautifulbeach.bunn-leisure.co.uk/about-ourbeautiful-beach.aspx HR Wallingford, 2002. Southern North Sea Sediment Transport Study, Phase 2: Sediment Transport Report. Report EX4526. HR Wallingford, 2011a. Hopton Coastal Studies: Wave Modelling. Report EX 6680, Release 1.0, 80pp. HR Wallingford, 2011b. Great Yarmouth. Beach and nearshore monitoring report. EX 6469, Release 1.0, 76pp. HR Wallingford, 2012a. Hopton Coastal Studies: Numerical Hydrodynamic and Sediment Transport Modelling. Report EX 6595, 270pp. HR Wallingford, 2012b. Hopton Coastal Studies: Numerical Hydrodynamic and Sediment Dispersion Modelling. Report EX 6595Addendum 2, 50pp. HR Wallingford, 2013. Hopton Coastal Studies: Numerical Hydrodynamic and Sediment Dispersion Modelling. Report EX 6595-Addendum 3, 96pp Roelvink, J.A. Reniers A., van Dongeren, A., de Vries, J., McCall, R., Lescinski, J., 2009a. Modelling storm impacts on beaches, dunes and barrier islands. Coastal Engineering, 56(11-12), 1133-1152. Roelvink, J. A., Reniers A., van Dongeren, A., de Vries, J., Lescinski, J., & McCall, R., 2009b. XBeach model description and manual, Deltares/TU Delft, The Netherlands, 96pp. SMP (Shoreline Management Partnership), 2013. An Investigation into the causes of beach erosion and effects of the Outer Harbour development at Hopton-on-Sea. Volumes I - IV. Van Rijn, L. C., Walstra, D. J. R., Grasmeijer, B., Sutherland, J., Pan, S. & Sierra, J. P., 2003. The predictability of cross-shore bed evolution of sandy beaches at the time scale of storms and seasons using processbased profile models. Coastal Engineering, 47, 295-327.
