L UNIVERSITÉ DE PAU ET DES PAYS DE L ADOUR. Storm impact on engineered pocket beaches

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1 N o attribué par la bibliothèque THÈSE PRÉSENTÉE À L UNIVERSITÉ DE PAU ET DES PAYS DE L ADOUR ÉCOLE DOCTORALE DES SCIENCES EXACTES ET DE LEURS APPLICATIONS PAR Iñaki de Santiago González POUR OBTENIR LE GRADE DE DOCTEUR Spécialité: Génie Civil Storm impact on engineered pocket beaches Soutenue le 18 décembre 214 Après avis de N. Senechal Rapporteur D. Idier Rapporteur Devant la commission d examen formée de : S. Abadie Directeur de thése D. Morichon Co-Directeur de thése P. Liria Co-Directeur de thése N. Senechal Examinateur D. Idier Examinateur B. Castelle Examinateur V. Rey Examinateur P. Gaudin Président

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3 Storm impact on engineered pocket beaches Iñaki de Santiago Abstract The aim of this study is to understand the response of engineered pocket beaches to storms. To that end, a series of video images, field topographical measurements and depth-averaged (2DH) process-based model have been used. The beach of Zarautz was chosen as a study site due to its wave climate characteristics and beach configuration. It is an embayed beach composed by two well defined regions, a dune system and an engineered section. The offshore wave climate is characterised by a low directional variability. The 95 % of the cases ranges from W to N directions. The high energetic events are seasonally variable. Most of the storms take place during winter and autumn. The wave climate at the beach of Zarautz is almost unidirectional and it presents certain alongshore variability. The temporal and spatial variability of nearshore sandbars, using daily video observations over 2 years was carried out. In general the beach acts as an open beach like circulatory system but it may present cellular and transitional circulation during high energy events. The nearshore sandbars evolution covers a wide range of temporal and spatial variability. Interestingly, the western engineered and more sheltered section of the beach sometimes exhibits a different beach state to that of the eastern section. To study the response of the beach to high energy events, systemically designed topographic surveys were undertaken before and after storm events. The location of the rip currents seems to play a role on the beach erosion. Static and persistent rips during moderate high energy conditions may erode locally the beach intertidal zone. During high energetic conditions and spring tides the beach backshore and dune area is eroded. Dune and backshore sections become important as they act as a buffer, preventing the foreshore erosion. On other hand, during high energetic conditions coinciding with neap tides, the evolution of the foreshore, backshore and dunes might be sensitive to the wave characteristics rather than to the tidal range. The findings obtained from the video images and field measurements were completed by means of the XBeach process based model. Due to the lack of a pre-storm bathymetry the XBeach-Beach Wizard model was used in order to infer the surfzone features. The iii

4 iv possibility to force the model with non-uniform alongshore wave conditions was implemented. Results show that this new implementation improves the model skills. The XBeach calibration tests reveal that the results can vary considerably depending on the set of parameters chosen to run the model. Parameters such as short wave run-up, γ, γ ua, eps and h min seem to be relevant for the model calibration. A series of storm impact simulations were performed. A chain transport mechanism was found in which the sand is transported from the dunes to the intertidal zone, and never in the other way around. The erosion of the different sections of the beach is highly related to the tidal level rather that to the wave power. The main differences in the beach response between the natural and engineered sections are related to the sand budget. The complete loss of the backshore sand makes the intertidal zone weak to the storms (the chain transport is interrupted). This scenario is only likely to happen at the engineered sector due to the narrow backshore and the absence of a dune system. Some tests were performed in order to relate the storm magnitude to a certain value of beach erosion. These findings point out that, in general, the higher the storm power is, the larger is the beach erosion. However, the wave characteristics that define a given storm play an important role. Furthermore, in some cases a low power storm with high H s and T p can produce larger changes on the beach than a large storm with low H s and T p.

5 Acknowledgements Now, once the work is done, if I look back I can say that I enjoyed all the way. There were tough moments, but all of them contributed to increase my knowledge in different aspects of my life. I am grateful to have had the opportunity to develop a whole thesis related to the sea and beaches, a place that I have always loved and been linked to. I would like to express my gratitude to AZTI-Tecnalia for supporting the project over these years and the Université de Pau et des Pays de l Adour. First and foremost, I would like to thank the supervisors of my thesis, Stéphane Abadie, Denis Morichon and Pedro Liria for their inspiration, supervision and feedback during all the aspects of the project. I learned so much from you during my doctoral study. Stéphane Abadie, thank you for your curiosity and perseverance in understanding the intricacies of the model. The long hours spent discussing the physics of the problematic fed my knowledge. Denis Morichon, thank you for your unlimited guidance and encouragement, especially, during hard periods when I got run out of ideas. You always motivated me and proposed new approaches. Pedro Liria, thank you for teaching me a more practical way to understand the theory. Surfing days accompanied with debates of coastal dynamics were the best motivation possible. I would like to express my sincere gratitude toward the members of my graduation committee for their insightful comments and the great discussions. I particularly thank Bruno Castelle, for his comments and help during the first stage of my thesis. Ad Reniers, thank you for the useful discussion and for giving me the opportunity to visit your department at the University of Miami. I will never forget the delicious barbecued salmon, the intense football matches played in the greenish pool and the happiness of drinking a beer while watching the precision of Joe Flacco when passing the ball. Stella, Femke and Lennart, thanks for your big hospitality, I felt like I was at home. I thank my AZTI workmates for all the fun we had during this period. Jon, we have to admit that Real Sociedad games are not something extraordinary, but, if you add a nice conversation and tons of Chinese food, it becomes something extraordinary. Jon (Mapatxe), mountain trails and swimming in the sea in the early morning of February helped me to get away from my numerical waves at the worst times. Jorge, the human gecko, thanks for sharing with me these caramelitos surfeables of the Landaise coast. v

6 vi Carlitos, keep dancing, your Latin lifestyle reassures anyone. Guille, we didn t run so much, but we laughed a lot. Luis, thank you to your gofio breakfasts, I always got the extra energy I needed to face a hard day of programming. Manuel, thank you for your Fortran classes, without your help I would not have been able to conduct many parts of this PhD. Julien, thank you for the beers and champions league matches, they were a good way to calm down my boiling brains. Irati, my little Axpalor. Who would have thought that spending so many hours calibrating cameras and walking on the beach would have allowed me to know you so well? It has been a real pleasure meeting you. Also, I would like to thank my friend from the University of Miami, Atsushi. Thank you for showing me the best Japanese restaurants in town and drive me to those wonderful places where my bike could not reach; your hospitality was huge. Thanks to my master colleagues Miri, Lara, Alba, Manu, Vincent and Edu, who supported me and gave their opinion of the work. To my kuadrila. Thank you for still being my friends in spite of hardly seeing you during these years. Stefani, I owe you a lot, despite being physically far you have always been emotionally close. Finally, I wish to express my gratitude to my parents and sisters for their help, encouragement, and continuing support. Thank you all for putting up with me at my worse. Thanks ama and aita for letting me stumble and fall by myself to learn how to deal with the life s difficulties.

7 Contents Abstract Acknowledgements iii v Contents List of Figures List of Tables vii xi xix 1 Introduction Context Pocket beaches Engineered beaches Storm impact Storm impact scale Swash regime Collision regime Overwash regime Inundation regime Pocket beach circulation Sand dune systems Seawalls Storm impact modelling Descriptive conceptual models Models based on the equilibrium profile theory Process-based models Motivation Objective Study site Scientific questions Approach Method Thesis outline Wave climate Introduction vii

8 Contents viii 2.2 Wave dataset Offshore wave climate Mean wave climate Extreme wave climate Offshore storm power Nearshore wave climate Wave propagation method Mean wave climate Extreme wave climate Calibration of the return periods Nearshore storm power Conclusions Nearshore sandbar morphodynamics of the beach of Zarautz Introduction Material and methods Video monitoring station (KOSTASystem) Beach state classification Image smoothing algorithm Outer bar detection Results Inner bar morphology and dynamics Outer bar morphology and dynamics Accretionary evolution of the inner bar Accretionary evolution of the outer bar Discussion and conclusions Beach morphological response to storm events Introduction Material and methods Beach profiling Beach plan evolution Results Extreme wave conditions Profile analysis Transect volume evolution Dune evolution Plan view analysis Case 1: Relevance of rip current location Case 2: Relevance of storm magnitude Case 3: Relevance of storm magnitude coinciding with spring tidal conditions Discussion and conclusion XBeach: Numerical modelling Introduction Model philosophy

9 Contents ix 5.3 Model approach and governing equations Short wave propagation Roller energy propagation Wave flow and long wave propagation Sediment transport and bed level change Avalanching algorithm Bathymetry estimation by assimilation techniques (XBeach-Beach Wizard) Beach Wizard model description Model adaptation Verification of the boundary adaptation Sensitivity tests Results Influence of the initial bathymetry Influence of the Tr free parameter Influence of the wave forcing accuracy Discussion and conclusions Initial bathymetry Tr parameter Wave forcing accuracy Boundary adaptation performance: Sensitivity tests: Model calibration Offshore boundary conditions Model grid and bathymetry Calibration parameters Model parameters Wave spectra parameters Conclusions Storm impact simulations Storm of February 213: Hydrodynamic forcing variations Discussion and conclusions Storm of February 213: Single storm/storm cluster Discussion and conclusions Synthetic storm scenarios Results Discussion and conclusions Conclusions, recommendations and future perspectives Conclusions Research Questions Numerical modelling recommendations Future perspectives A Appendix A: Estimation of the directional spreading 139 B Appendix B: Wave dominated beach types 141

10 Contents x Bibliography 145

11 List of Figures 1.1 Basque Coast (northern Spain) beach examples. Left) Natural beach (Laida, Mundaka). Right) Engineered beach (La Zurriola, Donostia - San Sebastian) Examples of typical embayed beach circulations as described in Short and Masselink [1999], source: Castelle and Coco [212]. a) Cellular beach circulation with a rip current at the centre of the beach. b) Cellular beach circulation with one headland rip. c) Cellular circulation with two headland rips. d) Transitional beach circulation with one headland rip and additional rip channels away from the headland. e) Transitional beach circulation with one headland rip and two additional rip channels within the embayment. f) Normal beach circulation with one headland rip and six to seven additional rip channels along the beach Example of coastal structures. a) Groins and seawall (Anglet, France). b) Shore parallel breakwaters (Cambrils, Spain). c) Seawall (Zarautz, Spain) Conceptual model proposed by Sallenger [2] for scaling the storm impact on barrier islands. Source: U.S. Geological Survey Megarip circulation during storm wave conditions for Arrifana, source: Loureiro et al. [212]. Arrows provide flow-behaviour indications of the megarips, and dashed lines indicate rip-head plumes. The intense wave breaking across the entire surf zone is reduced within the rip-neck channel due to wave current interaction Profile evolution during a storm. Source: Van Thiel de Vries [29] Scour hole development in front of a seawall during storm conditions. Source: Adapted from De Vries [211] The beach of Zarautz (North Spain) The different sectors of the beach of Zarautz. Left) Natural sector. Right) Engineered sector Left) Bay of Biscay. Red dot: Bilbao Vizcaya buoy. Green dot: Donostia buoy. Yellow dot: Anglet buoy. Magenta dot: Saint Jean de Luz buoy. Blue dot: Study site (Zarautz). Right) Offshore wave dataset. The red highlighted line indicates the period where spectral information is available Left) Offshore wave rose. Right) Offshore Hs-Tp joint probability. Black dashed line indicates 1/19.7 steepness curve Directional offshore Hs-Tp joint probability Offshore wave directional spreading (DSPR). Vertical red dashed line highlights the 3 deg. spreading value (only used for reference) Seasonal offshore wave rose Seasonal offshore H s - T p joint probability xi

12 List of Figures xii 2.7 Left) Offshore wave rose (extreme events). Right) Offshore Hs-Tp joint probability (extreme events). Black dashed line indicates 1/19.7 steepness curve Extreme event seasonal occurrence Offshore extreme wave directional spreading (DSPR). Vertical red dashed line highlights the 3 deg spreading value (only used for reference) Top) Weibull fitting curve. Bottom) H s return periods a) Offshore storm duration histogram. b) Offshore inter-storm duration histogram Offshore storm power. Top - left) Maximum H s registered within a storm. Top - right) Mean T p registered within a storm. Bottom - left) Mean θ p registered within a storm. Bottom - right) Storm duration. The horizontal lines correspond to 1, 3 and 5 year return period limits Left) Cumulative energy spectrum. White dots represent propagated bins. Right) Cape San Anton filtering effect (red shadowed directional band). Red dashed line indicates the wave propagation model boundary limit. Red and yellow dots indicate the location of the Nortec Awac and Teledyne RDI 6 wave recorders deployed during one month period Left) Computational meshes used for the wave propagation. Right) Examples of wave propagation Transformation coefficients. a-b) Wave height transformation coefficients (a: West side of the beach, b: East side of the beach). c-d) Wave direction transformation coefficients (c: West side of the beach, d: East side of the beach) Validation of the matrix propagation methodology against the real measures at two sides of Zarautz beach (depth around 18 m), during a 1-month period Nearshore wave roses. Left) West side. Centre) Central zone. Right) East side Alongshore variability at the seaward boundary of the beach of Zarautz Left) Nearshore Hs-Tp joint probability. Right) Nearshore wave directional spreading (DSPR) Return period calibration. Left) H s. Right) Storm power. Top) Comparison of the return periods with the 23 years dataset (red) and 1 years dataset (blue). Bottom) Fitting curve relating the 23 years dataset and 1 years dataset a) Nearshore storm duration histogram. b) Nearshore inter-storm duration histogram Nearshore storm power. Top - left) Maximum H s registered within a storm. Top - right) Mean T p registered within a storm. Bottom - left) Mean θ p registered within a storm. Bottom - right) Storm duration. The horizontal lines correspond to 1, 3 and 5 year return period limits Camera resolution. Top) The beach of Zarautz. Centre) Angular resolution. Bottom) Radial resolution Image smoothing. Left top) Raw image. Left bottom) Smoothed image. Right) Relation between intensities of adjacent images

13 List of Figures xiii 3.3 Bar detection example. Red dashed line represents the final detected bar. Black dashed line is a transect represented in terms of intensity (blue line) in the right side of the image. Green dashed line represents the maximum intensity location Top) Empirical δ distribution function. Bottom) δ histogram Top) Probability of beach states occurrence. Centre) Residence time and standard deviation (hatched bar). Bottom) Mean significant wave height at the engineered (light) and natural (dark) sections for the inner bar Left) Time stack of alongshore deviation lines. Right top) Mean outer bar position. Right bottom) Wave characteristics. Black line represents the offshore characteristics. Red dashed line represents the nearshore characteristics Accretionary evolution of the inner bar (see text for explanation) Accretionary evolution of the outer bar (see text for explanation) Beach profile location (black lines) and fictitious seawall extension (red dashed line) Scheme of beach and dune volume estimation Shoreline detection and interpolation at different tidal stages (October 211). Black lines represent the measured profiles. coloured lines represent the video-detected shoreline Interpolation method accuracy test. Top) Regular transects are indicated by black lines and the additional transects are indicated by red lines. Bottom) Differences between regular campaign and additional transect campaign Top) Relation between storm duration and its relevance. Bottom) Relation between storm relevance nearshore and offshore Top) Time series of offshore significant wave height (H s ), red lines represents high-energy events and vertical black lines the timing of beach surveys. Centre) Volume changes, black crosses represent data gaps. Bottom) Averaged cumulative volume changes Top) Dune evolution between survey 14 and survey 15. Bottom) Astronomical tidal elevation (blue) and instantaneous waterline elevation (red-dashed) computed by empirical formulation (Stockdon et al. [26]) Intertidal erosion/accretion patterns between surveys 1-2. a) Offshore H s (dark blue) and H s at the seaward boundary of the study site (Blue). Grey line indicates the astronomical tidal elevation. b) Offshore wave period. Storms are highlighted by red lines. c) Elevation differences between surveys 1 and Intertidal erosion/accretion patterns between surveys a) Offshore H s (dark blue) and H s at the seaward boundary of the study site (Blue). Grey line indicates the astronomical tidal elevation. b) Offshore wave period. Storms are highlighted by red lines. c) Elevation differences between surveys 12 and 13. d) Elevation differences between surveys 13 and Transect evolution during surveys

14 List of Figures xiv 4.11 Intertidal erosion/accretion patterns between surveys a) Offshore H s (dark blue) and H s at the seaward boundary of the study site (Blue). Grey line indicates the astronomical tidal elevation. b) Offshore wave period. Storms are highlighted by red lines. c) Elevation differences between surveys 14 and Synthetic test cases. a) Alongshore non uniform boundary example (H west = 1 m, H east = 1.3 m, T = 11 sec., θ = ). b) Alongshore uniform boundary example (H mean = 1.15 m, T = 11 sec., θ = ). c) Synthetic case wave data series. Black dashed line represents the western boundary input. Coloured lines represent eastern boundary input. Red line is 1% larger than black dashed line. Green line is 3% larger than black dashed line. Blue line is 5% larger than black dashed line RMSE error of each cross-shore transect of the beach. a-c) cross-shore RMSE error for the NUB (black line) and UB (black dashed line). d) Relative error computed as x NUB x UB x UB 5.3 Transect elevation differences. a) Initial and target profiles. b-c-d) Differences between target elevation and final result. Dashed red line represents the differences at the eastern transect using UB. Red line represents the differences at the western transect using UB. Dashed black line represents the differences at the eastern transect using NUB. Black line represents the differences at the western transect using NUB. b) test with 1% of alongshore variability. c) test with 3% of alongshore variability. d) test with 5% of alongshore variability Alongshore boundary characteristics. Top) Wave energy alongshore variability. Centre) Mean wave energy and its standard deviation. Bottom) Mean wave incidence direction and its standard deviation a) Target bathymetry (March 213). b) Initial bathymetry (June 212). c) Result obtained applying UB & Tr = 5. d) Result obtained applying NUB & Tr = 5. e) Result obtained applying UB & Tr = 1. f) Result obtained applying NUB & Tr = a) Target bathymetry (March 213). b) Initial bathymetry (linear). c) Result obtained applying UB & Tr = 5. d) Result obtained applying NUB & Tr = 5. e) Result obtained applying UB & Tr = 1. f) Result obtained applying NUB & Tr = a) Target bathymetry (March 213). b) Initial bathymetry (opposite to target). c) Result obtained applying UB & Tr = 5. d) Result obtained applying NUB & Tr = 5. e) Result obtained applying UB & Tr = 1. f) Result obtained applying NUB & Tr = Relative errors obtained at the different simulations with respect to the default values (UB and Tr = 5). Square marks represent the tests performed with June 212 bathymetry as initial bathymetry. Circle marks represent the tests performed with Linear bathymetry as initial bathymetry. Triangle marks represent the tests performed with Opposite bathymetry as initial bathymetry. The surf zone represents the area where: -4 < depth (m) -1. The shoaling zone represents the area where: depth (m) RMSE error of each cross-shore transect of the beach along the surf zone (-4 < depth (m) -1)

15 List of Figures xv 5.1 Sequence of storms during the 1 st and 14 th of February at the seaward boundary of the study site. Storms are highlighted by red lines Computational grid. Top) The computational grid including the bottom elevation. Black dashed line indicates the transition from engineered (left side) to natural zone (right side). Bottom) Grid spacing in the cross-shore axis D eps parameter calibration. Top) Profile response to different parameter values. Horizontal dashed blue lines represent the mean water level and the high water level. Bottom) RMSE error values for different sections of the profile (LWL = from low tidal level to mean tidal level; HWL = from mean tidal level to high tidal level; DWL = from high tidal level to top of the profile) and for different parameter values. Vertical dashed black line indicates the model default value D γ ua parameter calibration. Top) Profile response to different parameter values. Horizontal dashed blue lines represent the mean water level and the high water level. Bottom) RMSE error values for different sections of the profile (LWL = from low tidal level to mean tidal level; HWL = from mean tidal level to high tidal level; DWL = from high tidal level to top of the profile) and for different parameter values. Vertical dashed black line indicates the model default value D γ parameter calibration. Top) Profile response to different parameter values. Horizontal dashed blue lines represent the mean water level and the high water level. Bottom) RMSE error values for different sections of the profile (LWL: from low tidal level to mean tidal level; HWL: from mean tidal level to high tidal level; DWL: from high tidal level to top of the profile) and for different parameter values. Vertical dashed black line indicates the model default value D h min parameter calibration. Top) Profile response to different parameter values. Horizontal dashed blue lines represent the mean water level and the high water level. Bottom) RMSE error values for different sections of the profile (LWL: from low tidal level to mean tidal level; HWL: from mean tidal level to high tidal level; DWL: from high tidal level to top of the profile) and for different parameter values. Vertical dashed black line indicates the model default value D short wave run-up parameter calibration. Top) Profile response to different parameter values. Horizontal dashed blue lines represent the mean water level and the high water level. Bottom) RMSE error values for different sections of the profile (LWL: from low tidal level to mean tidal level; HWL: from mean tidal level to high tidal level; DWL: from high tidal level to top of the profile) and for different parameter values. Vertical dashed black line indicates the model default value D calibration. Prefix S, correspond to the different sectors of the beach. Each boxplot (in a given subplot) represents RMSE error values for different sections of the profile (left: entire profile; centre: from mean tidal level to top of the profile; right: from low tidal level to mean tidal level) Calibrated profiles. Top) Differences in elevation between computed and measured profiles. Bottom) Measured and computed profiles

16 List of Figures xvi D calibration. Wave spectral shape relevance. Prefix S, correspond to the different sectors of the beach. Each boxplot (in a given subplot) represents RMSE error values for different sections of the profile (left: entire profile; centre: from mean tidal level to top of the profile; right: from low tidal level to mean tidal level) Wave spectral shape relevance. RMSE error comparison RMSEn RMSEc RMSE c Wave spectral shape relevance. Top) Profile volume erosion during 6 hours simulation. Bottom) Profile response to different spectral shapes Scheme of volume estimation for the different sections of the beach Volumetric beach changes due to Real storm impact. A) H s and tidal level (η). Blue line indicates H s, red line highlights the storm presence and black line indicates tidal elevation. INT) Intertidal volume evolution. BACK) Backshore volume evolution. DUNE) Dune volume evolution. Dashed black line refers to the natural section and the solid black line to the engineered sector Volumetric beach changes due to tide inverted storm impact. A) H s and tidal level (η). Blue line indicates H s, red line highlights the storm presence and black line indicates tidal elevation. Grey line represents the real storm characteristics and evolution. INT) Intertidal volume evolution. BACK) Backshore volume evolution. DUNE) Dune volume evolution. Dashed black line refers to the natural section and the solid black line to the engineered sector Volumetric beach changes due to wave inverted storm impact. A) H s and tidal level (η). Blue line indicates H s, red line highlights the storm presence and black line indicates tidal elevation. Grey line represents the real storm characteristics and evolution. INT) Intertidal volume evolution. BACK) Backshore volume evolution. DUNE) Dune volume evolution. Dashed black line refers to the natural section and the solid black line to the engineered sector Relative volumetric differences between real storm and tide inverted storm (black lines) and between real storm and wave inverted storm (red lines). Solid lines indicate engineered sector and dashed lines indicate natural sector Volume interchange between intertidal and backshore (top panels) and between dune and backshore (bottom panels). Blue dots refer to natural section and red dots refer to engineered sector Wave power effect on the erosion/accretion patterns. INT) Intertidal zone. BACK) Backshore zone. DUNE) Dune zone. Blue dots refer to natural section and red dots refer to engineered sector Tidal effect on the erosion/accretion patterns. INT) Intertidal zone. BACK) Backshore zone. DUNE) Dune zone. Blue dots refer to natural section and red dots refer to engineered sector

17 List of Figures xvii 5.3 Volumetric beach changes due to storm cluster and stand-alone storm impact. A) H s and tidal level (η). Blue line indicates H s, red line indicates storm presence and black line indicates tidal level. INT) Intertidal volume evolution. DRY) Backshore volume evolution. DUNE) Dune volume evolution. Dashed line refers to the natural section and the solid line to the engineered sector. Black line refers to storm cluster whereas red line refers to stand-alone storm Relative volumetric differences between grouped and stand-alone bathymetries after storm 1, 2 y a) Initial bathymetry. b) Final bathymetry after storm 1 in storm group mode. c) Final bathymetry after storm 1 in stand-alone mode. d) Final bathymetry after storm 2 in storm group mode. e) Final bathymetry after storm 2 in stand-alone mode. f) Final bathymetry after storm 3 in storm group mode. g) Final bathymetry after storm 3 in stand-alone mode Synthetic storms. A) Storms representative of 1 year return period. B) Storms representative of 3 year return period. C) Storms representative of 5 year return period. D) Storms representative of 1 year return period. Orange line: H s 5years = 7.2 m. Orange dashed line: H s 1year = 5.7 m. Green line: T = 16 sec. Green dashed line: T = 12 sec. Black solid line: Spring tide. Black dashed line: Neap tide Volumetric beach changes for different types of synthetic storms during neap tide. INT) Intertidal volume evolution. BACK) Backshore volume evolution. DUNE) Dune volume evolution Volumetric beach changes for different types of synthetic storms during spring tide. INT) Intertidal volume evolution. BACK) Backshore volume evolution. DUNE) Dune volume evolution Volumetric beach changes during a 5 years return period synthetic storms with different characteristics. H s = 7.2 and T p = 16 sec storm is represented by a magenta line and H s = 5.7 m and T p = 16 sec storm is represented by a red line B.1 Schematic illustration of the six wave dominated beach types with their general physical characteristics and patterns of wave breaking, bars troughs and currents (from Short [1999])

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19 List of Tables 2.1 Parameters of the Weibull fittings (eq. 2.1) and extreme H s related to different return periods. All quantities are expressed in [m] Storm parameters statistics. sd refers to the storm duration values and isd refers to the inter-storm duration values Basic statistical parameters of matrix propagation methodology against the real measures H s [m] and Storm power [Mw h m 1 ] values before and after the calibration process Storm power parameters statistics. sd refers to the storm duration values and isd refers to the inter-storm duration values Characteristics of storm events. Values between parentheses correspond to nearshore. H s, T p and θ has been averaged over the high energy events Characteristics of February 213 storms at the seaward boundary of Zarautz Relative differences at the end of the simulation for the tide inverted and wave inverted tests xix

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21 Chapter 1 Introduction 1.1 Context Half the world s population lives within 6 km of the sea. In fact, the population densities in coastal regions are about three times higher than the global average (Small and Nicholls [23]). The climate change consequences according to the IPCC (Intergovernmental Panel on Climate Change), include an accelerated rise in sea level of up to.6 m or more by 21; an intensification of tropical and extra-tropical cyclones and larger extreme waves and storm surges (Solomon [27]). Coasts will be exposed to increasing risks such as coastal flooding, structure damages and beach erosion. Because of that, the understanding of the coastal evolution and its response to the action of the sea is of great societal relevance and vital to develop a correct coastal planning and management (Ferreira [25]). The present work is focused on the beach erosion problematic, which is one of the most widely investigated topics in the coastal engineering community. The research in this field is required at geographical locations that can hold a large number of energetic events or on the contrary, in those areas where despite of the low energetic wave climate but due to the nature of the ground, the coast is more vulnerable to the action of the sea. The local wave climate together with the beach morphology strongly affects the evolution of the system (e.g. Smit [21]; Morton [22]). The current work is carried out at the northern Spanish coast (Basque Coast). This region is characterized not only by being located in a highly energetic region but also by presenting a complex coastline. Open beaches are almost absent in this region; however, there are plenty of pocket beaches of different dimensions and shapes. Furthermore, the wide range of pocket beaches 1

22 Chapter 1. Introduction 2 dimensions encountered along this coast, could make some of them to behave as open beach like systems (de Santiago et al. [213]). On other hand, along the Basque Coast, man-made modifications are present at different scales and grades. Most of the beaches present non-natural modifications and only few of them are still pristine (Fig. 1.1). Figure 1.1: Basque Coast (northern Spain) beach examples. Left) Natural beach (Laida, Mundaka). Right) Engineered beach (La Zurriola, Donostia - San Sebastian). 1.2 Pocket beaches Pocket beaches are common worldwide along rocky environments (Short and Masselink [1999]), covering the 5% of the world s beaches (Inman and Nordstrom [1971]; Short and Masselink [1999]). These type of beaches are sand reservoirs characterized by being confined between hard lateral boundaries, which present several tens to few kilometres in length (Hsu et al. [21]). They have been given several names as headland embayed beaches, structurally controlled beaches (Short and Masselink [1999]), spiral beaches (Krumbein [1947]; LeBlond [1972]) and hooked beaches (Rea and Komar [1975]) among others. The main particularity of pocket beaches is that the sand reservoir is conserved due to the lateral limits (if these boundaries extend far offshore enough from the closure depth). It implies (in contrary to open systems) that they can be studied as isolated systems where no gain or loss of sand is performed. Regarding their shape, due to the intrinsic characteristics of this type of beaches (grain size, lateral boundaries, beach length etc.) and the mean wave conditions, the beach adopts a stable form both in profile and planform, which is known as equilibrium state. It is common on these beaches to present a curved shore at the lee of a headland followed by a gentle transition of a relatively straight shore on the downdrift end. However, sometimes the hooked zone is barely existent and the planform becomes symmetric. The presence of lateral boundaries can, to some degree, impact the wave-driven circulation along the embayment. According to previous observations (Short and Masselink

23 Chapter 1. Introduction 3 [1999]; Castelle and Coco [212]) the beach can present three simplified circulatory patterns (Fig. 1.2). (1) Open beach like circulation, both presenting headland rips and large number of rips along the beach; (2) transitional circulation with headland rip(s) and an increasing influence of the embayment size and shape on the surf zone circulation; (3) Cellular circulation with longshore flows dominating within the embayment, and strong seaward megarips occurring at one location or both ends of the embayment. Figure 1.2: Examples of typical embayed beach circulations as described in Short and Masselink [1999], source: Castelle and Coco [212]. a) Cellular beach circulation with a rip current at the centre of the beach. b) Cellular beach circulation with one headland rip. c) Cellular circulation with two headland rips. d) Transitional beach circulation with one headland rip and additional rip channels away from the headland. e) Transitional beach circulation with one headland rip and two additional rip channels within the embayment. f) Normal beach circulation with one headland rip and six to seven additional rip channels along the beach. 1.3 Engineered beaches Engineered beaches are designed for a unique objective, the coastal protection. For that purpose, an engineered beach may present different levels and types of human made modifications. These modifications range from sand nourishment or dredging to the construction of hard structures (e.g. dikes, seawalls, breakwaters). Anthropogenic modifications of the system produce an alteration (to some degree) in the behaviour of the beach response to a given event. The understanding of the coastal structure alterations on the system represents a scientific and engineering challenge.

24 Chapter 1. Introduction 4 Depending on the type of structure and its dimensions, the repercussion on the system is different. Some constructions have the objective of modifying the beach. For example, groins and shore parallel breakwaters (also called headland breakwaters) are usually designed to retain sand (Fig a and b). In the case of groins, the alongshore sediment transport is cut up and the material is trapped, while in the case of the shore parallel breakwaters, a shoreline bulge is produced in the sheltered area behind the breakwater. On the other hand, seawalls (Fig c) are vertical structures used to protect backshore areas from heavy wave action, and in lower wave energy environments, to separate land from water. Thus, the main objective of the seawalls is not the modification of the system but its protection; however, they may produce undesirable modification depending on their design (see Section 1.4.4). Figure 1.3: Example of coastal structures. a) Groins and seawall (Anglet, France). b) Shore parallel breakwaters (Cambrils, Spain). c) Seawall (Zarautz, Spain). 1.4 Storm impact The impact of a storm depends upon a wide variety of parameters. Morton [22] stated that the principal factors affecting the beach erosion are related to the storm characteristics but also related to the nature of the beach (degree of flow confinement, antecedent topography and geologic framework, sediment textures, vegetative cover, and type and density of coastal development). In other words, the response of beaches with different characteristics (e.g. pocket and open beaches or natural and engineered beaches) do not follow the same patterns Storm impact scale The storm impact scale proposed by Sallenger [2] is widely accepted to schematically describe the nature of coast response to storms (Fig. 1.4). This scale distinguishes

25 Chapter 1. Introduction 5 between the swash, collision, overwash and inundation regimes. The limits between each regime are based on the elevation of the run up (upper limit) and the run down (lower limit). Considering how run up/down varies relatively to the dune toe/crest, the storm impact regimes can be defined. The limits between regimes represent thresholds where processes and magnitudes of impacts change dramatically. Figure 1.4: Conceptual model proposed by Sallenger [2] for scaling the storm impact on barrier islands. Source: U.S. Geological Survey. Swash regime This regime occurs when the swash is confined to the foreshore of the beach seaward of the dune or berm crest (Fig a). The swash motions can be discretized into infragravity and incident components. Due to the formation of wave groups, bound infragravity waves are formed (Tucker [195]), which are later released by the wave breaking. On other hand, the incident swash is simply the result of wave-bywave interactions with the beach face after wave breaking. However during storm conditions, (Raubenheimer and Guza [1996]) show that even when the incident band swash is saturated, infragravity swash is not, meaning that infragravity swash is dominant. Infragravity waves are reflected off the beach and depending on the beach configuration and directional properties of the incident wave spectrum, both leaky and trapped infragravity waves can be generated, which also contribute to the swash spectrum (Huntley et al. [1981]). Collision regime As the run up increases, the water layer will eventually collide with the base of the dune (Fig b) forcing the dune erosion (Shih and Komar [1994]; Smith et al. [1994], Ruggiero et al. [1996]). The eroded sand from the dune is then transported offshore and alongshore (depending on the wave and bathymetrical conditions) and usually does not return to reconstruct the dune. Overwash regime If the run up continues to increase, the overwash of the dune crest occurs (Fig c). This regime occurs through a combination of oceanographic and foreshore geomorphologic factors. Matias et al. [21] summarizes the factors controlling the frequency and intensity of overwash and the resulting morphologies. These include marine conditions (e.g. Fisher et al. [1974]), the orientation of a coast relative to the storm (e.g. Fletcher et al. [1995]), nearshore bathymetry (e.g. Ritchie and Penland

26 Chapter 1. Introduction 6 [1988]), beach topography (e.g. Leatherman [1976]), backbeach elevations (e.g. Morton and Sallenger [23]), dune morphology (e.g. Donnellyand Sallenger [27]), engineering structures (e.g. Hayden and Dolan [1977]), location and orientation of footpaths and roads (e.g. Nordstrom and Jackson [1995]), and buildings on the shorefront (e.g. Hall et al. [199]). Intensive overwash acting in association with high sea levels (e.g. storm surge) can lead to dune/barrier breaching and therefore create the potential for large-scale inundation of low-lying coastal areas. Inundation regime This regime occurs if the storm-induced sea level is sufficient to completely submerge a barrier island (Fig d). The processes that occur along the beach during this regime are not completely well understood (Sallenger [2]) Pocket beach circulation During storm conditions, some pocket beaches may present cellular circulation (Fig. 1.5), which is characterized by the strong control of the headlands over the beach circulation. Rips only take place at either the centre of the embayment or at one or both ends of the embayment. Figure 1.5: Megarip circulation during storm wave conditions for Arrifana, source: Loureiro et al. [212]. Arrows provide flow-behaviour indications of the megarips, and dashed lines indicate rip-head plumes. The intense wave breaking across the entire surf zone is reduced within the rip-neck channel due to wave current interaction. High energy events can lead to the development of headland megarips (Short and Masselink [1999]). The high velocities presented by the seaward flux together with the large extension of the megarips, lead to the erosion of the beach and deposition at the lower shoreface or even the inner shelf (Short [1985]; Short and Masselink [1999]; Short

27 Chapter 1. Introduction 7 [21]). Previous work supports this fact suggesting that such currents are able to extremely erode the beach and even the foreshore of the dune (e.g. Thom [1968]; Short and Hesp [1982]) Sand dune systems During storm events, high waves (comparing to mean conditions) reach the shore. The energy gradients occurring during the wave breaking generate high gradients in the radiations stress, inducing the super elevation of the mean water level at the shoreline. Because of this, the wave action may reach the dune toe by pulses that erode episodically the dune front (Fig. 1.6). High waves generated by a storm, induce large mass flux towards the shore. Due to the conservation law, this excess of mass flux has to be compensated. In case of waves propagating perpendicular to the shore, the onshore induced mass flux is compensated by an offshore directed return flow below the wave crest (undertow current). Those waves that are breaking at the shoreface, stir up sediment into suspension to then be transported offshore by the undertow currents. In case of alongshore non-uniform wave heights or non-uniform nearshore topography, rip currents may appear. Both non-uniform scenarios induce to alongshore gradients in radiation stress and/or set-up. The forces arising from set-up and radiation stress gradients will combine to drive a current directed away from regions of larger waves to lower waves (Troels and Masselink [1999]). The outgoing flow may be important on the transport of sediment out of the beach. In the course of the storm a new beach profile is formed (storm profile). The episodic contact of the water layer with the dune develops an erosional scarp. The scarp gradually retreats due to episodic slumping of the dune face (Van Gent et al. [28]). The sediment taken from the dune supplies sand to the swash and surf zone, which then is transported seawards by the (infragravity) backwash motions and undertow. Hence, the surf zone depth is reduced and the breaker zone is moved farther offshore. A reduced amount of waves will reach the upper part of the beach and dune face and only the lower waves (transporting less energy) will reach the shore Seawalls Seawalls are usually constructed to prevent coastal erosion and protect properties near the coast. The impact of those structures on the beach is dependent upon the size/shape of the wall and upon its position with respect to the shoreline and surf zone (Short

28 Chapter 1. Introduction 8 Figure 1.6: Profile evolution during a storm. Source: Van Thiel de Vries [29]. and Masselink [1999]). Greater impact is expected to occur when they are vertical, impermeable and are placed within swash or surf zone (Short and Masselink [1999]). In the presence of such structures, the hydrodynamics of the beach may not follow the natural pattern. Usually, the amount of sediment at this section is smaller than in a profile backed by a dune field. The lack of sediment avoids the formation of a proper storm profile. Waves do not dissipate (wave breaking dissipation) all the energy along the new profile and tend to break at the seawall front. Incoming waves impact the structure, causing water to shoot upwards. When the water falls back down, the force on the seabed brings the sediment into suspension (Bush [24]). Then, the sediment is transported seaward and a scour hole may develop (Fig. 1.7). Sometimes, the reflected energy can interact with incoming waves to set up a standing wave that causes intense scouring of the shoreline (French [21]). Figure 1.7: Scour hole development in front of a seawall during storm conditions. Source: Adapted from De Vries [211]. In case of hybrid systems (combination of dunes and structures), the amount of sediment available for erosion at the engineered sector reduces with respect to the dunes. This is represented by a difference in the elevation of the foreshore. During a storm, the water level reaches the intersection between the dunes and the seawall. The sediment is then transported from the dune profile to the seawall profile. The

29 Chapter 1. Introduction 9 loss of sediment to the seawall profile causes the dune profile to reach the storm equilibrium profile at slower rate than undisturbed dune transects. One reason to describe such behaviour could be explained by longshore currents generated due to differences in the water level. The sand taken from the dune and deposited on the breaker zone generates energy dissipation by wave breaking. In front of the seawall, the waves are still high as there is no sand budget to construct a bar and dissipate the energy. The differences in the alongshore wave heights means that there are also differences in the wave set-up (higher water level at the dune zone that at the engineered zone). The difference in water level between the two zones create a longshore current flowing from the dune side to the seawalled zone transporting sediment and slowing down the process of storm profile generation (De Vries [211]). In some cases, the longshore current is accelerated due to the constriction of the seawall. When this current exits, the dune portion next to the seawall is severely eroded (Short and Masselink [1999]). However, the seawall effect on the beach response is still barely understood. It is usually stated that they are responsible of beach erosion both in front of them and near them (Kraus [1988]). Examples of beach erosion near seawalls have been documented (Weggel [1988]), but also, the absence of any effect is identified too (Basco et al. [1997]). Rakha and Kamphuis [1997] concluded in their work (carried out using a numerical model) that the reflected wave had a small effect on the beach profile evolution, and reduced (slightly) the erosion close to the seawall. In addition, McDougal et al. [1994] concluded that the reflected wave had a small effect on the prediction of the beach profile development. Kraus [1988] evaluated the state of art on the understanding of seawall behaviour and concluded that beaches with and without seawalls exhibit similar behaviour with regard to short term erosion and recovery. The controversy found in the literature reveals that the coastal science community is still lacking a good understanding of the physical effects that seawalls have on beaches. 1.5 Storm impact modelling Several models have been presented so far to model the storm impact on dune systems. Although beach erosion processes are complex, if these processes are simplified (by making a number of assumptions), we can still obtain reasonably good results. There are three types of models relevant for modelling the beach systems (Roelvink and Brøker [1993]): (1) Descriptive conceptual models (e.g. Sallenger [2]); (2) Models based on the equilibrium profile theory (e.g. Bruun [1962]) and (3) Process based models (e.g. Roelvink and Brøker [1993]).

30 Chapter 1. Introduction Descriptive conceptual models This type of model describes and classifies the response of the beach during a storm based on basic physical processes. One of the most extended model is the one described by Sallenger [2], which has been already described in Section Models based on the equilibrium profile theory The main assumption in this group of models is that the sediment exchange in the alongshore direction is negligible, hence the profile erosion processes is addressed as a 1D problem. The profile during a storm develops towards a new equilibrium shape that better withstands the storm conditions. Equilibrium models typically fail in complex situations and are usually only applicable to the collision regime. One of the most extended model is the DUROS model described in Vellinga [1982]. This model is time independent and predicts the post-storm profile depending on the wave and sediment conditions without taking into account the pre-storm profile. Its applicability is limited to the dune erosion only. Another widely used model is the Convolution Model, developed by Kriebel and Dean [1993]. It is a 1D time dependent model, in which the system responds to the water level and breaking wave height. The model assumes that beaches respond towards a stable or equilibrium form in an exponential manner Process-based models The main difference of the process based models with respect to the equilibrium profile models is that in the former case, the storm erosion problematic is addressed taking into account the interaction between the relevant physical processes. These types of models are more complex and the computational cost is higher than equilibrium-type models. They can be applied to a wide range of systems and during different regimes, however they must be properly calibrated (Quevauviller [214]). Because not all the physics involved during the storm duration are well understood or because the process is computationally not affordable, process based models present a series of parametrizations. If the system is alongshore uniform and the cross-shore processes are considered more relevant than the alongshore processes, 1D or 2DV models can be used.

31 Chapter 1. Introduction 11 One example of 2DV process based models is the DUROSTA (Steetzel [1993]) model. It is a dune erosion time dependent numerical model, based on instantaneous sediment transport rates. The basic assumption is that the net local cross-shore sediment transport rate can be computed as the product of local flow velocity with the distribution of sediment concentration. On other hand, SBEACH calculates dune/beach erosion and bar formation and movement produced by storm waves and water levels. It is a 1DV semi-empirical time-dependent model on the basis of time-averaged process descriptions of wave transformation and sediment transports. Sometimes, due to the complexity of the coastal system profile mode approach will be ineffective and an area model (2DH or 3D) is required. This alongshore non-uniformity can be the result of anthropogenic construction such as sea walls, and revetments, but also from natural causes, such as the variation in dune height along the coast or the beach cusps on the shoreface. For this purpose, the XBeach (Roelvink et al. [29]) model was developed, to deal with the impact of storms and hurricanes on complex sandy barrier islands (see Chapter 5). 1.6 Motivation Although the number of world s pocket beaches is comparable to the number of open beaches, studies about pocket beaches are still scarce. Furthermore, globally known study sites that have served as a test scenario for a vast number of research projects are characterized by being open beaches (e.g. Duck, Egmond, Le Truc Vert, Surfers paradise etc.). At the moment pocket beach scenarios are limited. In Europe two relevant sites can be mentioned, eastern Spain (e.g. Barceloneta) and southern Portugal (e.g. Amoreira, Monte Clerigo, Arrifana). On other hand, the existent controversy in regard with the effects of seawalls on the beach evolution is a strong reason to think that there is still work to do in this field. Confusion and disagreement in the literature is compounded by the lack of sufficient field data and inconclusive physical and theoretical models (Ruggiero and McDougal [21]). On other hand, in the last decades the western coast of Europe has held a large number of storms that have caused significant coastal damages. A major flood recorded in 1953 in the UK and Dutch coast driven by a combination of a severe wind storm and a high spring tide caused devastating effects. A more recent Atlantic storm (Xynthia) battered Western Europe in 21. The high waves combined with the high water level reached by the effect of the storm surge caused several damages. The high occurrence and the effects caused by storms have pointed out an urgent need to predict the response of coastal areas and (re-)design coastal protection for future events. Despite of that, the

32 Chapter 1. Introduction 12 knowledge on the storm occurrence and impact on the coastline is still scarce in the European community (Ciavola et al. [211]). Consequently, all this makes the study of the response of pocket beaches not only of great interest for the scientific community, but also, of great importance for future coastal management strategies. 1.7 Objective Previous authors have studied the impact of lateral contours on embayed beaches. The response of dune systems to high energy conditions has also been investigated. Many studies (with no clear conclusions) have been carried out regarding the impact of seawalls on open beaches. However, the response of embayed systems that combine engineered and natural zones have never been studied so far. In this document, a study of hybrid pocket beaches is presented. In order to clarify the problematic, a series of specific questions are addressed in the following subsection. 1.8 Study site The beach of Zarautz is located in the Basque Coast (northern Spain) within the Bay of Biscay (Fig. 1.8). It is a 2 km long embayed beach, North-Northwest facing. It has a quasi-rectilinear plan shape and it is laterally delimited by two rocky headlands. The beach can be divided into two distinct areas (Fig. 1.9). In the eastern part, a dune system that covers 3% of the entire beach is found. The dune system is part of the Iñurritza biotope. In contrast, the remaining 7% is backed a seawall. The seawall is a concrete vertical seawall, which varies its height along the beach. At the western section it is placed at around 4 m above the mean sea level while at the eastern section it is placed at around 9 m above the mean sea level. The sediment mean grain size is.2 mm < d 5 <.45 mm, classified as fine medium sand. The distribution of the sediment size is variable along the beach. The finest fraction of sediment is located at the western side of the bay, in the most protected area. The slope (β) of the beach ranges from.2 in the western engineered part to.6 in the eastern natural part. Tides along the Basque Coast are semidiurnal and mesotidal, with a maximum spring tidal range of 4.7 m and maximum tidal elevation of 2.2 m above the mean sea level (MSL).

33 Chapter 1. Introduction 13 Figure 1.8: The beach of Zarautz (North Spain). Figure 1.9: The different sectors of the beach of Zarautz. Left) Natural sector. Right) Engineered sector. 1.9 Scientific questions Beach morphological changes are mainly produced by the incoming wave characteristics. Since this report intends to address the beach response to high energy conditions the first set of questions to be answered is: What characterizes an energetic event (storm)?

34 Chapter 1. Introduction 14 What are the storm characteristics offshore? What are the storm characteristics nearshore? Are offshore storms representative of the nearshore storms? Along the French-Spanish border of the Bay of Biscay the presence of embayed beaches with engineered sections are common. Usually they are hybrid systems with sections of concrete walls and sections of dunes or wide backshores (e.g. Hendaye, Anglet, Zarautz). This, together with the number of storms that are generated around the area, makes this region suitable for the study of this type of systems. The second set of questions to be answered is: Do the natural and engineered sectors of a hybrid pocket beach present the same morphology? During a storm, do the natural and engineered sectors of a hybrid pocket beach respond in the same manner? During a storm, what is the tidal and wave height sequence order influence on the beach response? During a storm, what is the initial bathymetry influence on the beach response? Which role plays the distance of the seawall to the mean water level on the beach response? Is the storm power representative of the beach erosion? 1.1 Approach Method To answer the research set of questions and to finally understand the objective of the thesis, a wave propagation model (deep to intermediate waters), a 2DH process-based morphological numerical model, field measurements and video images are used. Both real and synthetic storms effect have been analysed in an engineered pocket beach (described in Section 1.8). The wave propagation model output, field measurements and the video images (indirectly) serve as an input of the process based model, which includes the nearshore wave transformation, generation of currents, sediment transport and bed-level update.

35 Chapter 1. Introduction Thesis outline The wave climate for both offshore and nearshore areas is studied in Chapter 2. It comprises the description of the mean and extreme wave characteristics. The definition of what is an energetic event (storm) and a formulation representing the power of the storms is described as well. A wave propagation methodology developed in this chapter is used to force the process based model. Video images were used to describe the morphological evolution of the study site in Chapter 3. This chapter allows to investigate the morphologies encountered along the different sections of the beach as well as the temporal scales at which those features take place. This chapter constitutes the first step in understanding the engineered and natural section particularities. Pre and post storm profiles together with intertidal bathymetries are analysed in Chapter 4. These measurements allow to understand medium term evolution of each measured profile and to obtain the erosion accretion volumes before and after storms. Also the erosion/accretion patterns along the beach are analysed, giving relevant information about the role of the seawall and dune system on the beach erosion. Chapter 5 includes the results of numerical modelling tests. This allows to investigate of the role of the water level and the storm cluster sequence order. In addition, the relevance of wave power on the beach erosion as well as the effect of the wave parameters is investigated. Chapter 6 (Synthesis), the findings are summarized and the scientific questions are discussed.

36

37 Chapter 2 Wave climate 2.1 Introduction Previous studies about the wave climate at the beach of Zarautz are absent. Only information on a larger scale (e.g. Bay of Biscay, North Atlantic) or regarding regions nearby the study site (e.g. Northern Spain, South West of France) can be found in the literature (Butel et al. [22]; Abadie et al. [26]; Dupuis et al. [26]; Izaguirre et al. [212]; among others). Despite not specific, those studies are of great value for a better understanding of the wave conditions. The wave climate at the Bay of Biscay basin is driven by the strong winds of the North Atlantic Ocean generated waves. These storms are eastward directed and reach European Atlantic and North African coasts as strong swells where they are one of the main factors influencing the local weather. A deep study of the wave climate at the southern part of the French Atlantic coast was conducted by Abadie et al. [26]. Eight years of numerical model (WAVEWATCH III (Tolman [22])) data was used for the offshore wave conditions analysis. The main conclusions (regarding the wave climate) were that; (1) the swells around this area are characterized by low direction variability, mostly approaching from 3 deg. (2) Wind seas are scarce. (3) Extreme wave events have highly energetic characteristics ( H s 1 = m). The existence of wave climate spatial variability at the French side of the Bay of Biscay was described by (Butel et al. [22]). Three different buoys were used for the analysis. They concluded that the waves present a lower steepness in the southern part of the bay associated to swells travelling mainly from W-NW directions. The data obtained at the 17

38 Chapter 2. Wave climate 18 southernmost part exhibited the highest wave heights, mainly because this area is more exposed to the North Atlantic storms. On the Spanish side of the Bay of Biscay, the spatial variability is also corroborated by the Puertos del Estado wave climate analysis (PuertosdelEstado [1991]). The database comes from instrumental data belonging to REMRO (Clemente [21]). The analysis shows that the wave heights at the northern Spanish coast increases westwards, which is closer to the source of generation and more exposed to NE and SW sectors. To successfully characterize the wave climate at the nearshore, it is necessary to collect the wave data close to the point of interest, since deep water wave characteristics are not applicable to coastal areas. Nearshore buoys are scarce, hence wave propagation models are applied generally. So far, the wave climate propagation to the nearshore is conducted by: (1) statistical approaches, mostly based on neuronal networks. The goal is to define a transfer function relating the offshore wave data with the nearshore wave data. These models allow the simulation of the underlying processes without applying any physical meaning (e.g. Kalra and Deo [27]; Browne et al. [27]). (2) Wave propagation models, in which the physical processes are taken into account. They can be applied in nested grids (downscaling) where larger scale models (deep water) are nested to smaller scale models (intermediate waters). An example of this kind of approach is found in Rusu et al. [28] were re-analysis HIPOCAS (Soares et al. [22]) deep water wave data is propagated to the Portuguese coast by mesoscale numerical model SWAN. (3) Hybrid wave propagation models, which consist on the propagation of only some representative sea states of the full dataset (e.g. Camus et al. [211]) to establish a transfer function that links offshore wave data to nearshore wave data. Finally, by means of interpolation algorithms this transfer function can be applied to the full dataset (e.g. PuertosdelEstado [1991]). In the present study, the computational cost of simulating the full data series with a wave propagation model makes unviable the use of method 2, hence a hybrid wave propagation model is used. In this case, the complete dataset is propagated instead of only some representative cases (see Section 2.4.1). 2.2 Wave dataset There are some wave buoys relatively close to the study site (Fig left). Regarding the location, the most suitable one is the Donostia buoy (green dot in Fig left). It is about 2 Km seaward from the study site, unfortunately it has a short dataset (27 - present). At the French coast two more wave buoys are present, Saint Jean de Luz buoy (yellow dot in Fig left) and Anglet buoy (magenta dot in Fig left), but as in the previous case, the dataset is short and what is more, they are moored at 5 m and

39 Chapter 2. Wave climate 19 2 m depth, respectively. Finally, to describe the offshore and nearshore wave climate, the Bilbao-Vizcaya s buoy data was analysed (red dot in Fig left). The buoy is placed at about 1 Km far from the study site and it is moored at 6 m water depth. The data (Fig right) is composed by 23 years ( ) of wave descriptive parameters (H s, T p, T m, θ p etc.) hourly spaced. Short time gaps ( 4 hours) in the dataset were linearly interpolated. In addition to that, during the period comprehended between the years there are also wave energy spectra available, with 1 hour time resolution. Each wave spectra was discretized in 25 frequency bins (df is variable) by 24 directional bins (dθ = 15 deg.) o N 3 44 o N Hs [m] Tp [sec] θp [deg] o W 3 3 o W 3 2 o W Year Figure 2.1: Left) Bay of Biscay. Red dot: Bilbao Vizcaya buoy. Green dot: Donostia buoy. Yellow dot: Anglet buoy. Magenta dot: Saint Jean de Luz buoy. Blue dot: Study site (Zarautz). Right) Offshore wave dataset. The red highlighted line indicates the period where spectral information is available. 2.3 Offshore wave climate Mean wave climate The wave climate along the Basque Coast is highly conditioned by its geographical setting (Gonzalez et al. [24]). As a result, the incidence angles of the wave fronts are confined to the IV-quadrant which cover the 95 % of the cases (Fig left). The joint probability distribution (Fig right) shows the link between the peak period (T p ) and the significant wave height (H s ) for the whole dataset. In order to have a reference of the sea state type, a 1/19.7 steepness curve has been added. According to Pierson-Moskowitz formulas (Pierson and Moskowitz [1964]), fully developed seas

40 Chapter 2. Wave climate 2 have a steepness lower than 1/19.7 in deep water as happened in the present case. The most frequent sea states lie along peak periods ranged between sec and significant wave heights between 1-2 m. Those relatively long periods are consequence of the long Atlantic fetch to the west of the Bay of Biscay. The triangular shape together with the positive skewness shown by the graph, points out that the peak period tends to increase with wave height. The directional joint probability (Fig. 2.3), reveals that there are differences between the sea states types coming from the different directions of the IV-quadrant. Western component sea states are composed by two types (Fig a). There is one gravity centre placed at H s 1 m and T p 4.5 sec linked to locally generated sea states and another one, around H s 1 m- T p 1 sec linked to more intense sea states (swells) that arrive from a further distance. Frequently, swells come from the WNW and NW directions. Those two directional bands represent the 82 % of the cases and show the highest values of T p -H s (Fig b to c). On other hand, NNW and N sea states are characterized by their lower T p and H s values (this can be seen clearer for the N component), mostly related to locally generated wind waves (Fig d to e). N 1.4 W 45% 35% 25% 15% 5% 5% 15% 25% 35% 45% S E <=4.5 <=4 <=3.5 <=3 <=2.5 <=2 <=1.5 <=1 <=.5 Hs [m] Hs [m] Tp [sec] probability Figure 2.2: Left) Offshore wave rose. Right) Offshore Hs-Tp joint probability. Black dashed line indicates 1/19.7 steepness curve. The directional spreading (DSPR; see Appendix A) associated to each direction of the IV-quadrant is shown in Fig The DSPR vary from 15 to 5 deg, with a main peak around 3 deg. Sea states approaching from the W direction are composed by two different groups of swell/sea states, hence its particular histogram shape. Sea states associated to WNW and NW directions are slightly biased towards values lower than 3 deg. On the contrary, NW and N sea states are slightly biased towards values higher than 3 deg. The differences in the histogram shape and values are mainly related to the geographical location of the generation of such events. WNW and NW sea states are associated to locally generated storms and distant (North Atlantic basin) generated

41 Chapter 2. Wave climate 21 1 a) W 1 b) WNW 1 c) NW Hs [m] 6 4 Hs [m] 6 4 Hs [m] Tp [sec] 1 2 Tp [sec] 1 2 Tp [sec] 1 d) 8 NNW 1 e) 8 N.3 Hs [m] 6 4 Hs [m] Tp [sec] 1 2 Tp [sec].15 probability Figure 2.3: Directional offshore Hs-Tp joint probability a) W 3 25 b) WNW 3 25 c) NW Frequency [%] Frequency [%] Frequency [%] DSPR [deg] DSPR [deg] DSPR [deg] 3 25 d) NNW 3 25 e) N Frequency [%] Frequency [%] DSPR [deg] DSPR [deg] Figure 2.4: Offshore wave directional spreading (DSPR). Vertical red dashed line highlights the 3 deg. spreading value (only used for reference). storms, whereas NNW and N sea states are locally generated (fetch limited), formed within the Bay of Biscay.

42 Chapter 2. Wave climate 22 winter spring W N 45% 35% 25% 15% a 5% 5% 15% 25% 35% 45% S E W N 45% 35% 25% 15% 5% a 5% 15% 25% 35% 45% S E <=4.5 <=4 <=3.5 <=3 summer N autumn N <=2.5 W 35% 25% 15% 5% a 5% 15% 25% 35% E W 35% 25% 15% 5% a 5% 15% 25% 35% E <=2 <=1.5 <=1 <=.5 S S Hs [m] Figure 2.5: Seasonal offshore wave rose. 1 winter.4 1 spring Hs [m] 6 4 probability Hs [m] 6 4 probability Tp [sec] 1 2 Tp [sec] 1 summer.7 1 autumn Hs [m] 6 4 probability Hs [m] 6 4 probability Tp [sec] 1 2 Tp [sec] Figure 2.6: Seasonal offshore H s - T p joint probability. The wave climate seasonality is analysed by splitting the dataset into four seasons (winter, spring, summer and autumn) and studying them separately (Fig. 2.5 and Fig. 2.6). There is a marked seasonal pattern. Even if, all the cases stem for the IV-quadrant in all the seasons (Fig. 2.5), variations in regard to direction are present. The occurrence of NW waves increases during summer (in which they are on a par with WNW waves) and

43 Chapter 2. Wave climate 23 during autumn; this is related to an extension of the high pressure ring over the Atlantic and a more northerly path of the storms. Winter and spring sea states are clearly biased towards the WNW directions. More energetic states are expected in winter, followed by autumn; spring and summer. Spring and autumn, both transitional seasons, present a bimodal like distribution. One of the modes is related to short periods and low significant wave heights while the other one represents swell-like energetic states. Winter (high wave heights and periods) and summer (low wave heights and periods) seasons show unimodal distributions, although they represent opposite conditions Extreme wave climate The approach followed to study the extreme wave climate is similar to the one carried out in the mean wave climate section (Section 2.3.1). A pre-selection of extreme data needs to be done before proceeding to the analysis. In statistics an extreme event is defined as such sample (i.e. sea state) that is deviated significantly from the mean of its distribution function. In engineering studies the most common parameter used to define whether a process is extreme or not is the wave height (H s ). In the extreme value theory, two methods are described to select the extreme values: (1) Annual maxima method and (2) Peaks Over Threshold method (Burcharth [1988]). The main drawback of the Annual Maxima method is that it only allows the selection of one value per year, then, the data series are largely reduced. In the present case the Peaks Over Threshold method (POT) is used. Unfortunately, one of the difficulties is to define a correct H s threshold value that describes an energetic sea state. An H s value that is only exceeded by the 8-1% of the time is a commonly agreed criteria among scientist (e.g. Dorsch et al. [28]; Rangel-Buitrago and Anfuso [211a]). In some studies it is also pointed out that the correct threshold would be such H s value able to contribute to the beach change (i.e. Dolan and Davis [1992]; Rangel-Buitrago and Anfuso [211b]). In the present work, only values with a probability of occurrence less than 1% are considered extraordinary which corresponds to H s 3.5 m. Fig left, shows the directional distribution of the extreme events. The extreme wave climate compared to the mean conditions is confined to a narrower directional band. Still, The two main directions, like in the mean wave climate, are the NW (31% ) and the WNW (58.6% ). However, the relative importance of those directions is substantially higher (89.6% of the total cases). The general H s - T p joint distribution (Fig right) shows that the extreme wave conditions are linked to higher wave periods (T p = sec) than the mean/low wave

44 Chapter 2. Wave climate 24 N % 45% <= % <=7 25% <=6.5 8 W 15% 5% 5% 15% E <=6 <=5.5 <=5 Hs [m] 7 6 probability 25% <= % 45% <=4 <= % S Hs [m] Tp [sec] Figure 2.7: Left) Offshore wave rose (extreme events). Right) Offshore Hs-Tp joint probability (extreme events). Black dashed line indicates 1/19.7 steepness curve. conditions. However, the range of peak periods related to the extreme events is quite broad. The probability of occurrence of the extreme events varies according to the season of the year (Fig. 2.8). The vast bulk of the extreme events take place during winter followed by autumn and spring. Nevertheless, there are some extraordinary events occurring during summer as well Frequency [%] winter spring summer autumn Figure 2.8: Extreme event seasonal occurrence. The directional spreading (Fig. 2.9) presents the same range of values as the mean conditions (15-4 deg); but the highest probability of occurrence lies around 25 deg unlike the mean conditions. Generally, high energetic events are generated far from the

45 Chapter 2. Wave climate 25 Bilbao Vizcaya buoy O (1 3 ) m. These sea states travel enough distance to be well directionally dispersed (low directional spreading) and arrive to the study area as swells a) W 3 25 b) WNW 3 25 c) NW Frequency [%] Frequency [%] Frequency [%] DSPR [deg] DSPR [deg] DSPR [deg] 3 25 d) NNW 3 25 e) N Frequency [%] Frequency [%] DSPR [deg] DSPR [deg] Figure 2.9: Offshore extreme wave directional spreading (DSPR). Vertical red dashed line highlights the 3 deg spreading value (only used for reference). 1.8 buoy data weibull fit Probability Hs [m] Hs [m] buoy data weibull fit 95 % confidence bounds Return period [years] Figure 2.1: Top) Weibull fitting curve. Bottom) H s return periods. The study of the H s return period involves the analysis of the cumulative frequency distribution of the extreme events. Most commonly used methods for extreme value

46 Chapter 2. Wave climate 26 analyses of wave heights include fitting either the Fisher-Tippet Type 1 distribution (also known as Generalized Extreme Value distribution) or the Weibull distribution (Tucker and Pitt [21] ) to the observed events (Morton et al. [1997]). In the present case a Weibull type distribution (eq. 2.1) is chosen: ( ( ) Hs α γ ) P (H s ) = 1 exp β (2.1) where α, β, γ are the location, scale and shape parameters respectively. This distribution function is widely used in coastal engineering type of problems. Table 2.1: Parameters of the Weibull fittings (eq. 2.1) and extreme H s related to different return periods. All quantities are expressed in [m] Dataset α β γ H s 1 H s 3 H s 5 H s 1 Bilbao Vizcaya Buoy WW TD Biscarosse Yeu Biscay The resulted fitting curve is then used to extrapolate the data resumed in the 2.1 table and Fig The H s wave statistics (Table 2.1) of Bilbao Vizcaya buoy are of similar order comparing them to previous works carried out at the Bay of Biscay. For instance, Abadie et al. [26] calculated wave statistics and gave the wave heights values associated to different return periods at two sites: N W (TD1) and 44 N 2 3 W (WW3). In the same Atlantic zone, Butel et al. [22] found the annual wave height values at the three sites: N, 1.32 (Biscarosse), N, 2.42 W (Yeu) and 45.2 N, 5 W (Biscay) Offshore storm power The study of storm condition has been largely investigated. Many authors have already described different parameters that should be considered when defining its magnitude. Traditionally, storm risk assessment studies are mainly based on only one representative parameter, the wave height (Isaacson and MacKenzie [1981]). However it seems obvious that the wave height itself does not capture all the information needed to represent the storm magnitude and its derived effects. The damaging potential of a storm depends upon many parameters (Corbella and Stretch [213]). Wave height:

47 Chapter 2. Wave climate 27 The first and one of the most important factors to mention is the wave height. The higher the wave, the larger is the energy (E H 2 s ) impinged towards the coast and thus the grater might be the damages on it. Wave period: The wave period plays a relevant role in coastal structure damaging and sand erosion processes (Van Gent et al. [28]; Van Thiel de Vries et al. [28]). It is an important parameter for coastal structure design and is widely used for the calculations of forces exerted by waves on structures. Furthermore, the wave period is also linked to the wave group celerity which affects the wave power. Wave direction: Wave direction has significant consequences in sediment transport trends and can lead to localized erosion and deposition zones. For example, the direction together with the beach configuration can produce sheltered areas (wave shadowing) modifying the erosive processes (Jacob et al. [29]). It is also important on the magnitude of the forces exerted by the waves on coastal structures. For example, Goda [21] states that waves approaching a given obstacle at right angles exert larger forces on it. Inter-storm duration: The time gap between storms is relevant at the time of infer the possible coastal damages (Ferreira [25]; Loureiro et al. [212]) but also important at the time of estimate if two energetic events belong or not to the same source of generation (i.e. events belonging to the same storm). The beach equilibrium concept (Bruun [1954]; Dean [1977]; Vellinga [1982] among others) states that a given beach, can reach a mean configuration (both cross-shore and alongshore) if the wave conditions are maintained constant during a certain period of time. If the beach equilibrium has not taken place after a given storm (i.e. storm of too short duration) it is expected to keep evolving towards its equilibrium during the following set of storms. On other hand, a series of storms can be of greater importance than the erosion potential of a single much larger storm (Thom and Hall [1991]; Castelle et al. [28]). The beach is expected to be weak to face another storm (of appropriate magnitude) during the recovery period. Therefore, the impact of a storm is a compromise between the storm magnitude, storm duration and the inter-storm period. Storm duration:

48 Chapter 2. Wave climate 28 The magnitude of a storm is not only matter of wave height and period. The time during this storm is active is also relevant. In fact in several formulations (commented in the following) the magnitude of a storm is assessed by considering the storm duration. Water level: The water level (combination of astronomical tide, meteorological tide and wave set up) affects the wave transformation along the surf zone and modifies the breaking location. High energy events coinciding with high water levels affect the upper part of the beach (i.e. dry beach, dunes) (Splinter et al. [214]) and coastal structures (i.e. seawalls, dune revetments). In any case, this parameter is only relevant at the nearshore, since offshore wave conditions are not affected by the water level. The magnitude of a storm cannot be represented by a unique of the previously mentioned parameters. Different approaches are available in the literature combining some of those parameters trying to define the storm magnitude. One of the most used method is the one developed by Dolan and Davis [1992]. They described the storm magnitude by its H s and duration in hours (t d ). td H 2 s dt (2.2) Maybe less employed but more physically relevant is the storm index based on the energy flux (F = Ec g ) where c g is the wave group velocity. The storm magnitude is obtained by integrating the energy flux over a storm duration (e.g. CERC [1984]). td Ec g dt (2.3) In the present work this formula (eq. 2.3) is used together with some restrictions that somehow take into account the effect of the tidal effect and the inter-storm period. On other hand, the wave direction is not considered in any way. Since the tidal regime is semidiurnal, the minimum storm duration should be at least of 12 hours (Rangel- Buitrago and Anfuso [211a]) in order to account for the action of the storm over at least a whole tidal cycle. Also, a minimum inter-storm period of 24 hours has been established to ensure storm interdependence. Hence, two consecutive storms separated by less than 24 hours would be considered a single storm. This inter-storm interval is comparable to mid-latitude extreme events (e.g. mid latitude cyclones) occurring on a time scale of 24 hours approximately (Oke [1987]).

49 Chapter 2. Wave climate 29 Fig a, presents the histogram of storm duration. The most frequent registered value is below 5 hours. The storm duration vary between 12 to around 4 hours. The inter-storm duration is presented in Fig b. It ranges from days to months. The high variability is related to the seasonality (shown in Fig. 2.8). During winter and autumn seasons, several storm reach this part of the Bay of Biscay (low inter-storm period), but, once the low energetic seasons start (spring and summer), long periods between storms are expected a) Frequency [%] Storm duration [hours] 4 b) Frequency [%] Inter storm duration [hours] Figure 2.11: a) Offshore storm duration histogram. b) Offshore inter-storm duration histogram. Fig relates the storm power to different parameters. The analysis manifests the existence of a link between the maximum storm H s value and the power of it (R 2 =.5). Yet, there is some scatter indicating that despite the existence of such correlation some exceptions may occur, mostly at high storm power values. Regarding the period and the direction, there is no clear relation that links the variables to the power, although as the power increases the scatter of the plot diminishes and converges towards similar values. This effect is explained by the source of the storm since high storm values are confined to a narrower direction band. Finally, a clear relation between the storm duration and its power is found (R 2 =.9). Table 2.2 summarizes the most important parameters related to the storms.

50 Chapter 2. Wave climate 3 Figure 2.12: Offshore storm power. Top - left) Maximum H s registered within a storm. Top - right) Mean T p registered within a storm. Bottom - left) Mean θ p registered within a storm. Bottom - right) Storm duration. The horizontal lines correspond to 1, 3 and 5 year return period limits. Table 2.2: Storm parameters statistics. sd refers to the storm duration values and isd refers to the inter-storm duration values H s [m] T p [sec] θ p [deg] sd [hours] isd [hours] Storm power [Mw h m 1 ] Mean σ Nearshore wave climate Wave fields can be significantly altered during their propagation to the nearshore. The grade of alteration depends upon its characteristics (being the wave period and the direction of incidence the most important parameters) and the characteristics of the area where they are propagated (i.e. coastal features and underlying seabed). To define the wave climate at the seaward boundary of the study site, it is necessary to propagate all the offshore sea states ( 876 runs). In order to make the task computationally affordable and avoid long and tedious wave propagation simulations, a simple methodology that leads to a fast wave energy spectrum propagation, was developed. This method is based on previous studies (Camus et al. [29a]) that deal with similar computational issues (Camus et al. [27]; Camus et al. [29b]).

51 Chapter 2. Wave climate Wave propagation method Ten years (24-213) of offshore wave climate were analysed, based on the hourly wave directional spectra derived from the Bilbao Vizcaya buoy measurements. The spectrum propagation allows obtaining a more accurate data. For example, if there is a mix of sea states (bimodal spectrum), relevant information would be lost if only the parameters characterizing the spectrum (H s, T p and θ p ) are propagated, instead, if each bin of the spectra is propagated the bimodal evolution would be obtained at the end of the simulation. Therefore, 1 years data-series of wave spectra are used instead of 2 years of wave spectra representative characteristics. The offshore cumulative energy spectrum of the available data (Fig left) shows that most of the energy ( 75%) is concentrated at bins placed around degrees and frequencies.1745 Hz-.625 Hz (5.73 sec 16 sec) θ [deg] Energy [%] f [Hz] Figure 2.13: Left) Cumulative energy spectrum. White dots represent propagated bins. Right) Cape San Anton filtering effect (red shadowed directional band). Red dashed line indicates the wave propagation model boundary limit. Red and yellow dots indicate the location of the Nortec Awac and Teledyne RDI 6 wave recorders deployed during one month period. The coastal area surrounding the study site is rugged and complex. It was necessary to use a model capable to deal with the wave refraction and diffraction processes. For that, the monochromatic REF/DIF1 model was used (Kirby et al. [1994]; González et al. [27]). This model is based on the parabolic version of the mild slope equation (Berkhoff [1974], eq. 2.4), which resolves the wave phase information, refraction and diffraction: (cc g η)+σ 2 c g c η = (2.4) where, c is the wave celerity, c g is the wave group celerity, σ is the radian frequency and η is the water free surface.

52 Chapter 2. Wave climate 32 The wave propagation method consists of two steps. 1. Pre-propagation step: The goal is to obtain the propagation coefficients at the seaward boundary of Zarautz (red dashed line in Fig right). The boundary is composed of 21 nodes, separated by about 1 m. Only such cases that affect the study site were propagated (represented by white dots in Fig left). The propagation was performed over a high-resolution multibeam bathymetric data. Different meshes where set up (Fig left), so that could be used to propagate all cases within the restrictions of the model. The simulations were initiated with a wave height value equal to one (H = 1m), in order to obtain the transformation coefficients (Fig right and Fig. 2.15), which are obtained by: H coef = H nearshore H offshore Dir coef = Dir nearshore Figure 2.14: Left) Computational meshes used for the wave propagation. Right) Examples of wave propagation. Low periods (< 6.3 sec) related to directions 27 deg - 3 deg were not propagated. It can be stated that, low period wave components are filtered by the cape San Anton (red shadow zone in Fig right). Those components are not affected by the local depth before they reach the cape, hence, they do not refract towards the study site. As an example, if we consider a wave component with a T = 6.3 sec and obtaining, by means of linear wave theory, its wave length (L) in a given point close to the cape (where the water depth (h) is approximately 3 m) is 62 m. This wave component near the cape is still in deep water (h > L/2 = deep water), so the refraction process cannot take place and the wave component keeps its trajectory without any directional perturbation. These components can still diffract. However, due to its small periods the shadowing effect will be very intense, which together with the predominantly small amplitude related to these

53 Chapter 2. Wave climate 33 components (explained previously in Section Fig. 2.3), means that the amount of energy would be in any case very low. 2. Propagation step: The goal is to propagate the offshore wave energy density spectra to the seaward boundary of Zarautz. For that, two propagation coefficients matrix are used at each node (one wave height transformation matrix and one wave direction transformation matrix). In Fig. 2.15, four examples of the wave transformation coefficient matrix are shown. Fig a (West side of the beach) and b (East side of the beach) are wave height transformation matrix whereas Fig c (West side of the beach) and d (East side of the beach) are wave direction transformation matrix. Note that the coefficients vary with the direction, frequency and location. The coefficients related to western directions present smaller wave height transformation values and higher directional variations. In order to propagate a wave energy density spectrum in a straight forward fashion, first the offshore ) wave energy density is transformed to a matrix of wave heights (Edfdθ = H2, then a matrix multiplication is performed between offshore wave 8 spectrum and the wave heights transformation coefficient matrix. The direction bins are also transformed by means of the wave direction transformation matrix. Finally, the wave spectrum is transformed back into energy density spectrum (now at the nearshore). 45 a) b) c) d) θ [deg] coef [m] θ [deg] coef [m] θ [deg] coef [deg] θ [deg] coef [deg] f [Hz] f [Hz] f [Hz] f [Hz] Figure 2.15: Transformation coefficients. a-b) Wave height transformation coefficients (a: West side of the beach, b: East side of the beach). c-d) Wave direction transformation coefficients (c: West side of the beach, d: East side of the beach). It is important to mention that the methodology is not suitable for simulations in the surf zone (because of triads interactions and wave breaking are not taken into account) or where nearshore currents affect the wave transformation. On the other hand, it has to be taken into account that during the wave propagation, any local wave generation

54 Chapter 2. Wave climate 34 (i.e. wind generated waves) or non-linear interaction between wave-components (i.e. quadruplets) cannot be simulated. Fig shows the model and field data comparison. The model is validated against field measurements undertaken during a 1 month period (April-211). Two acoustic wave recorders (NORTEK AWAK 1, and TELEDYNE RDI 6) were deployed at both ends of the beach at about 18 m depth. The model output shows a good agreement with the field data (Fig Table 1). Hs [m] WEST Measured Modeled EAST 13/4 22/4 1/5 1/5 13/4 22/4 1/5 1/5 Tp [sec] /4 22/4 1/5 1/ /4 22/4 1/5 1/5 4 4 θp [deg] /4 22/4 1/5 1/5 Date 3 13/4 22/4 1/5 1/5 Date Figure 2.16: Validation of the matrix propagation methodology against the real measures at two sides of Zarautz beach (depth around 18 m), during a 1-month period. The peak period jumps (around 29/4 and 4/5) may indicate the presence of bimodal sea states, in which both sea and swell components have similar energy. Despite of that, the low error values obtained and the good fit representing the general evolution trend during the comparison period, highlights the robustness and accuracy of the methodology. Alongshore wave variability was present during the field campaign. The mean wave height was 24% lower at the western part than at the eastern part of the beach. This is consistent with the configuration of the site and with the modelled results. Yet, the model underestimates the wave height alongshore differences between both ends of the beach (those are around 1% lower than in the reality). The statistical results (BIAS) suggest that at the western part the wave height might be over-estimated resulting in a underestimation of the alongshore wave variability.

55 Chapter 2. Wave climate 35 Table 2.3: Basic statistical parameters of matrix propagation methodology against the real measures H s [m] T p [sec] θ p [deg] West East rmse BIAS.12.2 rmse BIAS rmse BIAS Mean wave climate Wave roses of three different locations (West, Centre and East) along the Zarautz seaward boundary are represented in Fig Both the refraction process that tends to bend the wave fronts parallel the shore together with the wave filtering out produced by the San Anton cape (described in Section 2.4.1), results in a quasi-unidirectional climate in the study area. Furthermore, swells arriving from the W related to high wave periods may rotate nearly 9 degrees arriving normal to the shore. However, they lose most of the energy in their journey to the coast. The alongshore H s and θ p variability is represented in Fig It can be seen that some differences exist between both ends of the domain regarding the H s and θ p. The western side of the bay is more sheltered and wave heights tend to be smaller. Looking at the directional component, in the more sheltered area (West) the wave trajectories are almost perpendicular to coast, while at the other end of the beach they can arrive with certain angle of incidence ( O (1 1 ) deg ). The nearshore joint probability (Fig left) shows that the most frequent sea states lie along peak periods ranged between 9-12 sec and significant wave heights between m. This slightly higher periods compared to the offshore mean wave climate is the effect of the high frequency filtering effect of the cape San Anton and wave refraction. Regarding the directional spreading (Fig right) it varies from 8 to 2 deg and the main peak lies around 14 deg. Comparing these values to the offshore mean wave conditions (3 deg) it can be seen that the directional spreading decreases considerably during the propagation of the wave spectra.

56 Chapter 2. Wave climate 36 N 5% 35% 2% W 5% 5% 2% 35% 5% S E N 8% 65% 5% 35% 2% W 5% 5% 2% 35% 5% 65% 8% S E N 65% 5% 35% 2% W 5% 5% 2% 35% 5% 65% S E <=.25 <=.5 <=.75 <=1 <=1.25 <=1.5 <=1.75 <=2 <=2.25 Hs [m] Figure 2.17: Nearshore wave roses. Left) West side. Centre) Central zone. Right) East side. 2 Hs variability [%] Hs [m] θp [deg] x [m] Figure 2.18: Alongshore variability at the seaward boundary of the beach of Zarautz Extreme wave climate Calibration of the return periods It has been already mentioned that there are only 1 years of wave spectra available (24-213) to characterize the wave climate at Zarautz seaward boundary. It is known

57 Chapter 2. Wave climate Hs [m] 6 5 probability Frequency [%] Tp [sec] DSPR [deg] Figure 2.19: Left) Nearshore Hs-Tp joint probability. Right) Nearshore wave directional spreading (DSPR). that there are climatic cycles in the Bay of Biscay that combine periods of high energy with low energy (Izaguirre et al. [212]). Since the offshore and nearshore wave dataset present different duration, the 1 year offshore dataset is compared against the 23 year offshore dataset to detect if both series present the same wave statistics. Hs [m] years dataset 1 years dataset storm P [Mw h m 1 ] years dataset 1 years dataset Return period [years] Return period [years] 1 year dataset Hs [m] Hs Fitted function year dataset Hs [m] 1 year dataset storm P [Mw h m 1 ] storm P Fitted function year dataset storm P [Mw h m 1 ] Figure 2.2: Return period calibration. Left) H s. Right) Storm power. Top) Comparison of the return periods with the 23 years dataset (red) and 1 years dataset (blue). Bottom) Fitting curve relating the 23 years dataset and 1 years dataset. Fig left top and Fig. 2.2 right top, show the relation between 23 year dataset and 1 year dataset for H s and storm power. It can be seen that the 1 year dataset is slightly more energetic than the 23 years dataset. This means that this period is composed by more energetic events than the whole dataset. For example during this period the presence of the storm Klaus (Liberato et al. [211]) was recorded. In order to improve the accuracy of the return period estimation and avoid the overestimation of the wave heights a transformation function can be obtained (Fig left

58 Chapter 2. Wave climate 38 bottom and Fig right bottom) which allows the scaling of the data. The final result is shown in Table 2.4. Table 2.4: H s [m] and Storm power [Mw h m 1 ] values before and after the calibration process Dataset H s 1 H s 5 Storm power 1 Storm power 5 1 years dataset Corrected dataset Nearshore storm power The histogram of storm duration is represented by Fig a. The values of storm duration at Zarautz seaward boundary are slightly lower than the duration of the offshore storms. The values vary between 12 to 26 hours. On other hand, the inter-storm duration (Fig b) present higher values than the inter-storm periods recorded at offshore storms (see Table 2.5 and Table 2.2). The high variability is related to the seasonality (shown in Fig. 2.8). Table 2.5 summarizes the most important parameters related to the storms. Fig relates the nearshore storm power to different parameters. The transformation undergone by the wave fields makes the storm power at deep water significantly different to storm power found in the study area. The extreme wave height threshold ( H s 1% ) value considered is 2.3 m now and the storm power is approximately two times reduced. As occurred in the offshore dataset there is some correlation between the H s and duration of the storm with the storm power (R 2 =.67 and R 2 =.87, respectively). On the contrary, the period and direction have no correlation with the storm power. Table 2.5: Storm power parameters statistics. sd refers to the storm duration values and isd refers to the inter-storm duration values H s [m] T p [sec] θ p [deg] sd [hours] isd [hours] Storm power [Mw h m 1 ] Mean σ

59 Chapter 2. Wave climate a) Frequency [%] Storm duration [hours] 4 b) Frequency [%] Inter storm duration [hours] Figure 2.21: a) Nearshore storm duration histogram. b) Nearshore inter-storm duration histogram. Figure 2.22: Nearshore storm power. Top - left) Maximum H s registered within a storm. Top - right) Mean T p registered within a storm. Bottom - left) Mean θ p registered within a storm. Bottom - right) Storm duration. The horizontal lines correspond to 1, 3 and 5 year return period limits.

60 Chapter 2. Wave climate Conclusions The present chapter presents the analyses of the wave climate both offshore and at the seaward boundary of the study site. For this, real data (offshore) as well as numerical wave model data (nearshore) is used. Twenty three years of wave representative conditions are available to analyse the offshore wave climate. The main conclusions are described in the following: The 95 % of the cases are confined to the IV-quadrant where two main directions are dominant, NW-WNW. Western component sea states are composed by locally generated and more developed sea states. Frequently, swells come from the WNW and NW directions. On the other hand, NNW and N sea states are mostly related to partially-developed sea states. The wave characteristics change depending on the season of the year, explained by the influence of the two action centres governing the North Atlantic ocean, the Azores High and the Iceland Low (Wooster et al. [1976]; Vitorino et al. [22]). The extreme wave climate compared to the mean conditions is confined to a narrower directional band. The vast bulk of the extreme events take place during winter and autumn. Storms are characterized by means of eq The storm duration ranges between 12 to 4 hours while the inter-storm period varies between days to months. The existence of a positive trend is found between the maximum storm H s value and the power of it (R 2 =.5). There is no clear relation that links the T p and θ p to the storm power. Finally, a clear relation between the storm duration and its power is found (R 2 =.9). Overall, the results obtained from the previous analysis are consistent with the geographic nature of the site and the atmospheric patterns of the region. The analysis is also consistent with the previous studies (e.g. Butel et al. [22]; Gonzalez et al. [24]; Abadie et al. [26]; Dupuis et al. [26]) carried out in the Bay of Biscay. The nearshore wave climate is calculated propagating a 1 years of offshore wave spectra dataset. The methodology is a variant of the hybrid wave propagation models. The comparison between real measurements and model results during one month period verifies the good model skills. The main conclusions are that: The wave climate at the seaward boundary of Zarautz is quasi-unidirectional and almost normal to the shore. The wave sheltering produced by the San Anton cape

61 Chapter 2. Wave climate 41 generates some differences between the west and east side of the beach. The wave periods related to the mean wave climate are slightly higher than those found offshore, mainly caused by the high frequency filtering produced by the San Anton cape. The opposite response is found regarding the wave heights due to the energy loss during the refractive processes. As occurred in the offshore dataset there is some correlation between the H s and duration of the storm with the storm power (R 2 =.67 and R 2 =.87, respectively). Regarding, the T p and θ p, there is no correlation with the storm power. The storm magnitude formulation is sensitive to the wave height and especially the duration of the storm. The direction and the period do not correlate with the magnitude of the storm. However, it is shown that the variability of the wave period and direction, decrease with increasing storm power. The presence of some scatter on the plots suggest the existence of similar storms (in terms of wave power) with different wave characteristics (H s and T p ). This makes to think if the magnitude of a given storm calculated with the storm power magnitude formula (eq. 2.3) might be representative or not of the beach erosion.

62

63 Chapter 3 Nearshore sandbar morphodynamics of the beach of Zarautz 3.1 Introduction The temporally variable and very energetic wave climate (see Chapter 2) in the Bay of Biscay makes this meso-tidal coastal area highly dynamic, with beaches often presenting complex three-dimensional sedimentary structures more or less influenced by the presence of headlands. These lateral boundaries can modify the wave characteristics, and therefore impact the beach circulation and surf zone by limiting the development of longshore currents, rips and rip feeder currents (Masselink and Short [1993]; Short [1996]). In the case of intense beach urbanization, the construction of coastal structures, such as seawalls, can also impact both the hydrodynamic regime of a beach, inducing changes in sediment transport and the beach morphology (Kraus [1988]; Pilkey and Wright III [1988]; Bernabeu et al. [23]). Even though engineered pocket beaches are common beach systems, long term (on the time scale of years) studies addressing their morphodynamics are scarce (Gallop et al. [211]). For open beaches, beach state classification is often performed using the convenient scheme of Wright and Short [1984], hereinafter referred to as the WS-model. This model, This chapter is based on: de Santiago, I., Morichon, D., Abadie, S., Castelle, B., Liria, P., and Epelde, I. (213). Video monitoring nearshore sandbar morphodynamics on a partially engineered embayed beach. Proceedings 12th International Coastal Symposium (Plymouth, England), Journal of Coastal Research, Special Issue No. 65, pp , ISSN

64 Chapter 3. Nearshore sandbar morphodynamics of the beach of Zarautz 44 valid for micro-tidal and wave-dominated environments, is based on the dimensionless fall velocity (eq. 3.1): Ω = H b w s T (3.1) where H b is the wave breaker height (m), w s is the sediment fall velocity (m/s) and T is the wave period (s). The WS-model allows to distinguish three distinct beach types: two extreme states, dissipative (Ω > 6) and reflective (Ω < 1), and one intermediate state (1 < Ω < 6). The intermediate beach state is divided into four beach types: Longshore Bar and Trough (LBT), Rhythmic Bar and Beach (RBB), Transverse Bar and Rip (TBR) and Low Tide Terrace (LTT). In meso/macro tidal environments, tidal range becomes important to beach morphodynamics. The tidal range and its translation rate, will determine where and how long the action of the waves will act upon the beach. This will affect the sediment transport and the development of morphological structures (Davis Jr et al. [1972]). In order to consider the impact of the tidal range, Masselink and Short [1993] added the non-dimensional relative tide range parameter to the WS-model (eq. 3.2): where TR is the mean spring tide range (m). RT R = T R H b (3.2) Commonly, the beach classification provided by the WS-model for open beaches is referred to as normal beach circulation. However, the presence of headland can, to some degree, impact wave-driven circulation along the embayment and alter this normal situation. Based on the pioneer work of Masselink and Short [1993], Castelle and Coco [212] developed a non-dimensional embayment scaling parameters to quantify the degree of headland impact on beach circulation (eq. 3.3): δ = Lγ bβ H s (3.3) where L is the embayment length (m), γ b is the breaking parameter (here equal to.73; Battjes and Stive [1985]), β is the surf zone slope and H s is the significant wave eight.

65 Chapter 3. Nearshore sandbar morphodynamics of the beach of Zarautz 45 δ represents the number of surf zone widths, X s, that fit into an embayment of length L. Based on different embayed beach observations they pointed out that cellular circulation is generally observed for δ 9, transitional circulation for 9 < δ < 16 and normal circulation for δ 16. The present chapter (Chapter 3), based on the analysis of 2 years (21-212) of daily time-exposure video images, aims to apply the WS-model, combined with RTR and δ parameters, to describe the morphodynamics of a partially engineered pocket beach. The objective is twofold. The first goal is to asses the validity of the beach classification model to describe this complex pocket beach. The second objective is to determine whether its engineered and natural sections exhibit contrasting behaviours. 3.2 Material and methods Video monitoring station (KOSTASystem) In June 21, a KOSTASystem ( video station was set up on top of the western headland of the beach of Zarautz at approximately 9 m above the mean sea level. Figure 3.1: Camera resolution. Top) The beach of Zarautz. Centre) Angular resolution. Bottom) Radial resolution.

66 Chapter 3. Nearshore sandbar morphodynamics of the beach of Zarautz 46 The station is composed of four cameras: two of 12 mm lens covering the whole beach system, and two of 25 mm covering the dry part of the beach as well as the surf zone. Every 2 minutes, snapshots and time-exposure images are stored, which are the average of 6 individual snapshots sampled at.5 Hz. The images are rectified (Holland et al. [1997]) and merged to obtain plan view images spanning 23 m and 8 m in the longshore and cross-shore directions, respectively. The accuracy of the photogrammetric transformation ranges from.5 m to.45 m for the angular resolution and from 1 m to 9 m for the radial resolution (Fig. 3.1) Beach state classification The inner bar morphological analysis was carried out by visual classification based on the WS-model (see Appendix B). The analysis was performed separately for the engineered and natural parts of the beach. The main limitation of this method is the subjectivity involved in it (Ranasinghe et al. [24]). To avoid this issue, the visual classification was carried out by different experts separately. This sensitivity avoiding technique has also been applied in previous studies (Lippmann and Holman [199]). In the majority of the cases the same beach state was chosen by the different partners of the expert panel. In case of discrepancy, a common consensus was achieved Image smoothing algorithm Since each camera points to a different location of the beach, the light incidence grade at each camera is different. This results in a rectified image with strong intensity shifts between the stitched images. In order to improve the image quality and make possible the use of the automatic detection tools (e.g. bar detection tool, see Section for more information), an image smoothing is needed. There are different approaches to deal with this problem. Some of those methods use image histogram comparisons (Grundland and Dodgson [25]; Brown and Lowe [27]) instead of the pixel by pixel comparison. Others instead, work along pixel regions (like the LRM method explained in Schowengerdt [26]). In the present work a different approach is implemented, which gives reasonable results for the working purposes. The algorithm consists of three steps: 1. Stitching detection:

67 Chapter 3. Nearshore sandbar morphodynamics of the beach of Zarautz 47 First, the image is transformed from the RGB colour space to Intensity colour space. Then, vertical abrupt intensity changes are detected, which are related to the exact position of image overlapping. 2. Intensity comparison: A reference image is selected (in this case the one covering the offshore area), afterwards a common pixel transect between the reference image and the image to be smoothed is chosen. Later, a polynomial function of degree n that best fits the data, in a least squares sense, is found. 3. Image correction: The equation obtained in the previous step is applied to correct the target image (see example in Fig. 3.2). a) y = 1.165x Intensity 19 b) Intensity Figure 3.2: Image smoothing. Left top) Raw image. Left bottom) Smoothed image. Right) Relation between intensities of adjacent images Outer bar detection The evolution of the outer bar was studied by tracking the bar position with an automatic algorithm (see example at Fig. 3.3). The method is based on the premise that wave breaking mainly occurs over shallow zones (bars) generating almost permanent white (high luminosity) foamed areas (Lippmann and Holman [1989]). The resulting timex image will show low intensity (dark) zones where the wave breaking is absent and high intensity (light) zones at breaking areas, which most of the time coincides with the bars and the shoreline location. A series of alongshore equally spaced intensity transects were subtracted from the timex images, where the break zones were clearly visible as bell-shapes. Using a zero-crossing analysis, the location of the bar crest was selected to be the position of the maximum

68 Chapter 3. Nearshore sandbar morphodynamics of the beach of Zarautz 48 intensity values between adjacent zero up-crossing and down-crossing points, along a cross-shore intensity profile. 2 y [m] y [m] x [m] intensity Figure 3.3: Bar detection example. Red dashed line represents the final detected bar. Black dashed line is a transect represented in terms of intensity (blue line) in the right side of the image. Green dashed line represents the maximum intensity location. There is always a significant error (O (1-1) m) when locating the cross-shore position of the bar crests (Enckevort and Ruessink [21]). This is mostly due to the translation of the breaking zone resulting from the changes in wave characteristics and tidal level (Lippmann and Holman [1989]; Lippmann and Holman [199]; Enckevort and Ruessink [21]; Alexander and Holman [24]). In order to reduce the differences between the detected bar positions and the real bar positions, similar tidal level (mean low tide ±.25 m) and wave conditions (1.75 m > H s < 2.75 m and T p > 1 s) were chosen for the analysis. Due to the temporary malfunctions of the camera system and poor image quality (e.g. fog, rain drops and sun glint), the amount of available images was reduced to a total of 525.

69 Chapter 3. Nearshore sandbar morphodynamics of the beach of Zarautz Results Inner bar morphology and dynamics The presence of beach lateral boundaries modifies the circulatory patterns of the system (Short [1999]; Castelle and Coco [212]). Fig. 3.4 shows the probability of occurrence of each type of circulatory system described by the parameter δ (eq. 3.3). The cumulative probability function (Fig top) shows that the beach presents cellular circulation during the 2% of the time, transitional circulation during 3% of the time and open beach like circulation during 5% of the time. Hence, generally the beach acts as an open beach-like circulatory system but it may present cellular and transitional circulation during high energetic events. 1.8 Probability.6.4 Normal Transitional.2 Cellular Cellular Transitional Normal Probability [%] δ Figure 3.4: Top) Empirical δ distribution function. Bottom) δ histogram. The visual analysis of the 2 years of daily timex indicates that the entire beach exhibits an intermediate beach state, which is consistent with the estimation of the dimensionless fall velocity 1 < Ω < 6. The presence of rip current(s), namely headland rip(s), occurring at one or both ends of the bay were observed most of the time, as they are common features on embayed beaches (Castelle and Coco [212]). In addition, a variable number of rip channels were also observed further along the beach, reaching a maximum number of 9, with a common strong longshore variability of the rip channel wavelength. According to the WS-model, from June 21 to May 212, the inner bar went through all the states within the intermediate classification (LBT-RBB-TBR-LTT). Variations of beach states occurrence and persistence were observed along the beach, revealing the existence of

70 Chapter 3. Nearshore sandbar morphodynamics of the beach of Zarautz 5 two compartments, which correspond to the engineered and natural section. Those two sections are studied separately and represented graphically in Fig Engineered section: The analysis of the images showed that the most common and stable shape was the lowest energy intermediate state (LTT). It appeared 61% of the time, followed by TBR (25%), RBB (11%) and LBT (3%) states. The residence time shows that low states were more persistent than higher states. The period between winter storms was long enough to let the beach evolve downstate during the lower energy post-storm conditions. However, the beach was not able to reach the reflective state. The large variability (explained by the high standard deviation) in the residence time of the LTT state, can be related to the stochastic factor of the reset events. Once the beach reached the most stable state (LTT), it needs a high-energy event to evolve up-state. Due to the randomness in the occurrence of such events, the variability in the time of residence is increased. All transitions from higher to lower energy states occurred sequentially following the WS-model. On other hand, transitions to higher states did not follow a specific pattern. This means that, for up-state sequences, the final state was relatively independent of the previous one, which was not the case for down-state transitions. The uppermost beach state detected in the site (LBT) was associated to the highest mean wave conditions (H s = 4.5 m - H b = 3.1 m). Rhythmic states (RBB-TBR) were associated with lower mean wave conditions (H s = m - H b = m), and finally the LTT state was associated to the weaker mean energy conditions (H s = 1.5 m - H b = 1 m). This behaviour is similar to that reported in previous studies. Natural section: The most common and stable state of the inner bar along the natural section was LTT, which was observed 88% of the time. The TBR and RBB states were less observed ( %) and the presence of an alongshore-uniform bar (LBT) was never observed. The residence time of the beach states, shows a large difference between the LTT and the TBR-RBB states, suggesting a higher inner bar stability compared to that along the engineered section. The pattern of the beach state transition was similar to the one seen in the engineered section. Up states sequences were independent of its previous state, while

71 Chapter 3. Nearshore sandbar morphodynamics of the beach of Zarautz 51 down-state transitions were not. In contrast, the number of transitions in this section was 5% less than in the engineered part. The values of mean H s recorded during LTT, TBR and RBB beach states were respectively about 11%, 3% and 28% higher than the wave height measured for the same beach states in the engineered section. 1 Probability.5 Residence time [days] R LTT TBR RBB LBT D R LTT TBR RBB LBT D Hs mean [m] R LTT TBR RBB LBT D Beach state Figure 3.5: Top) Probability of beach states occurrence. Centre) Residence time and standard deviation (hatched bar). Bottom) Mean significant wave height at the engineered (light) and natural (dark) sections for the inner bar Outer bar morphology and dynamics The outer bar detection algorithm was not applied during the first stages of the image sampling due to a problem related with the movement of the camera station. This problem caused a reduction of the sampling period to May May 212. The analysis of the outer bar evolution reveals that: (1) the outer bar displays alongshore non-uniform features throughout the entire surveyed period and (2) the sandbar remains stable or migrates slowly onshore during low energy conditions and it rapidly migrates offshore during high energy conditions. Along the engineered part, the RBB morphology prevails, whereas along the natural part the outer-bar state alternates between RBB and TBR, the latter being the most persistent state. Fig. 3.6 displays the alongshore deviation lines for the outer bar given by eq. 3.4:

72 Chapter 3. Nearshore sandbar morphodynamics of the beach of Zarautz 52 D(y, t) = x d (y, t) x u (y, t) (3.4) where x d (y,t) denotes the detected cross-shore positions of the bar, and x u (y,t) the cross-shore positions of the bar position trend at a given time t. Horizontal fluctuations of bluish and reddish colors correspond to landward and seaward deviations respectively and represent the alongshore non uniform bar features, in addition, the vertical shift of the color bands represent the alongshore migration of the bar features during the study period May11 Jul x [m] Date Sep11 Nov11 Jan Landward( ) Seaward(+) Hs [m] 2 May11 Jul11 Sep11 Nov11 Jan12 Mar Mar Alongshore distance [m] 8 May11 Jul11 Sep11 Nov11 Jan12 Mar12 Date Figure 3.6: Left) Time stack of alongshore deviation lines. Right top) Mean outer bar position. Right bottom) Wave characteristics. Black line represents the offshore characteristics. Red dashed line represents the nearshore characteristics. The systematic horizontal alternation of colors indicates that the outer bar never became alongshore-uniform (LBT state) during the surveyed period even following severe storms (black dashed line in Fig left). An explanation is that, because of the geological constraints, sandbar three-dimensionality often increases with increasing wave energy on embayed beaches (e.g. Enjalbert et al. [211]). The variability of the horizontal interval between color bands indicates that the outer bar exhibits different non-uniform features, which is consistent with a previous study dealing with alongshore non-uniformities of sandbars (Van Enckevort et al. [24]). The vertical displacement of the color bands location in the western part of the bay shows the merging of two outer-bar bays in July 211 associated with the rapid migration of the left-hand bay (arrow 1 in Fig left) whereas the outer-bar bays seem more stable along the eastern section of the beach (arrow 2 in Fig left). Surprisingly, the alongshore bar migration seems to be more effective during fair weather conditions. The mean cross-shore position of the outer bar was calculated. Its temporal variation is compared to the wave time series (Fig right). During fair weather conditions, the

73 Chapter 3. Nearshore sandbar morphodynamics of the beach of Zarautz 53 mean outer-bar cross-shore position remains quasi-steady or migrates slowly onshore. In contrast, it migrates rapidly far offshore, by about 8 m, within a few days following a very energetic storm event (H s 7.5 m). Then, as the significant wave height decreases, the mean cross-shore position moves shoreward at a much lower rate compared to the seaward migration rate Accretionary evolution of the inner bar Fig. 3.7 shows a typical full down-state sequence following a reset that reveals significant difference in the sandbar response between the natural and engineered sections. The inner-bar reset occurred during the storm of November, 21. The storm was characterized by a maximum significant wave height of 9.7 m, a maximum peak period of 18.2 sec, and waves approaching from NW. (a) LTT Outer bar (b) LBT Uniform inner bar Inner bar (c) RBB Irregular inner bar (d) RBB Rips Coupled (bar-shore) (e) TBR Rips (f) LTT Outer bar Decoupled (bar-shore) Inner bar Figure 3.7: Accretionary evolution of the inner bar (see text for explanation). For clarity, the description of the beach evolution first focuses on the western engineered part. The first image of the sequence (Fig a), taken before the storm, shows an outer crescentic bar attached to a LTT inner bar. During the storm, the inner bar moved up-state into a LBT state (Fig b) with a reasonably alonsghore-uniform bar crest located about 1 m from the shoreline. Ten days after the event (Fig c), the inner bar developed patterns alongshore as it moved into the RBB state with no concurrent significant change of the beach face. In Fig d, 16 days after the storm, the inner bar is still in a RBB state. An interesting evolution is that the beachface now develops features with shoreline rhythms coupling out-of-phase with the inner bar,

74 Chapter 3. Nearshore sandbar morphodynamics of the beach of Zarautz 54 that is, with the seaward bulges in the shoreline facing the inner-bar bay. This type of coupling has only been scarcely observed (e.g. Castelle et al. [21]; Orzech et al. [211]). Later on, 43 days after the storm (Fig e), the crescentic bar is attached to the shore. Accordingly, the inner bar evolved into a TBR state with shoreline rhythms now coupling in-phase the inner bar, that is, with seaward bulges in the shoreline facing the rip channels, which is the most common shoreline-sandbar coupling type (e.g. Ruessink et al. [27]; Castelle et al. [21]). At the end of the sequence, 69 days after the storm (Fig f), the inner bar exhibits a LTT state with reminiscent, less obvious, in-phase coupling between the shoreline and the inner bar. The evolution along the natural eastern part of the beach did not follow the evolution described above. Starting from a similar situation, a LTT inner-bar state with an outer crescentic bar attached to the inner bar (Fig a), after the storm, the inner bar rapidly evolved into a RBB (Fig c) and subsequently into a TBR state (Fig d). At this time, the situation became very complex as the outer-bar and inner-bar patterns progressively mingle, therefore limiting the interpretation of the inner-bar state Accretionary evolution of the outer bar Fig. 3.8, displays a typical down-state sequence of the outer bar, associated with an overall slow onshore migration of the system, during fair weather conditions. In the first image (Fig a), the outer bar exhibits crescentic patterns at a narrow range of wavelength along the whole embayment with a mean of about 4 m. Throughout the sequence, the inner bar remained in a LTT state. In the next image (Fig b), taken 49 days later, the outer bar moved onshore and became asymmetric, mainly in the eastern part of the beach where the bar horns were linear transverse oriented (NE-SW) and connected to the inner bar. In the western part, connection of the outer bar to the inner bar occurred 118 days later (Fig c) and was associated with the formation of well-developed megacusps coupling in-phase with the outer bar, that is, with the same mean wavelength O (4m).

75 Chapter 3. Nearshore sandbar morphodynamics of the beach of Zarautz 55 (a) Day 1 (b) Day 49 Attached bars (c) Day 118 Attached bars Figure 3.8: Accretionary evolution of the outer bar (see text for explanation). 3.4 Discussion and conclusions A 2-year dataset of time exposure images of the beach of Zarautz was analysed in order to study the morphology and dynamic of a partially engineered beach. Observations show that this embayed beach exhibits an open beach like circulation, which is consistent with the non-dimensional headland impact parameter of Castelle and Coco [212]. The effects of the geological constraints are mainly concentrated at the boundaries, where headland rips were present most of the time. Only during storms, beach circulation can become transitional. In fact, the geological constraints can explain why the outer bar never became uniform alongshore during severe storm, corroborating previous observations on a similar embayed beach (Enjalbert et al. [211]). Otherwise, the morphological evolution along the beach follows the common beach classification given by the WS-model. The outer-bar alongshore non-uniformity varied in time and space. The evolution of its mean cross-shore position displays a clear relation with the significant wave height time series. It migrates offshore during high energy conditions and remains steady or migrates slowly onshore during low energy conditions. During the survey period, the bar moved 8 m off-shore within only 3 days coinciding with the storm event of December, 211.

76 Chapter 3. Nearshore sandbar morphodynamics of the beach of Zarautz 56 In addition, a rapid alongshore migration of an outer-bar bay (arrow 1 in Fig left)was captured, that contrasts with the behaviour of the bays further along the embayment. This is presumably due to the merging of two bays at x 11 m in July 211 as previous numerical modelling effort showed that the merging and splitting of three-dimensional sandbar patterns can result in odd rapid migration of some of the morphological patterns (Castelle and Ruessink [211]). On the engineered part of the beach, the full down-state sequence of the inner bar is about 5% longer than along the natural part. The study of beach states residence times, shows that low energy morphological states are more persistent than high energy states. Following a reset event (high energy condition), fair weather conditions are usually long enough to enable down-state transitions. Yet, wave conditions prevailing along the Zarautz beach are energetic enough to prevent the formation of a two dimensional reflective state, as the most reflective observed state was LTT. In contrast, the high energy events required to maintain the longshore uniform inner bar (LBT) state were scarce. The inner-bar LBT state was only observed along the engineered section, whereas the uppermost state reached by the natural part was RBB. However, in the eastern part of the beach, the mingling of the outer and inner bars prevents the discrimination of their behaviour. Overall, the outer bar control over the inner bar seems to be less pronounced on the western side of the beach. This study provides the first assessment of the morphodynamics of the double sandbar system of the embayed beach of Zarautz. In this contribution, the behaviour of Zarautz beach was discussed in the framework of widely accepted morphological schemes (e.g. Wright and Short [1984]; Masselink and Short [1993]). Differences in beach morphology between the engineered and natural parts of the beach may be due to alongshore variability of hydrodynamics resulting from the combinations of headland boundary effects and alongshore non-uniformity of wave conditions. Additional investigations considering topographic surveys are needed to better understand the role of the engineered section on the global morphological behaviour of the beach.

77 Chapter 4 Beach morphological response to storm events 4.1 Introduction Storm events are major drivers of beach erosion on sandy beaches. They may also cause coastal flooding and infrastructure damages. The response of the beach to such events is linked to different scale processes. Those, include variations of the atmospheric pressure (large-scale), onshore winds (meso-scale) and wave breaking (local-scale). Some studies show that the damages due to several moderate magnitude storms can be comparable or even greater than a single storm of higher magnitude (e.g. Lee et al. [1998]; Ferreira [25]; Callaghan et al. [28]). This can arise when the frequency of storm occurrence exceeds the recovery period of the beach (Morton et al. [1995]). Conversely, in Coco et al. [214] is demonstrated that a sequence of extreme storms does not necessarily result in cumulative erosion and suggests that a cautionary approach to storm clustering is needed. On other hand, in some cases it has been observed that high energetic events can rework sediment onto the beach and rebuild it (Hill et al. [24]). The beach response can be even more complex in case of embayed beaches or if coastal structures are present. This kind of complex environment has been less studied in the literature. As a result of the constraining and protective effects of coastal lateral boundaries, the hydrodynamic behaviour of the beach can be altered. This leads to particular growth of morphological patterns such as the development of topographic controlled This chapter is based on: de Santiago, I., Morichon, D., Abadie, S., Liria, P., and Epelde, I. (213). Effect of winter storms on a partly engineered embayed beach: The case of Zarautz beach (north of Spain). Proceedings 7th International Conference on Coastal Dynamics (Arcachon, France), pp

78 Chapter 4. Beach morphological response to storm events 58 rips during fair weather conditions (Short [1985]), development of headland megarips during high energy conditions (Masselink and Short [1993]) and headland bypassing of subaqueous sand (Masselink and Short [1993]) among others. In the presence of coastal anthropogenic structures, Hall and Pilkey [1991] stated that there are three types of erosion associated with engineered beaches: (1) placement loss, (2) passive erosion and (3) active erosion. However, there is a big controversy stating whether a seawall can actively impact or not the shoreline on sandy beaches (Comfort and Single [1995]). For example, Mossa and Nakashima [1989] after a three year study of storm impact on seawalled beaches and natural beaches concluded that the volumetric loss at the engineered beach were greater than in the natural one, but on other hand, it experienced a greater recovery. In an attempt to fill this gap, the present chapter (Chapter 4) proposes a study devoted to a partly engineered embayed beach. It is based on a combination of in situ topographic surveys and indirect video imagery measurements performed before and after storm events. The focus is on the comparison between the behaviour of the natural part and the response of the engineered part of the beach by estimating the beach volumetric changes and the beach shape modification for different storm conditions. 4.2 Material and methods From November 211 to February 213, fifteen topographic surveys were carried out in order to measure the beach volumetric changes. Those surveys were undertaken systemically prior to high energetic events and after the high energetic events coinciding with low tides (preferentially during spring tides). Also, between prolonged periods of fair weather conditions, some additional surveys were taken. Two different approaches were carried out when processing the data. First, a series of beach profiles were undertaken to account for the cross-shore evolution of the different sections of the beach and second beach profiling was combined with video image to account for the 3D-evolution of the foreshore Beach profiling Eleven profiles covering the different sectors of the beach were measured (Fig. 4.1) using a Trimble RTK-GNSS (Real Time Kinematic Global Navigation Satellite System). The alongshore profile spacing was set to 2 m approximately and the cross-shore profile points were measured every 3 m. The cross-shore transects were extended from the wall

79 Chapter 4. Beach morphological response to storm events 59 base or top of the dune up to, at least, the mean low water level (LWL). Profile volumes (m 3 per m of profile width) were calculated by integrating the sand volume above the mean low water level (Fig. 4.2). To facilitate the comparison between compartments, a fictitious wall-foot was extended from the adjacent wall in the dune zone. P1 P11 Sector 1 P6 P7 P8 P9 P1 P2 P3 P4 P5 Figure 4.1: Beach profile location (black lines) and fictitious seawall extension (red dashed line). The sediment variation along the profile was assumed to be representative of the sediment interchange between the subaerial - intertidal beach and the subtidal beach. The volume of the dune was calculated by integrating the sand volume landward from the fictitious wall (Fig. 4.2). The reference beach volume of each profile was the volume computed during the first campaign. Seawall Elevation V Dune V Beach LWL Cross shore distance Figure 4.2: Scheme of beach and dune volume estimation Beach plan evolution To monitor the alongshore sand migration, both direct (topographic surveys) and indirect (KOSTASystem images) procedures were combined.

80 Chapter 4. Beach morphological response to storm events 6 Every 2 min, over a rising or falling tidal cycle, the intersection between the waterline edge and the dry part of the beach was detected, based on the contrast shift that occurs between the white foam and the reddish color of the sand (e.g. Russ [21]). Once the shoreline position was identified, its elevation was derived by interpolating the in situ measured transects over the contours resulting from the shoreline detection (Fig. 4.3). Finally, the topographical data points obtained from the series of shoreline contours were used to build a digital elevation model (DEM). It has to be mentioned that those maps only cover the intertidal zone, leaving out of range the back shore and dunes. In addition, it has to be taken into account that due to the interference of a tree that appears at the lower part of the image, the interpolated foreshore is computed only from transect 2 to transect 11. Figure 4.3: Shoreline detection and interpolation at different tidal stages (October 211). Black lines represent the measured profiles. coloured lines represent the videodetected shoreline. Most of the intertidal mapping algorithms (e.g. Plant and Holman [1997]; Aarninkhof et al. [23]; Uunk et al. [21]) are based in the combination of parametric formulas for the water level elevation and video imaging. The problem is that on beaches with complex foreshore topography, like Zarautz, the use of an alongshore-averaged beach slope may result in high run-up estimation errors (Stockdon et al. [26]). This method avoids the need of parametric formulas to calculate the water level elevation by means of the use of real measured values. The main drawback is to know the number of transects needed to obtain a reasonable skill.

81 Chapter 4. Beach morphological response to storm events z [m] Figure 4.4: Interpolation method accuracy test. Top) Regular transects are indicated by black lines and the additional transects are indicated by red lines. Bottom) Differences between regular campaign and additional transect campaign. Due to the length of the beach and the short time elapsed between high and low tide, to conduct more than 11 transect-measurements during low tide is highly difficult. A campaign was designed to test the accuracy of the method. In the campaign (Fig top) some additional transects were taken. The differences between using the preset transects (Fig. 4.1) and using additional transects were less than ±.1m (Fig bottom). 4.3 Results Extreme wave conditions All energetic events encountered within the survey period (November 211 February 213) were propagated following the procedure described in Section A total of 27 (28) storms were recorded offshore (nearshore), of which 24 were common storms both offshore and nearshore. Those events occurred mainly during autumn and winter (51% and 42% respectively) followed by spring (7%). Storms registered durations, range from 12 to 263 hours and the maximum H s recorded reached 9.1 m offshore. The mean direction of all storm events comes from the IV-quadrant, which is consistent

82 Chapter 4. Beach morphological response to storm events 62 with the wave climate in the Basque Coast (see Chapter 2 for more information). In Table 4.1 the characteristics of the five most energetic events are resumed and sorted from the most to the least energetic based on eq Table 4.1: Characteristics of storm events. Values between parentheses correspond to nearshore. H s, T p and θ has been averaged over the high energy events N Date Duration [h] H s [m] T p [sec] θ [deg] Storm P [Mw h/m] 1 19/1/ (26) 4.7 (3.2) 13.8 (14.1) 37 (342) 44.2 (2) 2 12/12/ (14) 5.5 (3.8) 15.7 (15.4) 37 (346) 34.1 (15.2) 3 5/2/ (85) 5.5 (4) 13.8 (14.4) 316 (347) 2.4 (1.7) 4 2/1/ (1) 4.8 (3.5) 15 (15.2) 311 (347) 18.2 (8.6) 5 1/12/ (59) 5.7 (3.6) 12.9 (13) 298 (339) 12.1 (5.5) Fig. 4.5 shows that the relevance of a given storm tends to show differences depending on the location (offshore/nearshore). This means that, despite of the transformation of wave conditions when travelling to the nearshore, high magnitude (and long duration) storms tend to be of great importance both offshore and nearshore. However, there are differences when these storms are of lower magnitude (usually of short duration). Storm duration [h] Offshore Nearshore Index nearshore Index offshore Figure 4.5: Top) Relation between storm duration and its relevance. Bottom) Relation between storm relevance nearshore and offshore.

83 Chapter 4. Beach morphological response to storm events Profile analysis The analysis of the beach profiles provides discrete information of the system. Both pre/post storm erosion/accretion volumes and the cumulative effect along the whole period are studied. Also, the dune response due to the effect of storms is analysed in the following section Transect volume evolution The beach was split into three alongshore sections with similar characteristics to simplify the description (Fig. 4.1). Sector 1 represents the most western profiles of the engineered section. This area of the beach is facing north and the backshore width is the shortest of the 3 sectors. Sector 2 represents the central part of the beach; all the profiles are still backed by a rigid seawall and are facing NNW. The profiles of Sector 3 are placed in the eastern part of the beach; they are representing the transition and natural zone of the beach. One of them is backed by a seawall and the rest of the profiles are backed by the dune, those profiles are facing NNW too. Transect volume changes time series(fig. 4.6) are presented in this section. Although belonging to the same sector, profiles 1-2 and 3-4 exhibit different erosion/accretion patterns. The variability existing in profiles 3-4 is greater than the one observed in profile 1-2. At sector 2, all transects seem to have a similar behaviour, oscillating between gain/loss phases. However there are exceptions. At sector 3, there is a loss of sand tendency with high variability at profile 11. During the winter of (between survey 1 and survey 5), including the second most energetic storm event (storm 2 lying between surveys 3 and 4), all the transects lost part of the profile sand (see Fig. 4.6 centre). Because of the storm occurred during the mid-spring period (see period between survey 5 to 6); all transects but one (transect 1) lost part of their sand reservoir. From mid spring to the end of the season (between survey 6-7), no extreme events were recorded, but not all transects were able to gain sand. Summer of 212 (survey 7 to 8) was a clear recovering period. However, profiles 1 and 1 were an exception and did not follow this pattern. During fall of 212 (survey 9 to 12), a series of short energetic events occurred. Unexpectedly, a variable response is detected, where some of the transects gain sand while others are eroded. The winter of hosted three of the five most energetic events registered during the survey period (see storms 1, 3 and 5 in Table 4.1 or the period between survey 12 to 15). It should be highlighted that the combined effect of those series of storms produced the erosion of all profiles. However, the most impacted zones were the central section and eastern section of the beach.

84 Chapter 4. Beach morphological response to storm events 64 Despite the different response of the transects, overall the beach presents a seasonal behaviour. This can be seen in Fig. 4.6 (bottom panel) where it is shown that winter is an erosional period and summer is an accretional period. 1 S1 S2 S3 S4 S5 S6 S7 S8 S9 S1 S11 S12 S13S14 S15 Hs [m] 5 Nov11 Jan11 Mar12 May12 Jul12 Sep12 Nov12 Jan13 Mar13 P 1 9 X X X 7 X 5 X 3 X Nov11 Jan11 Mar12 May12 Jul12 Sep12 Nov12 Jan13 Mar13 X 8 V (m 3 /m) 8 Vc [m 3 /m] Nov11 Jan11 Mar12 May12 Jul12 Sep12 Nov12 Jan13 Mar13 Figure 4.6: Top) Time series of offshore significant wave height (H s ), red lines represents high-energy events and vertical black lines the timing of beach surveys. Centre) Volume changes, black crosses represent data gaps. Bottom) Averaged cumulative volume changes Dune evolution The dunes at the natural section presented significant changes during the storms occurred on February 213 (Fig. 4.7). During these events (see third storm in Table 4.1), an offshore maximum wave height of 9.1 m and maximum peak period of 18 sec were reached coinciding with spring tide. The combination of the high water level and the high energetic conditions produced a 2 m dune scarp at profile 1 and 1 m at profile 11. The dune retreat was of 4 m for profile 1 and 4.5 m for profile 11 and the volume of the dune was reduced by 4 m 3 /m and 1.5 m 3 /m respectively. Despite the fact that this event was the most dune-damaging event recorded until that time, the loss of sand along the foreshore was not so important. It seems that the sand of the dune and backshore worked as a buffer, mitigating the erosion of the foreshore. The dune scarp at profile 1 was more pronounced, in contrast, the backshore and foreshore along this transect were less modified.

85 Chapter 4. Beach morphological response to storm events Pre storm Post storm fic. seawall 1 fic. seawall Elevation [m] Z max Z max 2 SHWL HWL 2 SHWL HWL MWL LWL MWL LWL Cross-shore distance [m] Cross-shore distance [m] η [m] 2 2 2/3 2/1 Date Figure 4.7: Top) Dune evolution between survey 14 and survey 15. Bottom) Astronomical tidal elevation (blue) and instantaneous waterline elevation (red-dashed) computed by empirical formulation (Stockdon et al. [26]) Plan view analysis The analysis of contour maps is able to provide information on the foreshore of the beach. The gaps between profiles are filled with the data recovered from the interpolation between transects, providing continuous information of the intertidal zone of the beach Case 1: Relevance of rip current location The location of the rip currents along the beach can play an important role on the erosion of the foreshore. Between the end of October 211 and the beginning of November 211, two energetic events occurred. Those events were characterized by offshore mean H s of 4.3 m m and mean T p of 18.2 sec sec (Fig. 4.8 a-b), the duration of those storms were of 13 hours and 28 hours respectively with 36 hours of separation between them. The analysis of the images along this period shows the presence of a stable rip at the central section of the beach. This rip current was able to erode specifically the central zone of the beach (Fig. 4.8 c). In fact, it can be seen from Fig. 4.6 that the profile number 7 was the most affected on the beach, loosing 2 m 3 /m of its volume. In contrast, the profile 6 and 8, adjacent to the rip current, gained 11 m 3 /m and 21 m 3 /m, respectively.

86 Chapter 4. Beach morphological response to storm events 66 Another erosive point of the foreshore was located at the western part of the beach (close to the profile 11), but in this case a clear relation between an erosive process and the generation of a rip current could not be established. The response of the rest of the beach was quite homogeneous. The sand reservoir of the beach face, along at the MWL, was transported to the edge of the LWL. Hs & η [m] 1 5 a) 1/3/11 11/6/11 Tp [sec] 2 b) 1 1/3/11 11/6/ c) 1.5 y [m] Z (m) x [m] 1 Figure 4.8: Intertidal erosion/accretion patterns between surveys 1-2. a) Offshore H s (dark blue) and H s at the seaward boundary of the study site (Blue). Grey line indicates the astronomical tidal elevation. b) Offshore wave period. Storms are highlighted by red lines. c) Elevation differences between surveys 1 and Case 2: Relevance of storm magnitude In some cases, the erosion/deposition trends of the intertidal zone might present differences between the engineered and the natural zones. Beach response during survey 12-13: From mid-january 213 to the beginning of February 213, two energetic events occurred (Fig a to b). The first of them coincided with spring tides. Despite the fact that it lasted 75 hours offshore, its duration nearshore was only of 2 hours. The second storm is the most energetic (and the longest) recorded during the total length of survey period. It coincided with neap and spring tides. It lasted

87 Chapter 4. Beach morphological response to storm events 67 around 11 days both offshore and nearshore. It reached H s values of 7.7 (5.2) m and T p of 19.8 sec offshore (nearshore). Despite being low-powered, the first storm coincided with spring tides and reached a maximum water level of approximately 3.3 m (calculated by parametric formulas, i.e. Stockdon et al. [26]). During the first half of the second storm, neap tides occurred, but due to the higher energy conditions the maximum instantaneous waterline elevation was also of 3.3 m (approx.). During the first half of the second storm, the H s could have potentially caused a significant erosion, however, the beach did not clearly show such response (Fig c). The backshore of some parts of the engineered section maintained intact while the intertidal zone of the whole section eroded. On the other hand, at the transition and natural zone, the backshore stayed intact and the intertidal zone accreted. This is better seen in Fig. 4.1 where three different transects at different sections of the beach are shown. Hs & η [m] 1 a) 5 1/13/13 1/2/13 1/27/13 Tp [sec] 2 b) 1 1/13/13 1/2/13 1/27/13 6 c) 1.5 y [m] Z (m) d) y [m] Z (m) x [m] 1 Figure 4.9: Intertidal erosion/accretion patterns between surveys a) Offshore H s (dark blue) and H s at the seaward boundary of the study site (Blue). Grey line indicates the astronomical tidal elevation. b) Offshore wave period. Storms are highlighted by red lines. c) Elevation differences between surveys 12 and 13. d) Elevation differences between surveys 13 and 14 Beach response during survey 13-14:

88 Chapter 4. Beach morphological response to storm events 68 During the second half of the second storm the mid and upper intertidal part of the whole beach eroded and the lower beach zone accreted or did not record any changes (Fig d). This response corresponds to the theoretical erosion sequence, where the sand of the upper parts is relocated to the lower part of the beach. Unlike the first half of the second storm, this sequence occurs during neap tides evolving to spring tides, the maximum water level elevation is higher and the tidal range too. Profile 5 (engineered) Profile 8 (engineered) Profile 1 (natural) 5 S12 S13 S Elevation [m] HWL HWL HWL MWL MWL MWL LWL LWL LWL x [m] x [m] x [m] Figure 4.1: Transect evolution during surveys Case 3: Relevance of storm magnitude coinciding with spring tidal conditions It has been seen in Section that high energetic events do not necessarily erode the intertidal zone. A good illustration of this behaviour can be seen in Fig. 4.11, which displays beach volume changes in February 213 (between surveys 14 and 15). The foreshore of the sector 1 and the western part of sector 2 were eroded (profiles 1 to 7), with the highest erosion rate at the upper part of the beach. In contrast, the eastern part of the sector 2 and the major part of sector 3 gain sand.

89 Chapter 4. Beach morphological response to storm events 69 Foreshore gain of sand is concomitant with backshore and dune sand loss. The deposition of sand in section 2 might be the result of alongshore movement from the dunes to the seawalled zone. This could suggest that the transition zone between engineered and natural beach may locally modify the hydrodynamic pattern as reported in a previous study (De Vries [211]). Hs & η [m] 1 5 a) 2/3/13 2/1/13 Tp [sec] 2 1 b) 2/3/13 2/1/ c) 1.5 y [m] Z (m) x [m] 1 Figure 4.11: Intertidal erosion/accretion patterns between surveys a) Offshore H s (dark blue) and H s at the seaward boundary of the study site (Blue). Grey line indicates the astronomical tidal elevation. b) Offshore wave period. Storms are highlighted by red lines. c) Elevation differences between surveys 14 and Discussion and conclusion Eleven cross-shore profiles were tracked systematically over one year period at the beach of Zarautz. All profiles were measured before and after energetic events of different characteristics to obtain the sand gain/loss of the beach at different sections. Some additional surveys were carried out to follow the evolution of the beach during calm conditions as well. Two different approaches were used for the analysis of the volume evolution. On one hand, classical profile volume estimation was carried out to follow the volume changes along the surveyed period. Volumes were estimated integrating the sand volume above the mean low water level. Volume changes were considered to be representative of the sand interchange between the beach and the subtidal beach. On the other hand, a new method that combines both direct (topographic surveys) and

90 Chapter 4. Beach morphological response to storm events 7 indirect (image analysis) methods was used to obtain a series of foreshore continuous topography maps. Due to the complexity of the beach location the wave characteristics can be modified. Hence, all high energy events were propagated before calculating the storm index. To characterize the storm, an index based on the cumulative energy per meter wave crest was used. Based on this approach, 24 (offshore and nearshore) storms were registered during the survey period (November 211 February 213). The time series of cumulative volume changes for the different profiles do not reveal any significant differences between the engineered and natural sections. However, the greater stability detected in those profiles of lesser slope (i.e. profile 1 and 2) seems to provide a dynamic equilibrium along this section. This is consistent with previous studies. For example Newe et al. [1999] suggested that for high energy conditions, the beach response is strongly dependent on its slope, being more stable those areas with gentle sloping foreshores. One of the pioneers on the study of the relation between the beach response and its conformation (Wright [198]; Wright and Short [1983]) suggested that while the mobility of low sloping beaches (dissipative) is quite restricted to the dune/backshore, the steeply sloping beaches (reflective) are more susceptible to erosion along the foreshore. Analysis of the foreshore maps suggest that during high energy conditions erosive processes not only occur all over the beach, but also can occur at localized areas. In those specific cases there seems to be a clear relation between the location of rip currents and the erosive area. In fact, between the surveys 1 and 2, two of the less energetic extreme storms took place. In spite of this, the central part of the beach was significantly eroded. The images taken by the video station during this period show a clear presence of a stable rip current at that position. This is consistent with previous studies (Wright [198]; Short and Hesp [1982]) were the maximum erosion of the beach is observed in the lee of the rip creating mega-cusps on the system. Another scenario is encountered with high energy events occurring during spring or neap tides. In case of spring tides events, the storm seems to erode the backshore and dunes of the beach transporting the sand to the foreshore. In such cases the dune and backshore become important as they act as a buffer, preventing the foreshore erosion of the beach. On the other hand, when neap tides coincide with the presence of a high energetic event, the evolution of the foreshore might be sensitive to the wave characteristics rather than to the tidal range as those are decisive in the maximum level reached by the water layer. Despite that not clear difference is detected at the engineered/natural limit, Zarautz s response seems to be non-uniform along the beach. The variable amount of sand registered along the site together with the position of the wall and the different hydrodynamic

91 Chapter 4. Beach morphological response to storm events 71 patterns that are developed along Zarautz, appear to play a key role in its response to extreme events.

92

93 Chapter 5 XBeach: Numerical modelling 5.1 Introduction In the previous chapters, it was shown that the beach of Zarautz exhibits some different behaviours as a function of the beach section (engineered/natural) during both long term (Chapter 3) and short term (Chapter 4) periods. While long term morphological changes can be fairly well addressed by means of video monitoring techniques, the study of the response of this type of partially engineered embayed beaches to storm events is a much more challenging task. It is hazardous to draw conclusions on the response of the beach to storms impact based on the study of a limited number of events. In fact, storm characteristics are highly variable (Chapter 2). Furthermore, the temporal scales at which a beach is modified during storms, varies from days (bar migration) to seconds (dune slumping). Thus, a better understanding of the response of the beach and of the involved processes requires to consider a wide variety of storm conditions, in many cases only possible by the use of numerical models. There are several numerical models dealing with the morphological evolution of sandy coasts. Worldwide used processes based models, capture the most important physical processes and hence are a good choice for understanding the mechanisms acting underneath the problem. XBeach wave numerical model is used in this study. Previously Reniers et al. [24] presented a similar model approach. The main innovation of this model was the inclusion of the wave group induced bound long waves and the spatial and temporal scales at which the hydro-morphodynamic processes were solved. However, unlike XBeach, the dune morphodynamic module was not implemented yet. 73

94 Chapter 5. XBeach: Numerical modelling 74 Later, in Roelvink et al. [27a] and Roelvink et al. [27b] a first XBeach version was presented. In order to deal with dunes and the backshore evolution an avalanching mechanism providing a robust solution for slumping of sand during dune erosion was implemented. With the aim of modelling the storm impact on beaches, dunes and barrier islands, in Roelvink et al. [29] the model was compared against a number of test cases, both in 1D and in 2DH mode. They showed that it was able to reproduce the storm driven hydrodynamics and the morphological changes quite well with the standard set of parameters. So far, a number of numerical studies has been carried out not only to test the model but also to better understand the processes that drive the erosion on coastal zones and furthermore to develop coastal management projects or even to set operational models. Hurricane impact is one of the recurrent topics in which XBeach has been used. Shortly after the release of the model, two papers (Lindemer et al. [21]; McCall et al. [21]) where published in order to test and understand the effects of hurricane overwash and inundation. Regarding the sensitivity of the model, two contradictory conclusions were reached; while Lindemer et al. [21] stated that the model under predicted the magnitude of erosion, in McCall et al. [21] some of the parameters had to be tuned in order to avoid the over-erosion of the site. Beach morphology studies under moderate wave conditions have also been published. For example, Orzech et al. [211], investigated the formation of beach megacusps along the shoreline of southern Monterey Bay, CA. They pointed out that XBeach was able to hindcast measured shoreline change moderately well but overpredicted the erosion of the swash region and beach face. Rip current development and evolution has gained a lot of attention too. In Austin et al. [212] the development, validation, and evaluation of an operational rip current prediction tool is described. Winter et al. [214] challenged the model to run in a windy and obliquely incident wave area. In their study, XBeach was successfully applied using its default parametrization in contrast to Austin et al. [212] where the default wave breaking parametrization did evoke instabilities in the rip current model. However, one of the most studied topics is related to beach and dune erosion during high energetic events. Van Thiel de Vries [29] conducted a large-scale physical model test combined with the numerical model where (among other things) the sensitivity of simulated dune erosion to short waves and long waves was examined. In this work, the relevance of the role of low frequency motions is highlighted, since the exclusion of them may result of an underestimation (about 3%) of the dune erosion. Van Dongeren et al.

95 Chapter 5. XBeach: Numerical modelling 75 [29] published one of the first works of beach profile hindcasting using measurements of eight different sites along Europe. The results showed that despite the model skill in predicting the coastal profile, in most cases the erosion around the mean water line was overpredicted. The suggested causes are likely to be related to the modelling of onshore (asymmetry) transports which reduces the offshore transports due to undertow (currents) or the modelling of sediment motion in the swash zone. The good skill in predicting dune erosion is also mentioned in Splinter and Palmsten [212] or in Armaroli et al. [213]. But both studies coincide in the need of the model calibration. The recent implementation of new formulations and modules (e.g. Reniers et al. [213]; Van Thiel de Vries [212]) is facilitating the use of the model in a wide range of beaches. For example Van Thiel de Vries [29] and De Vries [211] tested the model performance at beach scenarios backed by seawalls and later Van Thiel de Vries [212] in a situation where the dune is partially protected with a revetment. In all the cases it is agreed that the scour hole that can develop near the toe of a dune revetment is underestimated by the model. Furthermore, although less relevant for the present study several papers have been written about gravel beaches and the XBeach applicability (i.e. Williams et al. [212]; Jamal et al. [214]). Finally, a new version of the model (XBeach-G) has been recently released to deal with these type of beaches (McCall et al. [214]). Also, in the recent past, the statistical approaches in combination with process based models (i.e. Li et al. [214]) are taking lead in order to conduct medium to large term analysis. In summary, it is clear that due to large amount of scientists using the model and its constant improvement, we are facing a robust and good skilled model for beach evolution. However, like all the numerical models it needs a calibration step before interpreting any model results (Kamphuis [21]). If a comparison with real measurements is not possible one can always turn to papers where a vast amount of tests have been conducted (i.e. Vousdoukas et al. [212]) choosing the most suitable set of values depending on the particularities of the study site. 5.2 Model philosophy The philosophy of the XBeach is to model processes in different regimes as described by Sallenger [2]. The wave energy is modelled on the scale of wave groups. This is done by means of the wave-action balance (e.g. Phillips [1977]). The wave energy released at wave breaking is first transferred to roller energy (Svendsen [1984]; Nairn et al. [199]; Stive and De Vriend [1994]) representing the momentum stored in surface

96 Chapter 5. XBeach: Numerical modelling 76 rollers, which leads to a shoreward shift in wave forcing. The wave-group forcing drives bound infragravity motions (18 deg out of phase with the short-wave groups). Once the wave group enters the surf zone the group modulation vanishes and the bound infragravity waves are released. These free long waves are reflected at the shoreline and can scape as a free wave or get trapped. The non-linear shallow water equations are used to resolve the mean and low-frequency flows. These equations are forced by radiation stresses to phase resolve bound and free infragravity waves. The sediment transport is driven by the mean currents and short and infragravity waves. The wave breaking generated turbulence together with the wave orbital motion are the main processes stirring up the sediment. The onshore sediment transport is parametrised in the present approach. Resolving the phase of infragravity motions allows the action of essential mechanisms for sediment transport. While the set of wave groups stir up the sediment, the bound long wave associated to this group (which is 18 deg out of phase with the group) transports the sediment in the offshore direction. Once the long waves are released, the wave long waves do not coincide with the short wave crests anymore, reversing the direction of the sediment transport. The sediment transport from the dry section (e.g. dunes) of the beach to the wet section (e.g. swash zone) is modelled with an avalanche algorithm, which takes into account that saturated sand moves more easily than dry sand. The sand slumping is triggered by the ups and downs of the swash zone dynamics, which reach this part of the beach eventually. 5.3 Model approach and governing equations Short wave propagation The wave energy is obtained from the time dependent version of the wave action balance equation (eq. 5.1). The directional distribution of the action density is taken into account whereas the frequency spectrum is represented by a single wave period (T e = m 1 m ), this method is similar to that shown in HISWA model (Holthuijsen et al. [1989]). A t + c xa x + c ya y + c θa = D w θ σ (5.1) The model description is derived from Roelvink et al. [27b]

97 Chapter 5. XBeach: Numerical modelling 77 The 2 nd and 3 rd left hand side (LHS) terms account for spatial advection of wave energy. Refraction is accounted for by the 4 th LHS term. D w accounts for the dissipation of wave energy due to breaking. A is the wave action, represented as: A(x, y, t, θ) = S w σ (5.2) S w represents the wave energy density in each directional bin, θ the angle of incidence with respect to the x-axis and σ the intrinsic frequency. The wave action propagation speeds in x and y directions (c x and c y respectively) are given by: c x = c g cos(θ) + u L c y = c g sin(θ) + v L (5.3) where u L and v L are the cross-shore and alongshore depth-averaged Lagrangian velocities respectively (to take into account the wave current interaction), and the group velocity c g is obtained from linear theory. The propagation speed in θ space is computed as: c θ (x, y, t, θ) = ( ) ( h h u sin θ x y cos θ + cos θ x sin θ u sin θ ) y cos θ + ( ) v v sin θ x y cos θ (5.4) This equation accounts for both bottom refraction (first term on the RHS) and current refraction (last two terms on the RHS). In the present study, the wave energy dissipation due to wave breaking is modelled according to Roelvink [1993] in the instationary mode: D = 2 α Q b E w T rep ( ( ) ) H 2 Q b = 1 exp, H = H max 8E ρgh, H max = γ tanh kh k (5.5)

98 Chapter 5. XBeach: Numerical modelling 78 In the stationary case, Baldock et al. [1998] is applied: D = 1 4 αq bρgf rep (Hb 2 H2 rms) ( ( ) ) 2 Hb Q b = exp H rms, H b =.88 k tanh [ ] γkh.88 (5.6) with α = O (1), ρ the water density, γ the breaker index, T rep representative period and f rep representative intrinsic frequency. The total wave energy is given by: E(x, y, t) = 2π S w dθ (5.7) The total wave dissipation, D w, is distributed proportionally over the wave directions: The bed friction dissipation is modelled as: D w (x, y, t, θ) = S w(x, y, t, θ) E w (x, y, t, θ) D w(x, y, t) (5.8) D f = 2 ( ) 3 ρπf πh 2 w (5.9) T rep sinh kh Finally, the radiation stresses are evaluated, by means of linear wave theory, by: ( cg S xx,w (x, y, t) = c (1 + cos2 θ 1 ) S w dθ 2 ( cg S xy,w (x, y, t) = S yx,w (x, y, t) = sin θ cos θ c S w S yy,w (x, y, t) = ( cg c (1 + sin2 θ 1 2 ) dθ ) S w dθ (5.1) Roller energy propagation The dissipation of wave energy serves as a source term for the roller energy balance which is coupled to the wave action/energy balance. The directional distribution of the roller energy is also taken into account and the frequency spectrum is represented by a single representative period (T e ).

99 Chapter 5. XBeach: Numerical modelling 79 S r t + c xs r x + c ys r + c θs r y θ = D r + D w (5.11) where the roller energy in each directional bin represented by S r (x,y,t,θ). The roller energy propagation speeds in x- and y- direction are given by: c x = c cos(θ) + u L c y = c sin(θ) + v L (5.12) where c is the wave phase velocity obtained from linear theory. The total roller energy dissipation is given by (Reniers et al. [24]), which is later distributed proportionally over the wave directions. D r (x, y, t, θ) = 2gβ re r c (5.13) where β r is the slope of the breaking wave front. D r (x, y, t, θ) = S r(x, y, t, θ) E r (x, y, t, θ) D r(x, y, t) (5.14) The roller contribution to radiation stress is given by: S xx,r (x, y, t) = cos 2 θs r dθ S xy,r (x, y, t) = S yx,r (x, y, t) = sin θ cos θs r dθ S yy,r (x, y, t) = sin 2 θs r dθ (5.15) Which are used to calculate the wave forcing. ( Sxx,w + S xx,r F x (x, y, t) = x ( Sxy,w + S xy,r F y (x, y, t) = x + S ) xy,w + S xy,r y ) + S yy,w + S yy,r y (5.16)

100 Chapter 5. XBeach: Numerical modelling Wave flow and long wave propagation For the low-frequency and mean flows the shallow water equations are applied. To account for the wave induced mass-flux and the subsequent (return) flow these are cast into a depth averaged Generalized Lagrangian Mean (GLM) formulation (Andrews and McIntyre [1978a]; Andrews and McIntyre [1978b]; Walstra et al. [21]). To that end, the momentum and continuity equations are formulated in terms of the Lagrangian velocity, u L, which is defined as the distance a water particle travels in one wave period, divided by that period. This velocity is related to the Eulerian velocity (the short-wave-averaged velocity observed at a fixed point) by: u L = u E + u S v L = v E + v S (5.17) where u S, v S represents the Stokes drift in x- and y-direction respectively (Phillips [1977]): u s = E w cos θ ρhc v s = E w sin θ ρhc (5.18) The resulting GLM-momentum equations are given by: u L t + u L ul x ( ul 2 + vl y u L fvl v h x u L ) y 2 = τ sx ρh τ bx ρh g η x + F x ρh (5.19) v L t + ul vl x ( vl 2 + vl y v L ful v h x v L ) y 2 = τ sy ρh τ by ρh g η x + F y ρh (5.2) η t + hul x + hvl y = (5.21) where, τ sx and τ sy are the surface shear stresses, τ bx and τ by are the bed shear stresses, η is the water level, F x F y, are the wave-induced stresses, v h is the horizontal viscosity and

101 Chapter 5. XBeach: Numerical modelling 81 f is the Coriolis coefficient. In eq and eg. 5.2 the RHS of the transport equations express the total force applied to a body of water and the LHS determines the response of the water body to this force. The 2 nd and 3 rd LHS terms of the transport equations account for advection. The 4 th LHS terms of the transport equations accounts for the Coriolis force. The 5 th LHS terms of the transport equations accounts for turbulent viscosity. The 1 st and 2 nd RHS terms account for the surface shear stress and bed shear stress respectively. The 3 rd RHS term in the momentum equations represents the forcing due to water level gradients. The 4 th RHS term in the momentum equations gives the wave force applied to a water body. The bottom shear stress terms are calculated with the Eulerian velocities as experienced by the bed: u E = u L u S v E = v L v S (5.22) Sediment transport and bed level change The sediment transport is modelled with a depth-averaged advection diffusion equation (Galappatti and Vreugdenhil [1985]). hc t + hcue x + hcve y + [ D h h C ] + [ D h h C ] = hc eq hc (5.23) x x y y T s Here, C represents the depth-averaged sediment concentration, D h is the diffusion coefficient, T s the adaptation time for the entrainment of sediment and C eq is the equilibrium concentration. Note that, small values of T s lead to nearly instantaneous sediment response. The entrainment/deposition of sediment is determined by the mismatch between the actual sediment concentration, C, and the equilibrium concentration, C eq, thus representing the source term in the sediment transport equation. Finally the bed-updating is given by: z t + f ( mor qx (1 p) x + q ) y = (5.24) y

102 Chapter 5. XBeach: Numerical modelling 82 where p is the porosity, f mor is a morphological acceleration factor of = O (1-1) (e.g. Reniers et al. [24]) and q x and q y represent the sediment transport rates in x- and y-direction respectively, given by: [ hcu E q x (x, y, t) = x [ hcv E q y (y, y, t) = y ] [ [ + D h h C ]] x x ] [ [ + D h h C ]] y y (5.25) (5.26) Avalanching algorithm The dune face erosion is modelled with an avalanche algorithm that takes into account a critical wet slope φ wet and a critical dry slope φ dry. The transition between the critical slopes takes place at a user specified water depth h switch. The maximum rate of dune erosion in the avalanche algorithm is specified by dz max. When the critical slope between two adjacent grid cells is exceeded, sediment is exchanged between these cells to the amount needed to bring the slope back to the critical slope. This exchange rate is limited by a maximum avalanching transport rate dz max. 5.4 Bathymetry estimation by assimilation techniques (XBeach- Beach Wizard) Nearshore bathymetrical data is essential for the numerical model calibration. The fast morphological changes that occur in the nearshore and the time needed to prepare a bathymetric campaign makes to have always an updated bathymetry at hand a difficult task. In the present case, the available information was an out-dated bathymetry. Because of that, the best solution to solve this issue was the use of data assimilation models. The bathymetry estimation using data assimilation methods has been previously applied by different scientist (Van Dongeren et al. [28]; Almar et al. [211]; Holman et al. [213], among others). At the moment two main algorithms are used for this purpose, cbathy (Holman et al. [213]) and Beach Wizard (Van Dongeren et al. [28]). Both methods have a similar philosophy and use video derived information, but tackle the problem by different approaches. While cbathy uses celerity maps combined with the linear dispersion relation to infer the bathymetry, Beach Wizard relates numerous

103 Chapter 5. XBeach: Numerical modelling 83 data sources (wave roller dissipation, wave celerity and intertidal bathymetry) to numerical model results. Despite the fact that Beach Wizard has the possibility to combine multiple data-inputs, the main and most important source of information is the videoderived roller energy dissipation, in which, is assumed that video intensity represents the wave roller dissipation (Aarninkhof et al. [25]; Van Dongeren et al. [28]). Beach Wizard has previously shown to be a practical and accurate tool when estimating the nearshore bathymetry. The model has been validated against both synthetic and real cases (Van Dongeren et al. [28]; Sasso [212]; Morris [213] among others). To the author s knowledge, this work constitutes the first attempt to apply Beach Wizard to a confined bay. In the following, the methodology and a model modification are first described. The model is then tested against synthetic cases. A sensitivity study is also carried out to define the robustness of the model Beach Wizard model description The Beach Wizard model is chosen for its limited number of free parameters and due to its remarkable skills using only roller maps as an input source (e.g. Egmond, The Netherlands in Van Dongeren et al. [28]). The model updates the unknown bathymetry, combining a prior bathymetry with a bathymetry estimated from remote sensing observations (eq. 5.27), through a Kalman type filter (Kalman [196]): h update = h prior + α(h obs h prior ) (5.27) where the h prior is the prior state bathymetry, h obs is a bathymetry estimated from remote sensing observations and α is a weighting factor. The key factor of the model, is to link the observed source (wave roller dissipation, video-derived intertidal bathymetry and radar-derived wave celerity) to a given depth (eq. 5.28), to then, derive changes in the bathymetry from the remote sensing observations: h update = h prior + α df dh ( df dh )2 + δ 2 (f f obs) (5.28) where f obs is an observed quantity (note that in the present work only image derived wave roller dissipation are used), f is a computed quantity, h is the water depth and δ is a noise level.

104 Chapter 5. XBeach: Numerical modelling 84 When using wave roller dissipation sources, the model will react by eroding (deepening the seabed) zones where observed dissipation is lower than computed dissipation and accreting (rising the seabed) when opposite situation is given (the reader is referred to XBeach Wizard user manual Van Dongeren [29] and Van Dongeren et al. [28] for a full description). The α parameter (eq. 5.29) is a weighting factor, which balances the impact of the uncertainties (σ 2 ): α = ( σprior 2 T s t σ2 obs + σ2 prior ) (5.29) where Ts and t are the simulation duration and the simulation time step respectively. The observed uncertainty (eq. 5.3) is related to: (1) the error of the measurements (in this case chosen as the 15% of the maximum value of the dissipation map), (2) the difference between the computed and the observed quantity (e.g. wave roller dissipation) and on (3) the gradient between the computed quantity and the water depth: σ 2 prior = ɛ2 + (f f obs ) 2 ( df dh )2 + δ 2 (5.3) Finally, the updated bathymetry uncertainty is calculated as follows: σ 2 update = αt s t σ2 obs (5.31) which will become σprior 2 in the next time step. The updated uncertainty (eq. 5.32) between consecutive simulations (between one image and the following image) is increased following a sigmoid-like function that evolves towards the natural uncertainty (σ evo ). The natural uncertainty is set to 1 m, and the rate at which this function reaches such value depends on the temporal scale free parameter (Tr). Basically this parameter controls the bathymetry uncertainty between adjacent runs. The new run uncertainty is the previous run uncertainty plus an extra uncertainty increment. For high Tr values the uncertainty increases at lower rate, meaning that the truthfulness of the previous bathymetry decreases slowly. This parameter depends on the sediment transport rates and it has a constant value for the whole domain and during the whole simulation. ( ) σ 2 (t j ) = σ 2 (t j 1 ) + (σevo 2 σ 2 (t j ))tanh 2 3 T r (t j t j 1 ) (5.32)

105 Chapter 5. XBeach: Numerical modelling 85 The assimilation model needs to be enforced through a hydrodynamic model in order to get the roller energy dissipation; this is achieved by running the XBeach wave module in a stationary mode Model adaptation So far, XBeach-Beach Wizard model was only adapted to work in sites where the offshore boundary conditions of the model, could be considered alongshore uniform. Hence, the boundary conditions consisted of the tidal elevation and a unique value of H rms, T rep and θ. This assumption is usually not suitable in confined bays since the lateral boundaries modify the wave conditions. Because of that, in the present case an alongshore varying boundary is also considered through a slight modification of the boundary input (eq. 5.33), which now depends also in the alongshore component. cos n (θ θ m (y)) e (y) = E(y) θmax θ min cos n (θ θ m (y)) θ (5.33) The energy at the boundary (E) is calculated as function of the H rms, T rep, θ and a given value of the power of directional distribution (n). In the case of alongshore varying boundary condition, the H rms and θ are alongshore varying while T rep and n are represented by a single alongshore averaged value Verification of the boundary adaptation The aim of the following section is to determine the accuracy of the new implementation (eq. 5.33). For that, alongshore uniform boundary (hereinafter referred to as UB) and alongshore non-uniform boundary (hereinafter referred to as NUB) are applied to determine whether the target bathymetry (uniform barred beach) can be recovered with both methods starting from a linear beach (Fig a). A 48 hours wave data series together with a semidiurnal.5 m amplitude tide are created. To quantify the effect of the alongshore wave variability degree, three different cases are set up. At one end of the beach (called East) a wave height difference of 1 % (Test-a) - 3 % (test-b) - 5 % (test-c) is imposed with respect to the other end (called West) (Fig c). The values in between, are linearly interpolated. The whole simulation is divided in a set of 15 minutes stationary runs, all of them computed over an alongshore uniform barred beach ( target beach) of 79 m alongshore distance and 39 m crossshore distance to obtain a sequence of synthetic roller dissipation maps (a total of 192).

106 Chapter 5. XBeach: Numerical modelling y [m] a) T west T east 1.5 H [m] c) H [m] y [m] b) T west T east 1.5 H [m] x [m] 2 4 time [hours] Figure 5.1: Synthetic test cases. a) Alongshore non uniform boundary example (H west = 1 m, H east = 1.3 m, T = 11 sec., θ = ). b) Alongshore uniform boundary example (H mean = 1.15 m, T = 11 sec., θ = ). c) Synthetic case wave data series. Black dashed line represents the western boundary input. Coloured lines represent eastern boundary input. Red line is 1% larger than black dashed line. Green line is 3% larger than black dashed line. Blue line is 5% larger than black dashed line. The intrinsic error of the model is assumed to be 15% of the maximum value of the dissipation map and the Tr free parameter is set to 5 days (default value). Once the synthetic roller dissipation maps are obtained, Beach Wizard is forced by: 1) Alongshore uniform boundary (UB) conditions and 2) Alongshore Non-Uniform boundary (NUB) conditions, using the synthetic roller maps as an input (as if they were real video images). The RMSE error of each cross-shore transect of the beach (Fig a to c) applying UB conditions, increases when increasing the wave variability. As the alongshore wave variability increases, the differences between the alongshore averaged wave height and correct wave height increases, affecting the roller dissipation response. Then, the erosion-deposition trends will systemically fail. On the other hand, the averaged and correct wave heights have similar values at the centre of the domain (around 4 m); hence both methods present a RMSE error close to zero in that section. The wave

107 Chapter 5. XBeach: Numerical modelling 87 alongshore variability intensity level also affects to the NUB method, but not in the same magnitude (O (<.2m)). The comparison between the RMSE errors of UB and NUB (for the whole bathymetry), displayed in Fig d, indicates that the modified version improves the results in around 75% - 95%. The differences between both methods increase as the alonghore boundary variability increases following a non-linear trend. Cross-shore transect differences (Fig b to d) are analysed in detail at two different locations (x = 16 m and x = 63 m, Fig a to b represented by T west and T east ). In the case of UB method, test-a presents the largest differences around the bar. At tests b and c, the differences are extended to the whole profile. However, there is not a significant deformation of the bathymetrical shape (not shown). There is a depth rising at West side and a depth lowering at East side, which is consistent with the model theory. On the other hand, elevation errors obtained implementing the NUB method (O (<.2m)) are derived from the finite length of the simulation and from the intrinsic errors of the model. rmse [m].4 a) d) rmse [m].4 b) error [%] 8 85 rmse [m].4 c) x [m] 9 95 Test 1 Test 2 Test 3 Figure 5.2: RMSE error of each cross-shore transect of the beach. a-c) cross-shore RMSE error for the NUB (black line) and UB (black dashed line). d) Relative error computed as x NUB x UB x UB 1.

108 Chapter 5. XBeach: Numerical modelling 88 Z [m] 2 a) 2 initial 4 target z [m].5 b) z [m].5 c) z [m].5 d) x [m] Figure 5.3: Transect elevation differences. a) Initial and target profiles. b-c-d) Differences between target elevation and final result. Dashed red line represents the differences at the eastern transect using UB. Red line represents the differences at the western transect using UB. Dashed black line represents the differences at the eastern transect using NUB. Black line represents the differences at the western transect using NUB. b) test with 1% of alongshore variability. c) test with 3% of alongshore variability. d) test with 5% of alongshore variability Sensitivity tests Since this is the first attempt to apply the model in confined bays, the model has been tested in order to verify its suitability in this type of scenario. For that, the model performance recovering a target bathymetry is tested by modifying (1) the initial bathymery, (2) the Tr free parameter and (3) the wave boundary accuracy. The target bathymetry used for the sensitivity tests was measured on March 213. At this period the beach shows a transitional state RBB-TBR (according to Wright and Short [1984] classification). The rhythmic transversal bars are almost attached to the shore. The waves break on the top of the shoreward bulges and at the shoreline edge. There is no wave breaking at the rip channels, suggesting that those are deep and well defined. Six rip channels are spotted along the beach, separated by approximately 25 m. The shoreline is rhythmic with megacusp formations. The length of the shoreline rhythmicity coincides with the length scale of transversal bars. The seaward horns of the

109 Chapter 5. XBeach: Numerical modelling 89 shoreline coincide with the landward bar bulges, while shoreline embayments coincide with the position of the rip currents. Around 5 time-averaged images (averaged over 2 minutes) were used. To guarantee that the beach state at the surveyed day and at the selected images was the same, only those video-data with a maximum of 5 days gap between the bathymetric-survey and the images were chosen. Additionally, a visual verification of the beach state (rip currents location, bar position, bar shape etc.) was done for each image. During the model implementation period (8 days), the wave components calculated at the seaward boundary of the domain show a wave energy increasing and a wave incidence angle lowering in the W-E direction (Fig. 5.4). This is consistent with the wave climate at the study site (see Chapter 2). Higher energy, with respect to the mean value, is recorded at the western part (-4 m) of the beach (Fig. 5.4). The high energy variability, may smooth the differences with respect to the mean value. The energy pivotal point is shifted towards the west, close to the center of the computed domain. Energy variability [% Energy [J/m 2 ] 3 x θp [deg] Alongshore distance [m] Figure 5.4: Alongshore boundary characteristics. Top) Wave energy alongshore variability. Centre) Mean wave energy and its standard deviation. Bottom) Mean wave incidence direction and its standard deviation.

110 Chapter 5. XBeach: Numerical modelling Results Influence of the initial bathymetry In order to quantify the influence of the initial bathymetry, three different synthetic scenarios are created. In the first test (Fig. 5.5) the model is initialized with an old bathymetry (June 212). As in March 213, there are also six rip channels, but neither the depth nor its locations are analogous to the initial bathymetry. For instance, the meandering rip (around x = 13 m) is displaced towards the East and is less pronounced. The beach presents a TBR- LTT state, with an alongshore rhythmic bar closer to the shore (wide terrace) and well developed rips. March 213 Initial bathy. (June 212) Y [m] a) Y [m] b) Uniform boundary & Tr = Non-Uniform boundary & Tr = 5 Y [m] c) Y [m] d) Uniform boundary & Tr = Non-Uniform boundary & Tr = 1 Y [m] e) f) X [m] X [m] Figure 5.5: a) Target bathymetry (March 213). b) Initial bathymetry (June 212). c) Result obtained applying UB & Tr = 5. d) Result obtained applying NUB & Tr = 5. e) Result obtained applying UB & Tr = 1. f) Result obtained applying NUB & Tr = 1. For the second test (Fig. 5.6) the model is initialized with a linear bathymetry. There is a complete absence of rips channels and bars at the surf zone. This scenario would

111 Chapter 5. XBeach: Numerical modelling 91 March 213 Initial bathy. (Linear) Y [m] a) Uniform boundary & Tr = 5 Y [m] b) Non-Uniform boundary & Tr = 5 Y [m] c) Uniform boundary & Tr = 1 3 Y [m] d) Non-Uniform boundary & Tr = 1 3 Y [m] e) X [m] f) X [m] Figure 5.6: a) Target bathymetry (March 213). b) Initial bathymetry (linear). c) Result obtained applying UB & Tr = 5. d) Result obtained applying NUB & Tr = 5. e) Result obtained applying UB & Tr = 1. f) Result obtained applying NUB & Tr = 1. represent a bathymetry just after a reset event (e.g. a bathymetry after a highly energetic storm or a series of storms). In the last case (Fig. 5.7), the bars are substituted by shoals and the shoals by bars. The initial bathymetry is the inverse situation to the solution. This situation might occur when the alongshore drift shifts laterally the bars and rips, filling the rips with a new bar and forming new rips where the previous bar-bulge was located. The results show that the model is sensitive to the initial beach morphology. However, both in test 1 and 2, the main patterns of the surf zone are recovered. The rip channels as well as the bars are placed at the correct locations. The main rip (located around x = 13 m) is well captured in both tests. On the other hand, due to the complexity of the initial bathymetry, test 3 is less accurate when representing the general morphology. Test 3, seems to reproduce the outer surf zone correctly (-4 < depth (m) -2.5) but is less accurate reproducing the inner surf zone (-2.5 < depth (m) -1). One of the

112 3 Chapter 5. XBeach: Numerical modelling 92 March 213 Initial bathy. (O pposite) Y [m] a) Y [m] b) Uniform boundary & Tr = Non-Uniform boundary & Tr = 5 Y [m] c) Y [m] d) Uniform boundary & Tr = Non-Uniform boundary & Tr = 1 Y [m] e) f) X [m] X [m] Figure 5.7: a) Target bathymetry (March 213). b) Initial bathymetry (opposite to target). c) Result obtained applying UB & Tr = 5. d) Result obtained applying NUB & Tr = 5. e) Result obtained applying UB & Tr = 1. f) Result obtained applying NUB & Tr = 1. reasons explaining such response is that, most of the images where taken at mid and low tide, due to that the waves break mostly at the outer surf zone (-4 < depth (m) -2.5), hence, more information is available at this section. In all the tests a deepening occurs close to the Eastern boundary (x = m). This is related to the image quality rather than to the model skills. The Eastern outcrop s shadow makes the wave foam intensity to be underestimated in that area Influence of the Tr free parameter Results show that the Tr parameter does not vary the capability of the model to allocate rips and bars, but it does smooth the model results. Increasing the Tr parameter the bathymetric features are less pronounced and both rights and wrongs are smoothed.

113 Chapter 5. XBeach: Numerical modelling 93 The relative errors between the model result applying default values (UB and Tr = 5) and modified values are shown in Fig Low Tr values (5 days) perform better at the surf zone (-4 < depth (m) -1) where the RMSE errors are 4% to 23% lower, while high values (1 days) of Tr perform better at the shoaling zone (depth (m) -4) where the RMSE errors are.2% to 7.7% lower. This is consistent with the theory that surf zone morphological changes have lower temporal scales than the shoaling zone. 3 Unif. bound. Tr = 1 Non Unif. bound. Tr = 5 Non Unif. bound. Tr = error [%] Entire domain Shoaling zone Surf zone Figure 5.8: Relative errors obtained at the different simulations with respect to the default values (UB and Tr = 5). Square marks represent the tests performed with June 212 bathymetry as initial bathymetry. Circle marks represent the tests performed with Linear bathymetry as initial bathymetry. Triangle marks represent the tests performed with Opposite bathymetry as initial bathymetry. The surf zone represents the area where: -4 < depth (m) -1. The shoaling zone represents the area where: depth (m) Influence of the wave forcing accuracy As stated before, the model is forced by wave roller dissipation (closely related to the wave characteristics) maps only, thus, the alongshore wave variability should have an impact in the model results. The cross-shore RMSE error calculated along the whole beach is shown in Fig The registered errors are in the range of m at the surf zone (Fig. 5.9). Higher RMSE values are recorded using opposite bathymetry as initial bathymetry. The RMSE values show an irregular fluctuation, related to the complexity of the beach alongshore features. Taking into account the alongshore wave energy pattern (Fig. 5.4), the same RMSE values (for UB and NUB methods) would be expected at the center part of the beach

114 Chapter 5. XBeach: Numerical modelling 94 and an error improvement (using NUB method) at both ends of it. Instead, NUB tests show less error than UB at the westernmost and central part (-1m) and similar error at the easternmost section of the site (1-18m). The differences between both methods reside only in the depth levels and not in the location of bars and shoals. The NUB method perform better both in the shoaling and surf zone (Fig. 5.8 and Fig. 5.9). RMSE [m] initial rmse UB Tr = 5 NUB Tr = 5 UB Tr = 1 NUB Tr = 1 Initial bathy. (June 212) Initial bathy. (Linear) RMSE [m] Initial bathy. (Opposite) RMSE [m] X [m] Figure 5.9: RMSE error of each cross-shore transect of the beach along the surf zone (-4 < depth (m) -1) Discussion and conclusions The relevance of (1) the initial bathymetry, (2) the Tr free parameter and (3) the wave forcing input accuracy, is tested Initial bathymetry The initial bathymetry shape, may affect the final model result. However, it can be inferred from the previous analysis that it could be compensated using a wide range of wave conditions and tidal levels. For example, the model obtains similar results when starting from a linear bathymetry (initial RMSE of 1.3 m), with no rip channels and bars, than starting with an outdated bathymetry (initial RMSE of.55 m) similar to the target bathymetry. This means that, despite of a large initial difference with respect to the target bathymetry, a good result can be achieved. On other hand, the model

115 Chapter 5. XBeach: Numerical modelling 95 performs better starting from an outdated bathymetry (initial RMSE of.55 m) or linear bathymetry (initial RMSE of 1.3 m), than starting with an opposite bathymetry (initial RMSE of 1.3 m). However, for this particular case it can be argued that the tidal range is not wide enough to update the inner surf zone properly. In conclusion, the initial bathymetry may affect the model results; but, it should not be a problem, provided that the images that are available cover a wide range of wave conditions and water levels. Yet, it might be difficult to obtain such range of conditions during a short period time Tr parameter The value of Tr parameter affects the final result. Changes in the depth level are observed but the main features of the final bathymetry are preserved. This value should be tuned according to the wave climate of the study site. For example, the expected value at an embayed beach (less exposed) would be greater than for an open beach in an area with similar offshore conditions. Moreover, the Tr should be variable throughout the study domain. It is well established that the morphological response time scale differs along the beach (surf zone, shoaling zone, swash zone etc.), hence, it should be consistent with this fact. Finally, if the study site presents a significant alongshore variability (both in morphology and in wave conditions), this value should also be consistent. The Tr fitting could be performed by either carrying out a field campaign, where the morphological change rates with respect to the beach zone and wave conditions are analysed or by a obtaining a general value from the literature Wave forcing accuracy Two different set of tests were carried out. Boundary adaptation performance: The synthetic test cases prove that Beach Wizard coupled to the NUB-XBeach works properly. Three tests with 1%, 3% and 5% of wave height alongshore variability imposed at the boundary were set. Using the UB method, the cross-shore transects RMSE errors are higher (O (.1m),O (.3m),O (.5m) for test a, test b and test c respectively) than using the NUB method (O (<.2m)). Furthermore, the errors related to NUB method are related to the finite length of the simulation and to the intrinsic errors implemented in the model (ε d = 15% of the maximum value at each image).

116 Chapter 5. XBeach: Numerical modelling 96 The differences along the cross-shore profile show the biggest errors located at the most likely breaking points (shoreline and bar). Even though changes in depth level are observed, the shape of the bathymetry is preserved. Therefore, no bar/through shift would expect when alongshore averaged boundary conditions are used. Sensitivity tests: The model shows a better performance using alongshore nonuniform boundary conditions (NUB) than using an averaged value (UB). However, the RMSE differences between both methods do not reproduce the improvement level seen in the synthetic cases. Some possible reasons which could explain such response are stated in the following: a) Time evolution of the alongshore variability: Although alongshore variability is present at the beach, it is not constant throughout the time. It may switch between periods of quasi-uniform to alongshore variable conditions. This situation may smooth the differences between both methods. b) Importance of the image colour : Roller imap quality is dependent on the image quality. Any anomaly in the image, such as sun glint, shadows, sea colour variability etc. will have an effect on the model result. Although the images are pre-processed (in order to avoid contrast shifts between the images that conform the rectified image) and handmade selected (in order to avoid any kind of image aberration), it does not ensure a perfect match between the derived roller map and the real one. c) Image resolution: Resolution of the rectified images decreases from W to E. This resolution lowering may have consequences when relating the pixel intensities with the corresponding bathymetric points. d) Alongshore RMSE error shift: Looking at the wave energy alongshore variability configuration, it would be expected a similar model performance (regarding both methods) at the centre of the beach and some differences at both ends. On the contrary, the model improvement is seen at mid and western section of the beach and none at the rest of the domain. There is also a wave direction alongshore variability that might alter the result. The variability at the boundary, may be transformed by the time that the waves reach the surfzone, so, the mean value would not coincide at the centre of the beach but at some point displaced from there. Because of that the improvement would be shifted according to the wave direction pattern. In addition, the errors might be diminished by adding multiple sources (celerity maps and intertidal bathymetries) to the data assimilation model, or/and, including more efficient techniques to isolate the active roller foam (Carini [214]) or/and applying another type

117 Chapter 5. XBeach: Numerical modelling 97 of image smoothing techniques (e.g. Brown and Lowe [27]; Grundland and Dodgson [25]). In summary, the relevance of using a set of images with a wide range of wave and tidal conditions is highlighted. The use of accurate wave boundary input it is also important. Finally, the Tr parameter should be tuned. In complex beaches, a pre-study of the wave climate might be necessary to know the wave alongshore variability. 5.5 Model calibration In order to calibrate the model, the series of storms recorded between the 1 st and the 14 th of February 213 were modelled. The dataset used for the model calibration was composed by pre/post-storm profiles, sediment granulometry and wave energy spectra at Zarutz seaward boundary. The lack of a pre-storm bathymetry forced the use of the XBeach-Beach Wizard model (explained in Section 5.4) to obtain the initial bathymetry (1 st of February 213) Offshore boundary conditions During the 1 st and 14 th of February, a sequence of three storms was recorded (see Fig. 5.1 and Table 5.1). The first storm of the sequence was the less energetic (in terms of storm power) and short in duration. The second storm was the most energetic, it lasted 85 hours and maximum wave heights (H max ) of 6.3 m were recorded coinciding with a wave peak period (T p ) of 17.2 sec. The last storm presented wave heights almost as high as in the second storm (H max = 5.9 m), but it coincided with shorted peak period (T p = 12.9 sec) and it lasted 59 hours. The tidal range during the storm sequence evolved from neap to spring tide. A total of 323 hours ( 14 days) were simulated. The model wave boundary was forced by wave spectra obtained from the hybrid wave propagation model (see Section 2.4.1). Table 5.1: Characteristics of February 213 storms at the seaward boundary of Zarautz Storm H max [m] T p [sec] θ p [deg] duration [hours] Storm power [Mwhm 1] Storm Storm Storm

118 Chapter 5. XBeach: Numerical modelling 98 Hs [m] 5 storm 1 storm 2 storm Tp [sec] θp [sec] η [m] Time [days] Figure 5.1: Sequence of storms during the 1 st and 14 th of February at the seaward boundary of the study site. Storms are highlighted by red lines Model grid and bathymetry A total of 7 images were processed using the XBeach-Beach wizard to obtain the bathymetry of the 1 st of February. The initial bathymetry was an old bathymetry measured in June 212. A Tr parameter equal to 5 days was chosen since in Section 5.4 has been demonstrated to perform better at the surf zone (relevant for the wave breaking and rip current development). The seaward boundary of the model was chosen as an alongshore non uniform boundary. In Fig the grid set up and the initial bathymetry is displayed. It can be seen that the beach is slightly rotated (1 deg) to avoid the inclination of the shoreline with respect to the boundaries. The location of the dune and seawalled zone is divided by a black dashed line located at around x = 139m. The seawall height varies along the beach. From x = m it is about 7.5 m above the mean sea water level while in the rest of the beach it is 4.5 m. At the bottom of the Fig the grid spacing in the cross-shore direction is displayed. At the offshore wave boundary x is largest (2 m). In the landward direction x decreases to a minimum of x = 4 m at the water line. The grid spacing in the y direction has a constant value of 1 m. The lateral boundaries are modelled as frictionless, impermeable walls. An absorbinggenerating boundary condition is applied at the seaward model boundary (Van Dongeren and Svendsen [1997]). This kind of boundary allows outgoing waves to leave the model domain and prevent them of being reflected back into the model.

119 Chapter 5. XBeach: Numerical modelling 99 y [m] z [m] x [m] x [m] y [m] Figure 5.11: Computational grid. Top) The computational grid including the bottom elevation. Black dashed line indicates the transition from engineered (left side) to natural zone (right side). Bottom) Grid spacing in the cross-shore axis. The input of the model boundary consist of a series of computed variance spectrum. Then XBeach uses the variance spectrum to construct a short wave envelope following Van Dongeren et al. [23] procedure Calibration parameters Model parameters XBeach presents a number of free parameters related to physical processes in it (i.e. hydrodynamics, sediment transport, and morphology, among others). However, it also presents some parameters that directly influence the morphodynamic evolution and are less obvious (Van Thiel de Vries [29]). Due to the large amount of parameters encountered in the model the calibration of all of them is not feasible. Only the parameters which have shown to be relevant (after preliminary test) as well as those mentioned in the literature are considered. These parameters are summarised as follows:

120 Chapter 5. XBeach: Numerical modelling 1 form: Defines the sediment transport equation applied by the model. During the preliminary tests it appeared to play an important role on the beach response. In the present case the formulation of Van Thiel de Vries [29] (eq. 5.34) was chosen: C eq = A sb h ( ) 1.5 (u E ) u 2 rms,2 u A ( ) 2.4 ss cr + (u h E ) u 2 rms,2 u cr (5.34) where u E is the Eulerian mean velocity, u rms the near-bed, short-wave orbital velocity, u cr is a critical velocity for the initiation of sediment motion, h is the water depth, and A sb and A ss are bed and suspended load coefficients, respectively, and are both functions of the sediment grain size and relative density, and of the local water depth. eps: Threshold depth for drying and flooding. It determines whether points are dry or wet. facua (γ ua ): Determines the wave asymmetry and skewness contribution in the sediment advection velocity. Zero value corresponds to absence of onshore sediment transport due to wave asymmetry and skewness. γ: Wave breaking parameter. h min : Threshold water above which Stokes drift is included. swrunup: Short wave run up. wetslp: Critical avalanching slope under water. dryslp: Critical avalanching slope above water. Preliminary tests suggest that the engineered zone is prone to show larger discrepancies (with respect to the real values) than the natural zone. In order to improve the model performance in this section of the beach, a series of 1D calibration tests were undertaken. For this purpose, the 4 th profile was selected (Chapter 4 - Fig. 4.1), since it is located at the centre of the engineered zone and hence it should be representative of this section. Fig shows the 1D tests with varying eps values. The values allowed by the model range between It is shown that lower values give less accurate results. The lower is the eps value the greater is the erosion of the profile. This is a consequence of the water layer inundating a wider portion of the profile, hence, eroding it by the effect of the return flow. All the sections of the profile follow the same response pattern (in terms of RMSE).

121 Chapter 5. XBeach: Numerical modelling 11 Depth [m] Pre storm Post storm eps =.1 eps =.5 eps = x [m] RMSE [m] Entire profile LWL profile HWL profile DWL profile eps [m] Figure 5.12: 1D eps parameter calibration. Top) Profile response to different parameter values. Horizontal dashed blue lines represent the mean water level and the high water level. Bottom) RMSE error values for different sections of the profile (LWL = from low tidal level to mean tidal level; HWL = from mean tidal level to high tidal level; DWL = from high tidal level to top of the profile) and for different parameter values. Vertical dashed black line indicates the model default value. Depth [m] Pre storm Post storm γ ua = γ ua =.15 γ ua =.25 2 x [m] RMSE [m] Entire profile LWL profile HWL profile DWL profile γua Figure 5.13: 1D γ ua parameter calibration. Top) Profile response to different parameter values. Horizontal dashed blue lines represent the mean water level and the high water level. Bottom) RMSE error values for different sections of the profile (LWL = from low tidal level to mean tidal level; HWL = from mean tidal level to high tidal level; DWL = from high tidal level to top of the profile) and for different parameter values. Vertical dashed black line indicates the model default value. Fig shows the 1D tests with varying γ ua values. The values allowed by the model range between -1. It is shown that higher values (greater onshore sediment transport

122 Chapter 5. XBeach: Numerical modelling 12 Depth [m] Pre storm Post storm γ =.25 γ =.45 γ = x [m] RMSE [m] Entire profile LWL profile HWL profile DWL profile γ Figure 5.14: 1D γ parameter calibration. Top) Profile response to different parameter values. Horizontal dashed blue lines represent the mean water level and the high water level. Bottom) RMSE error values for different sections of the profile (LWL: from low tidal level to mean tidal level; HWL: from mean tidal level to high tidal level; DWL: from high tidal level to top of the profile) and for different parameter values. Vertical dashed black line indicates the model default value. Depth [m] Pre storm Post storm h min =.1 h min =.4 h min = x [m] RMSE [m] Entire profile LWL profile HWL profile DWL profile hmin [m] Figure 5.15: 1D h min parameter calibration. Top) Profile response to different parameter values. Horizontal dashed blue lines represent the mean water level and the high water level. Bottom) RMSE error values for different sections of the profile (LWL: from low tidal level to mean tidal level; HWL: from mean tidal level to high tidal level; DWL: from high tidal level to top of the profile) and for different parameter values. Vertical dashed black line indicates the model default value. allowed) give less accurate results mainly at the dry and upper part of the profile. The lower the γ ua values is the greater is the erosion of the upper part of the profile. The

123 Chapter 5. XBeach: Numerical modelling 13 Depth [m] Pre storm Post storm swr = OFF swr = ON x [m] RMSE [m] Entire profile LWL profile HWL profile DWL profile 1 swr Figure 5.16: 1D short wave run-up parameter calibration. Top) Profile response to different parameter values. Horizontal dashed blue lines represent the mean water level and the high water level. Bottom) RMSE error values for different sections of the profile (LWL: from low tidal level to mean tidal level; HWL: from mean tidal level to high tidal level; DWL: from high tidal level to top of the profile) and for different parameter values. Vertical dashed black line indicates the model default value. role of the parameter is different for the different sections of the profile. In fact, the overall impact on the whole profile and on the lower part of the profile is low. Fig shows the 1D tests with varying γ values. The values allowed by the model range between.4-.9 (here modified to test a wider range of values.25-.6). It is shown that high and low values give less accurate results, it can be seen an inflexion point around The lower (larger) the γ is the greater (lesser) is the wave dissipation and the lower (greater) is the profile erosion. Fig shows the 1D tests with varying h min values. The values allowed by the model range between.1-1. It is shown that high values give more accurate results. Higher values, limit the stokes drift onshore mass transport and hence limits the correspondent return flow (which limits also the erosion). Fig shows the 1D tests with short wave run up activated/deactivated. It is shown that deactivating the short wave run up give more accurate results. Activating the short wave run up allows the water layer to reach upper zones of the beach. The erosion of the upper part of the profile is then overestimated. The preliminary 1D tests help to know the sensitivity of the model to the different parameters and to deduce the approximate range in which the optimal values are. Furthermore, the exact value for the on/off parameters can be deduced. This step helps

124 Chapter 5. XBeach: Numerical modelling 14 to save computing time for the following 2D cases. Regarding 2D cases, 24 tests were made combining different values of the following parameters (γ, γ ua, wetslp, dryslp). RMSE [m] S RMSE [m] S RMSE [m] S RMSE [m] ENT.45.5 γ γ ua.2.3 wetslp.9 1 dryslp Figure 5.17: 2D calibration. Prefix S, correspond to the different sectors of the beach. Each boxplot (in a given subplot) represents RMSE error values for different sections of the profile (left: entire profile; centre: from mean tidal level to top of the profile; right: from low tidal level to mean tidal level). Fig shows that the response of the beach to a given set of parameters depends mainly on the area of the beach that is being analysed. This indicates that there is no optimal parameter set-up that suits along the whole domain. However, the comparison between real and computed profiles reveal (Fig. 5.18) that the results are accurate enough to conclude the calibration phase. γ: Low γ values (.45) seem to perform better both along the entire beach and along the different sections of the profile. γ ua : It is not possible to obtain a unique value that satisfies equally the fitting of the model to the different sections of the profile. The same behaviour is seen in the 1D case, were a better performance in the upper part of the profiles means a poorer

125 Chapter 5. XBeach: Numerical modelling 15 1 Profile 2 1 Profile 6 1 Profile 9 1 Profile z [m] Pre storm Post storm Computed Depth [m] Cross-shore distance [m] 2 1 Cross-shore distance [m] 2 1 Cross-shore distance [m] 2 1 Cross-shore distance [m] Figure 5.18: Calibrated profiles. Top) Differences in elevation between computed and measured profiles. Bottom) Measured and computed profiles. result is the lower part. It shows that a complete lack of onshore transport due to wave asymmetry and skewness benefits the fitting of the profile bellow the mean water level whereas the presence of it favours the region above the mean water level. wetslp: The RMSE errors associated to this parameter vary depending on the profile section. A value of.2 presents higher adjustment level at the lower profile. In contrast, in the upper profile it appears to be independent of the wetslp value. This is because the parameter is only active when the cells are flooded. dryslp: This parameter is designed to work at dune and backshore areas. One could expect a different impact of the parameter depending on the sector of the beach. Surprisingly, the relevance of it seems to be low both on the different sectors of the beach and at the different sections of the profile. This suggests that it is a stable parameter or that the range of values used is too low to detect significant changes.

126 Chapter 5. XBeach: Numerical modelling Wave spectra parameters It is well known that wave groups are relevant regarding the formation of long waves. The wave group forced long waves are later released by the wave breaking in the surf zone. Those free long waves generate the ups and downs of the water layer along the beach. The formation of wave groups strongly depends on the wave spectral shape (i.e. sea state) (Van Der Meer and Hydraulics [1988]). Narrow banded sea states (swells) are characterised by the formation of well developed groups. Radiation stress gradients are large and the bounded long waves too. On the contrary, broad banded sea states have their energy widespread along a wider range of frequencies and directions. The interaction between the wave components lead to less marked wave groups, hence, lower radiation stress gradients and smaller long waves are formed. Because of that, one would expect different hydro/morphodynamic response of the beach when it is forced by different type of sea states. The model has been tested running three types of Jonswap spectra: Type a: Jonswap spetra with γ = 3.3 and n = 1. Type b: Jonswap spetra with γ = variable (fitted to computed spectra) and n = 1. Type c: Jonswap spetra with γ = variable (fitted to computed spectra) and n = variable (fitted to computed spectra). Fig shows the RMSE errors if the calibration storm (Section 5.5.1) is forced by different type of spectra. It is revealed that using a parametric spectrum the model is able to reproduce the beach response with the same order of accuracy as it does with the computed spectrum (more realistic). When comparing the errors obtained using computed spectra and parametric spectra (Fig. 5.2) it can be seen that overall the errors are lower when using the computed spectra; although sector three is an exception. Note that the model output does not improve if the Jonswap spectra parameters are fitted to a more realistic spectrum. Since the errors of the computed spectra and the parametric spectra seems not to differ drastically, four extra tests are carried out in order to measure the sensitivity of the model to frequency and directional spreading. The test consists in running 6 hours of a high energetic event (H rms = 5 m and T p = 15 sec) at a fixed tidal level with four types of spectra.

127 Chapter 5. XBeach: Numerical modelling 17 RMSE [m].4.2 Jons.a Jons.b Jons.c Comp. S1 RMSE [m].4.2 Jons.a Jons.b Jons.c Comp. S2 RMSE [m].4.2 Jons.a Jons.b Jons.c Comp. S3 RMSE [m].4.2 Jons.a Jons.b Jons.c Comp. ENT Figure 5.19: 2D calibration. Wave spectral shape relevance. Prefix S, correspond to the different sectors of the beach. Each boxplot (in a given subplot) represents RMSE error values for different sections of the profile (left: entire profile; centre: from mean tidal level to top of the profile; right: from low tidal level to mean tidal level). Type 1: Jonswap spetra with γ = 1 and n = 5. Type 2: Jonswap spetra with γ = 5 and n = 5. Type 3: Jonswap spetra with γ = 1 and n = 15. Type 4: Jonswap spetra with γ = 5 and n = 15. Fig shows that a higher dune portion is eroded when applying a narrow directional spectrum. The differences (in volume eroded) between narrow band spectra (T4) and mixed spectra (T3) results in a 6% difference, whereas the differences with respect to (T2) are of 3%. This explains the higher differences in RMSE errors recorded applying n variable. Previous authors have reported similar results, linking the spreading effect to hydrodynamic responses (Battjes [1972]; Feddersen [24]). The most reasonable way to understand the physics driving such response relies in the nearshore water level fluctuations. Wave radiation stress gradients drive alongshore

128 Chapter 5. XBeach: Numerical modelling Jons. γ = 3.3, n = 1 Jons. γ = var, n = 1 Jons. γ = var, n = var 15 error [%] S.1 S.2 S.3 ENT Figure 5.2: Wave spectral shape relevance. RMSE error comparison RMSE n RMSE c RMSE c 1. currents in the surf zone and lead to shoreline set-up (Longuet-Higgins and Stewart [1964]; Bowen et al. [1968]; Longuet-Higgins [197]). Since the set-up is dominated by S xx radiation stress component (cross shore), a narrow band spectrum related S xx may over or underestimate a broad band related S xx, resulting in a larger fluctuation of the water level at the shoreline. An overestimation of the set-up means that more waves reach the dune toe and backshore and as a result higher erosion rates are expected in those sections. Feddersen [24] clarifies the reasons of why narrow-band spectra overestimate the true radiation stress components in 8-m water depth on the Outer Banks, NC. He suggests that frequency spread is not the cause of the observed overestimations and demonstrates that the observed difference between the true and narrow-band radiation stresses is due to directional spread of the incident wave field.

129 Chapter 5. XBeach: Numerical modelling 19 V [m 3 /m] 5 1 T1: γ = 1, n = 5 T2: γ = 5, n = 5 T3: γ = 1, n = 15 T4: γ = 5, n = time [hours] Elevation [m] Initial T1: γ = 1, n = 5 T2: γ = 5, n = 5 T3: γ = 1, n = 15 T4: γ = 5, n = x [m] Figure 5.21: Wave spectral shape relevance. Top) Profile volume erosion during 6 hours simulation. Bottom) Profile response to different spectral shapes Conclusions In summary, the calibration step highlights the need of a preliminary test before any simulation is performed. Parameters such as short wave run-up, γ ua, γ, eps and h min seem to be relevant for the model calibration. Some parameters do not have physical meaning ( eps and h min ), so it is difficult to have a first guess of the value to use. However, perform some 1D test cases together with a literature review should be enough to obtain the desired value. Despite that 2D cases take longer computational time, these tests are relevant for the model calibration in cases where the beach alongshore nature is non-uniform. The result reveals that the model skill varies depending on the zone of the beach (dune section, seawalled section). There is no optimal parameter set that satisfies a perfect model result, however it can be found a suitable combination that leads to a reasonable calibration output.

130 Chapter 5. XBeach: Numerical modelling 11 The most relevant beach response detected is the overestimation of the erosion of upper part of the profile (at the engineered section) and the incorrect location of the pivotal point. Regarding the spectral parameter calibration, if the real spectrum is used, an error improvement of 25-5 % is detected in the engineered zone; however at the natural section the error is lower using a parametric spectrum ( 1-5 %). The model is more sensitive to the variation of the directional width than the frequency width. 5.6 Storm impact simulations The aim of the following section is to understand the morphodynamic response of the beach (intertidal zone, backshore and dunes) due to the storm impact and the role of the storm characteristics. First, the response of the beach to the February 213 storm (see Section for more detail) is analysed and then, some modifications in the hydrodynamic forcing are implemented. In Section 5.6.1, the objective is twofold. On one hand the relevance of the tidal evolution on the beach response is addressed and on the other hand, the impact of the storm cluster sequence order on the beach response is going to be studied. In Section the impact of each storm of the storm cluster is analysed separately. Finally, in Section 5.6.3, some synthetic storm scenarios are designed in order to know the relevance of the storm power magnitude in the beach erosion and to better understand the role of the parameters that conform a storm on the beach response Storm of February 213: Hydrodynamic forcing variations Two tests were designed to study the tidal and the storm cluster sequence order relevance on the beach response. In the first scenario, the tide signal was inverted whereas in the second scenario the wave conditions (H s, T p, θ) were inverted. The description of the beach response was performed by analysing the volumetric changes at the intertidal zone, backshore and dunes (Fig. 5.22). This was done for the engineered and the natural sections separately. Storm - Real case: Fig shows the beach volumetric evolution when it is forced by the real storm. The volumes shown in the graph are relative volumes ( V ol n V ol 1 V ol 1 1 ).

131 Chapter 5. XBeach: Numerical modelling 111 Figure 5.22: Scheme of volume estimation for the different sections of the beach. By the end of the simulation, the intertidal zone, backshore and dune sections are affected. At the dune zone and backshore only loss of sand is recorded. The intertidal zone combines stages of gain and loss of sand. The intertidal and backshore zones show similar tendency both at the natural and engineered sectors of the beach. During the first six days, there is a gradual but mild loss of sand along the intertidal zone. During these days the backshore is barely affected (coinciding with the peak of the storm). There is an inflexion point at the peak of the second storm (day 6), where the rate of change starts to increase at the backshore and intertidal sections, but following opposite responses. Between days 9 to 11 the tidal range starts to increase and despite the absence of any storm, the backshore and intertidal parts continue evolving. This points out that a H s value lower than the threshold H s (defining an energetic event) may also cause changes on the beach. From day 11 to the end of the sequence three erosive events are recorded at the dune zone coinciding with the third storm and spring tide. Note that the backshore at both sections of the beach is highly eroded ( -8 %). During this period the intertidal zone of the engineered section remains stable on contrary to the natural section where the intertidal zone gains sediment (at low rate).

132 Chapter 5. XBeach: Numerical modelling 112 η & Hs [m] 6 4 storm 1 storm 2 storm A Rel. vol. [%] 1 INT Rel. vol. [%] BACK. Rel. vol. [%] DUNE Time [days] Figure 5.23: Volumetric beach changes due to Real storm impact. A) H s and tidal level (η). Blue line indicates H s, red line highlights the storm presence and black line indicates tidal elevation. INT) Intertidal volume evolution. BACK) Backshore volume evolution. DUNE) Dune volume evolution. Dashed black line refers to the natural section and the solid black line to the engineered sector. Storm - Tide inverted case: Fig shows the volumetric evolution when it is forced by the tide inverted storm. The volumes shown in the graph are relative volumes ( V ol n V ol 1 V ol 1 1 ). To study the tidal relevance on the beach response the tidal signal is inverted maintaining the rest of the parameters as in the real case. From days 1 to 7 spring tide prevails. The backshore is eroded while the intertidal zone follows the opposite trend. During these days the erosion (deposition) rate at the backshore (intertidal zone) varies, presenting lower rates when there is no storm (day 3 to 5). From the end of the second storm (day 9) to the end of the record, the intertidal zone at the engineered section diminishes while at the natural sections maintains its volume. On the other hand the backshore remains constant during days 9 to 12 (neap tide) and present changes from the peak of the third storm on (transition to spring tide). The dune zone records three erosive events. These events are of smaller order to those recorded during the real case. As in the real case, the dune is affected when the backshore is highly eroded ( -8 %).

133 Chapter 5. XBeach: Numerical modelling 113 η & Hs [m] 6 4 storm 1 storm 2 storm A Rel. vol. [%] 1 INT Rel. vol. [%] BACK. Rel. vol. [%] DUNE Time [days] Figure 5.24: Volumetric beach changes due to tide inverted storm impact. A) H s and tidal level (η). Blue line indicates H s, red line highlights the storm presence and black line indicates tidal elevation. Grey line represents the real storm characteristics and evolution. INT) Intertidal volume evolution. BACK) Backshore volume evolution. DUNE) Dune volume evolution. Dashed black line refers to the natural section and the solid black line to the engineered sector. Storm - Wave inverted case: Fig shows the volumetric evolution when it is forced by the wave inverted storm. The volumes shown in the graph are relative volumes ( V ol n V ol 1 V ol 1 1 ). To study the wave storm order relevance on the beach response, the wave characteristics are inverted maintaining the tidal signal as in the real case. Both natural and engineered sectors follow similar trends. A gradual loss of sand takes place at the intertidal zone during the first eight days (neap tide). backshore presents a series of sequential erosive events during this time coinciding with the peak of the first storm (day 4 to 5). The A rapid loss (gain) of sand is recorded at the backshore (intertidal zone) from days 8 to 11, which coincides with the second storm and the transition to a larger tidal range. From the end of the second storm to the end of the record no major changes are recorded at the intertidal zone and backshore, despite the presence of the third and last storm. On the other hand, the dune area is only affected by the presence of the third

134 Chapter 5. XBeach: Numerical modelling 114 storm between days 13 to the end of the sequence coinciding with a highly eroded backshore (as occurred in previous cases). η & Hs [m] 6 4 storm 1 storm 2 storm A Rel. vol. [%] 1 INT Rel. vol. [%] BACK. Rel. vol. [%] DUNE Time [days] Figure 5.25: Volumetric beach changes due to wave inverted storm impact. A) H s and tidal level (η). Blue line indicates H s, red line highlights the storm presence and black line indicates tidal elevation. Grey line represents the real storm characteristics and evolution. INT) Intertidal volume evolution. BACK) Backshore volume evolution. DUNE) Dune volume evolution. Dashed black line refers to the natural section and the solid black line to the engineered sector Discussion and conclusions Changes at the engineered and natural sectors occur at the same time and following almost the same trend (loss or gain). However, by the end of the record, the engineered zone loses more volume (in relation to its initial volume) than the natural zone. Volumetric changes occur both during storms and between storms. The selected storm definition is indicative of an extreme event and ensures a change on the beach; however a lower storm threshold may also produce erosion/accretion of the different parts of the beach. Fig represent the relative differences ( V ol synthetic V ol real V ol real 1 ) between the real test and the modified tests for the different zones (intertidal, backshore, dune) and compartments (engineered, natural) of the beach. During the synthetic tests, the total

135 Chapter 5. XBeach: Numerical modelling 115 energy is conserved, however the order of the wave sequence (energy sequence) or the water level at what this energy reaches the coast is modified. 15 INT. V [%] BACK. V [%] DUNE V [%] Time [days] Figure 5.26: Relative volumetric differences between real storm and tide inverted storm (black lines) and between real storm and wave inverted storm (red lines). Solid lines indicate engineered sector and dashed lines indicate natural sector. Table 5.2: Relative differences at the end of the simulation for the tide inverted and wave inverted tests Tide inv. Wave inv. Intertidal Backshore Dune eng x nat eng x nat The final beach response is different in all the tests. Hence, the same energy distributed in a different way or reaching the coast at a different water level may have different consequences on the beach. This is more obvious for the tide inverted case (black lines in Fig. 5.26). It is seen that the volume differences fluctuate between positive and negative values. A rapid difference increase is recorded between days 1 to 6 which is only forced by the tidal effect. The maximum differences are spotted between days 6 to 9, coinciding with the second storm. Note that if the wave conditions are inverted (red lines in Fig. 5.26) the beach barely changes during the first 6 days (which coincide

136 Chapter 5. XBeach: Numerical modelling 116 Storm Real Storm Tide inverted Storm Wave inverted V (int.) [m 3 ] V (back.) [m 3 ] V (back.) [m 3 ] V (back.) [m 3 ] V (back.) [m 3 ] V (dune)[m 3 ] V (dune)[m 3 ] V (dune) [m 3 ] Figure 5.27: Volume interchange between intertidal and backshore (top panels) and between dune and backshore (bottom panels). Blue dots refer to natural section and red dots refer to engineered sector. of a period of neap tide). By the end of the simulation the differences are greater for the tide inverted case than for the wave inverted case (Table 5.2). These tests highlight the relevance of the water level on the beach response. The finding is consistent with Splinter et al. [214], in their work observed that storm sequencing did not significantly impact the total erosion volumes. Fig demonstrates the interconnection of the beach cross-shore sections (intertidal, backshore, dune). The time scales at which the backshore and intertidal zones are active are similar. On the contrary, dune area is occasionally active and it seems to be dependent on the grade of erosion of the backshore. The erosion accretion trends occurred at the backshore and dune area, are opposed to that happening at the intertidal zone. The opposite behaviour between the backshore and intertidal zones suggests that loss of sand at upper part of the beach acts as a buffer of the intertidal zone. Knowing this behaviour the same logic could be applied to the dune and backshore interaction. However this mechanism is not so evident. The erosion of the dune does not produce

137 Chapter 5. XBeach: Numerical modelling 117 V [m 3 ] V [m 3 ] Storm Real Storm Tide inverted Storm Wave inverted INT. BACK. V [m 3 ] DUNE P [Mwm 1] P [Mwm 1] P [Mwm 1] Figure 5.28: Wave power effect on the erosion/accretion patterns. INT) Intertidal zone. BACK) Backshore zone. DUNE) Dune zone. Blue dots refer to natural section and red dots refer to engineered sector. always the accretion of the backshore, but it may reduce the erosion of backshore and intertidal zones. The erosion trend shape ( stairs ) together with the temporal scales at which those events take place suggest that there must be a link to a certain process occurring at the same time intervals. Fig shows the relation between the wave power and erosion deposition trends of the intertidal, backshore and dune zones. It can be seen that the different parts of the beach are accreted and eroded both during low powered events and during high powered events. Fig shows the relation between tidal elevation and erosion deposition trends of the intertidal, backshore and dune zones. It is shown that intertidal erosion occurs at low tide while accretion takes place at high tide, on contrary the backshore is eroded and accreted at high tide. Dune zone, only presents erosive events occurring at high tide.

138 Chapter 5. XBeach: Numerical modelling 118 V [m 3 ] Storm Real Storm Tide inverted Storm Wave inverted INT. V [m 3 ] BACK. V [m 3 ] DUNE η [m] η [m] η [m] Figure 5.29: Tidal effect on the erosion/accretion patterns. INT) Intertidal zone. BACK) Backshore zone. DUNE) Dune zone. Blue dots refer to natural section and red dots refer to engineered sector Storm of February 213: Single storm/storm cluster In the previous section the effect of the three storms acting as a single storm (or storm cluster) was studied. In the present section the impact of each storm separately is analysed and then it is compared to the storm group impact. This allows the study of the impact of each storm acting separately, to compare the response of the beach to the storm cluster effect and to infer the initial bathymetry influence on the storm impact. Fig. 5.3 shows the evolution of the different zones of the beach (intertidal zone, backshore and dunes) for a situation in which the storms behave as stand-alone storms and in a situation in which the storms behave as a group of storms (storm cluster). Each stand-alone storm is forced by the same initial bathymetry, which corresponds to the initial bathymetry used for all the previous simulations (see Section for explanation). During the first storm, the differences of the volume evolution between stand-alone and grouped solution are minimal (maximum difference of 1.7 % at the backshore of the natural section). This is because the time gap between the beginning of the

139 Chapter 5. XBeach: Numerical modelling 119 η & Hs [m] Rel. vol. [%] Rel. vol. [%] Rel. vol. [%] storm 1 storm 2 storm Time [days] 1 INT. Storm Storm Storm Tim e [hours] Storm Storm Storm Tim e [hours] Storm Storm Storm Tim e [hours] Figure 5.3: Volumetric beach changes due to storm cluster and stand-alone storm impact. A) H s and tidal level (η). Blue line indicates H s, red line indicates storm presence and black line indicates tidal level. INT) Intertidal volume evolution. DRY) Backshore volume evolution. DUNE) Dune volume evolution. Dashed line refers to the natural section and the solid line to the engineered sector. Black line refers to storm cluster whereas red line refers to stand-alone storm. A BACK. DUNE. grouped simulation and the starting point of the first storm is short (less than 24 hours); the wave conditions during this period are low energetic, hence the beach does not evolve significantly. This means that the initial bathymetry when the first storm is taking place is the same for the stand-alone and grouped tests. During the second storm the differences between stand-alone and grouped solution increase compared to the first test (maximum difference of 6.9 % at the backshore of the natural section). The shape and the temporal scales at which the different sections are eroded/accreted are similar. Larger erosion (accretion) is seen at the backshore (intertidal zone) when running the storm using the grouped approach than using the stand-alone approach. The last storm, presents the largest differences (compared to the previous two storms) between the stand-alone and the grouped solution. Once again, the shape and the temporal scales at which the different sections are eroded/accreted are similar. Note that the differences at the backshore between the engineered and natural sections follow a similar trend both at stand-alone and grouped tests. This is not the case at the intertidal zone. In this section the response of the stand-alone storm and the grouped

140 Chapter 5. XBeach: Numerical modelling 12.5 storm group stand alone V [%] Figure 5.31: Storm 1 Storm 2 Storm 3 Relative volumetric differences between grouped and stand-alone bathymetries after storm 1, 2 y 3. storm shows a clear different response if compared to storm 1 and 2. Also, it is noticed that the dune zone is only active during the grouped test. This means, that somehow the bathymetrical evolution during the stand-alone storm preserves the backshore to be eroded and hence the dune erosion. Fig shows the relative loss of sand ( ( V ol end V ol ini V ol ini 1 ) ) for the whole domain (intertidal zone, backshore and dunes) running the stand-alone and grouped cases. The differences between the two approaches are nearly zero during the first storm. In contrast, in the second and third storms the differences are.5% and.8% respectively. Note that at the second storm, the erosion is greater using the stand-alone approach while in the last storm the opposite situation is seen. Taking into account that at the first case stand-alone and grouped tests are initialized with similar bathymetries it seems logical to obtain comparable result. As the bathymetry evolves, it differs from the initial bathymetry and the differences between the stand alone and the grouped tests increases. Fig shows the bathymetry development after each storm of the storm cluster evolution (Fig b-d-f) and after each stand-alone storm (Fig c e -g). This

141 a) y [m ] y [m ] y [m ] R1 R2 4 2 R x [m ] R5 4 c) e) g) R f) d) b) z [m] y [m ] Chapter 5. XBeach: Numerical modelling x [m ] 15 Figure 5.32: a) Initial bathymetry. b) Final bathymetry after storm 1 in storm group mode. c) Final bathymetry after storm 1 in stand-alone mode. d) Final bathymetry after storm 2 in storm group mode. e) Final bathymetry after storm 2 in stand-alone mode. f) Final bathymetry after storm 3 in storm group mode. g) Final bathymetry after storm 3 in stand-alone mode. shows qualitatively the main differences in the final bathymetry between stand-alone storm and storm cluster sequence. The initial bathymetry (Fig a) shows the presence of an irregular bar. Five main rip channels are spotted (Fig red dots), two of them with a meandering shape (Fig R3 and R4). After the first storm, the bathymetrical features are maintained (Fig b - c) both at the storm cluster and at the stand-alone storm. After the second storm, the meandering features disappear (Fig d), the rips channels are filled and the bar is smoothed, this effect is less marked at the stand alone storm. Finally (Fig c), after the third storm of the storm cluster the beach presents a quasi-uniform smooth bar, with hardly marked rip channels, however, if this storm is ran separately, some of the features are maintained.

142 Chapter 5. XBeach: Numerical modelling Discussion and conclusions Previous studies state that series of storms can induce strong erosion and important morphological changes (Birkemeier [1979]; Lee et al. [1998]; Loureiro et al. [212]). In some cases it is also stated that the combined erosion of successive storms was greater than the expected sum of average erosion for each storm (e.g. Morton et al. [1995]; Lee et al. [1998]; Ferreira [25]; Splinter et al. [214]). According to Lee et al. [1998], the hypothesis behind that is related to the destabilizing effect on the profile generated by the first storm and the insufficient time to recover before the subsequent set of storms. Furthermore, this hypothesis states that the deposited sediment in the bars and on the shoreface is loosely packed and easily eroded after the first storm so it is prone to remobilization. As a result, several storms in quick succession have a large impact on the morphology. If there is fair weather during long periods of time, the wave action will sort and compact upper shoreface sediments (Birkemeier [1979]) making it more difficult to erode. In the present work, the erosion accretion of the different sections of the beach, observed after stand-alone and cluster storms, seems to follow similar patterns driven by the waves and tides. However, the amount of sand eroded/accreted along the beach is different if the stand alone and cluster result are compared. This response can only be caused by the differences in the initial bathymetry. In fact, the greater the differences are in the initial bathymetry, the greater is the mismatch between the stand alone and cluster beach erosion predictions Synthetic storm scenarios The aim of this section is to analyse what is the relation between the storm power magnitude and the beach erosion. Also, the response of the beach forced by the different parameters that form the storm is analysed. To this end, a series of tests were designed (Fig. 5.33), combining four different storm power magnitudes (corresponding to 1,3,5 and 1 years return periods), with two different H s values (corresponding to 1 and 5 years return periods) and two different T p values (corresponding to common T p values at the study site). Since a storm of a given return period is formed by different combinations of H and T, the duration of the storm varies. Each test is run both during spring (tidal range of 3.75 m) and neap tides (tidal range of 1.9 m), hence a total of 32 tests are examined. The initial H s value of the storms is always H s 1% (H s = 2.3 m), and it gradually increases until it reaches the peak of the storm to mimic the behaviour of a real storm. Still and all, the H s constant value throughout the event does not occur in real cases.

143 Chapter 5. XBeach: Numerical modelling P = 8.7 [Mw h m 1 ] 1 P = [Mw h m 1 ] 8 8 Hs [m] - η [m] P = [Mw h m 1 ] 1 P = [Mw h m 1 ] 8 8 Hs [m] - η [m] Tim e [hours] Tim e [hours] Figure 5.33: Synthetic storms. A) Storms representative of 1 year return period. B) Storms representative of 3 year return period. C) Storms representative of 5 year return period. D) Storms representative of 1 year return period. Orange line: H s 5years = 7.2 m. Orange dashed line: H s 1year = 5.7 m. Green line: T = 16 sec. Green dashed line: T = 12 sec. Black solid line: Spring tide. Black dashed line: Neap tide Results Fig and Fig show the erosion (relative volume change = V oln V ol 1 V ol 1 1) that takes place at the different sections (engineered, natural) and zones (intertidal zone, backshore and dune) of the beach, associated to the different storm types. It can be seen in general lines that the beach evolution with respect to the return period of the storm is not linear and seems to follow a power law like function. This trend has been seen in previous studies (e.g. Ferreira [25]). In regard to the different zones of the beach, it can be seen that the most active areas are the backshore and intertidal zone. Dune area is only active during spring tide tests. It is noteworthy to mention that the dune area encountered at the engineered section corresponds to a particular section of the beach previously discussed in Chapter 4. The

144 Chapter 5. XBeach: Numerical modelling Engineered zone 2 Natural zone INT. Rel. vol. [%] Rel. vol. [%] BACK Rel. vol. [%] H = 5.7 T = 12 H = 5.7 T = 16 H = 7.2 T = 12 H = 7.2 T = Return Period [years] Return Period [years] DUNE Figure 5.34: Volumetric beach changes for different types of synthetic storms during neap tide. INT) Intertidal volume evolution. BACK) Backshore volume evolution. DUNE) Dune volume evolution. intertidal zone follows an inverse response to the backshore and dunes, suggesting the existence of feed-back between them. The degree of impact at the backshore of the engineered area is larger than in the natural section. The loss of sand at the backshore and dune mitigates the erosion of the intertidal zone. However, since the backshore and intertidal zones have different volumes (backshore volume < intertidal volume), a quasi-total loss of the backshore volume implies a low-order gain in the intertidal zone. Furthermore, not all the material removed from the backshore settles down at the intertidal zone but also drifts towards the sub-tidal zone. The effect of the tide is none other than the spatial shift of the wave action. During neap tide the wave action is restricted to a smaller area than during spring tide. The capacity to erode the backshore and dunes is reduced during neap tide. In fact, the dunes are intact during all the tests ran with neap tide. On the contrary, during spring tide there is a complete loss of the backshore zone at the engineered section.

145 Chapter 5. XBeach: Numerical modelling Engineered zone 3 Natural zone INT. Rel. vol. [%] BACK. Rel. vol. [%] Rel. vol. [%] H = 5.7 T = 12 H = 5.7 T = 16 H = 7.2 T = 12 H = 7.2 T = Return Period [years] Return Period [years] DUNE Figure 5.35: Volumetric beach changes for different types of synthetic storms during spring tide. INT) Intertidal volume evolution. BACK) Backshore volume evolution. DUNE) Dune volume evolution. Fig (see the engineered backshore and intertidal zone, magenta and red lines) shows that the loss of the backshore volume on the beach leads to a system vulnerability increase. The lack of a dry sand reservoir indirectly affects the evolution of the intertidal zone. This can be better seen in Fig where the evolution of the sand reservoir through the storm is represented. The figure shows the 5 year return period storm with H s = 7.2 and T p = 16 sec (magenta line) and with H s = 5.7 m and T p = 16 sec (red line). As the backshore and dune loss part of their sand the intertidal zone sand budget increases. After 1 (6) hours of simulation, the magenta (red) coloured test loses the 1% of the backshore (only at the engineered part). Then, the intertidal zone cannot maintain its sand budget. This chain reaction suggests a the existence of a link between both parts of the beach. On the other hand, it also suggests that the backshore plays a major role during erosive events.

146 Chapter 5. XBeach: Numerical modelling Engineered zone 3 Natural zone INT. Rel. vol. [%] BACK. Rel. vol. [%] DUNE Rel. vol. [%] Tim e [hours] Tim e [hours] Figure 5.36: Volumetric beach changes during a 5 years return period synthetic storms with different characteristics. H s = 7.2 and T p = 16 sec storm is represented by a magenta line and H s = 5.7 m and T p = 16 sec storm is represented by a red line Discussion and conclusions The loss of dune volume mitigates the erosion of backshore and intertidal zones. The presence of a seawall itself should not be a problem as long as its position relative to sea water level is sufficiently broad to allow the accumulation of the sand. Weggel [1988] study holds that the impact of the seawall is a function the seawall s location on the beach and on the water depth at the seawall s base. The present tests reveal that the loss of sand at the backshore generates a chain reaction facilitating the erosion of the intertidal zone too. It needs to be mentioned, that the short wave reflection is not taken into account in the model formulations. The tidal level seems to play a major role in the beach response. The erosion of the dunes is only active during spring tide. The backshore erosion is greater during spring tide and the intertidal erosion in some cases is greater too. The rates of deposition at the intertidal zone of the engineered sector for neap and spring tides are more similar to those found at the natural sector. This suggests that the impact of the tidal level is greater at the engineered section than at the natural sector.

147 Chapter 5. XBeach: Numerical modelling 127 During a storm, the backshore width is also relevant regarding the beach preservation. The complete loss of the backshore sand makes the intertidal zone weak to the storms. It can trigger a chain reaction where the lack of sand at the backshore accelerates the loss of sand at the intertidal zone. The storm power magnitude indicates what the integrated potential of the storm is. It is difficult to link a particular value of the storm magnitude to a certain beach erosion. The Fig and 5.35 indicate that the same storm magnitude formed by different H s and T p combinations can lead to a different beach response. Furthermore, a low return period storm power with high H s -T p values can generate greater beach changes than a high return period storm with low H s -T p values. In previous studies is suggested that the small variations in wave period ( T p < 5 sec) do not significantly influence the upper beach erosion (Carley et al. [1998]). It is also stated that the use of the wave integrated power (eq. 2.3) or the use of wave integrated energy to represent a storm (with similar wave periods) gave analogous results when linking them to the beach erosion (Splinter et al. [214]). This is not the case for the present study, where increasing the wave period ( T p = 4 sec) clearly increases the erosion of the dry and dune zone. This is also discussed in Van Thiel de Vries [29] where it is mentioned that the dune erosion volume and the dune retreat increases for a larger wave period. The amount of energy that reaches the dune face is expected to increase as the wave period increases.

148

149 Chapter 6 Conclusions, recommendations and future perspectives 6.1 Conclusions The overall goal of the study is to gain more fundamental knowledge on the response of engineered pocket beaches to storms events. Different approaches were used in order to better understand such response. The wave climate of the region both offshore and nearshore was studied. Then, to better understand the study site, the morphological response of the system in short and medium term was described by means of video imagery techniques and topographic measurements. Finally, using the XBeach numerical model the response of the beach to different storm conditions was analysed. The main conclusions of this study are described below. Quantification of extreme events offshore/nearshore in terms of storm cumulative energy The quantification of the storm magnitude was carried out. For that, a formula that integrates the most relevant parameters that form a storm was used. With this formula a given storm formed by several sea states and thus formed by a several H s and T p values, is represented by a unique value representative of the whole energy of the storm. The complexity of the sand bar system The beach of Zarautz is characterised by the presence of a double sand bar system most of the time. The outer bar is alongshore non uniform even during high energetic events. During the study period the effect of several storms were analysed. 129

150 Chapter 6. Conclusions, recommendations and future perspectives 13 However, none of these storms were able to force the beach towards a theoretical reset event where the outer bar goes from an alongshore non-uniform shape to a uniform system (e.g. Wright et al. [1985]; Lippmann and Holman [199]). Despite the fact that it is not a common response, some studies carried out both in open and pocket beaches have noted the same behaviour before (i.e. Van Enckevort and Ruessink [23]; Enjalbert et al. [211]). In these studies it is suggested that the bars of the system may be governed by a free behaviour, rather than by an external forcing. In this case, the system is dominated by non-linear feedback between forcing and response, resulting in self-organisational behaviour (i.e. Coco et al. [23]). On the other hand, because of the geological constraints, sandbar threedimensionality often increases with increasing wave energy on embayed beaches (e.g. Enjalbert et al. [211]). The relevance of the water level on the beach erosion In the present meso-tidal beach, the erosion is limited by the water level. Dunes and backshore are only eroded when the tidal level is higher than the mean tidal level. At this situation the intertidal zone is accreted since the cross-shore sand transport facilitates the deposition of the sand eroded at the upper part of the profile. In the course of mean/low tidal levels, the dunes and backshore are intact; conversely, the intertidal zone may be eroded. The beach erosion shows a clear dependence on the water elevation. The tidal level acts as a switch on/off mechanism that activates or deactivates the erosion/deposition of the cross-shore sections of the beach. This simple and well known finding suggests that the water level determines which cross-shore section is eroded rather than the wave power magnitude. The relevance of the sand reservoir on the beach erosion The cross-shore sand transport is essential in the beach evolution. During a storm the sediment of the dunes and backshore is transported to the intertidal and surf zone. In the present study site the sediment budget at engineered and natural sectors is different, being the sediment budget larger at the natural zone than along the engineered one. This is a common characteristic found in hybrid beaches since the seawall is usually constructed at the level of the dune face. If during a storm the action of the waves reaches the upper part of the beach, the backshore and dunes are eroded. Since the amount of sand in the engineered zone is limited, the backshore may disappear. This may lead to an engineered zone with an intertidal zone only. In contrast, at the natural zone there is practically no limitation of sand, and the mentioned situation is unlikely to happen.

151 Chapter 6. Conclusions, recommendations and future perspectives 131 Storm magnitude as a beach erosion indicator The results of the study reveal that the storm magnitude is not an accurate tool to predict beach erosion. A given storm magnitude composed by different H s and T p combinations can lead to a different beach responses. Hence, it is difficult to link a particular value of the storm magnitude to certain beach erosion. The erosion of the beach should be analysed taking into account the internal characteristics of the storm together with the water level and not only with an integrated value such as the storm power magnitude Research Questions A series of questions were addressed at the beginning of this work. The answers to these questions, sometimes partial, constitute also to the main conclusions of this study. The wave climate is a key factor in the understanding of the beach morphodynamics. Taking into account this statement, three questions were stated. What characterises an energetic event (storm)? The magnitude of a storm cannot be represented either by a single wave parameter or by a single sea state. The power of a given sea state is represented by two parameters; its wave height (representing energy = f(h 2 )) and period (representative of the group speed and therefore representative of the rate at which energy propagates). It can be stated that a storm is formed by an indeterminate number of sea states, so the magnitude (power) of a given storm can be assumed to be equal to the sum of all sea states that constitute it. td Ec g dt (6.1) However, the sea states that define a storm require some specific characteristics. In the present work, only the highest H s values with a probability of occurrence less than 1% are considered extraordinary. In addition, some restrictions that somehow take into account the effect of the tidal effect and the inter-storm period were taken into account too. To summarise, a storm is considered to be formed by sea states that present values higher than H s 1% ( 3.5 m offshore and 2.3 m at the seaward boundary of

152 Chapter 6. Conclusions, recommendations and future perspectives 132 the study site) during more than 12 hours. In addition, if two consecutive storms are separated by less than 24 hours, they are considered as a single storm event. What are the storm characteristics offshore? The extreme wave climate compared to the mean conditions is confined to a narrower directional band with sea states mainly arriving from the NW and WNW directions. The vast bulk of the extreme events take place during winter and autumn. This is the result of the two action centres governing the North Atlantic ocean, the Azores High and the Iceland Low (Wooster et al. [1976]; Vitorino et al. [22]). The storm duration ranges between hours to weeks while the inter-storm period varies between days to months. The existence of a positive trend is found between the maximum storm H s value and the power of it (R 2 =.5), however some scatter is found suggesting that large power storms may present low H s values and vice versa. There is no clear relation that links the T p and θ p to the storm power. Finally, a clear relation between the storm duration and its power is found (R 2 =.9). What are the storm characteristics nearshore? The storms registered at the seaward boundary of the study site are characterized by presenting some degree of variability regarding the H s, T p, storm-duration and inter storm duration. However, the directional variability is limited. The wave refraction process and the sheltering produced by the cape San Anton, makes the wave climate at the study area almost unidirectional. This is also reflected by the low directional spreading (compared to the offshore wave climate directional spreading). An alongshore variability in the wave characteristics is observed at the seaward boundary of Zarautz. The W side of the beach is more sheltered and the wave heights tend to be smaller. The wave trajectories are almost perpendicular to the coast in the western part of the beach, while at the other end they can arrive with certain angle of incidence ( O (1 1 ) deg ). There is some correlation between storm power and H s, and also with the storm duration (R 2 =.67 and R 2 =.87, respectively). On the contrary, the T p and θ p have no correlation with the storm power. Are offshore storms representative of the nearshore storms? The short answer to this question would be in general terms, no. The transformation undergone by the wave fields makes the storm power at deep water

153 Chapter 6. Conclusions, recommendations and future perspectives 133 significantly different do that found in the study area. The storm power and H s belonging to offshore storms are greater than those found in the study site. The wave period is slightly different and it presents higher values at the nearshore. This can be the effect of the high frequency filtering of the cape San Anton together with the wave refraction. The wave direction transformation is reflected as a very narrow directional band in the nearshore area compared to the offshore area. The directional spreading is also lower in the study site. The duration of storms in the nearshore is slightly lower than in deep water. This might be caused by W component storms, as they lose most of its energy in the propagation process. Hence, once reach the nearshore, their wave heights are low and cannot be considered extreme events. However it should be noted, that although the magnitude of a storm differs from deep water to the study site, if the storms are ordered from the highest to the lowest; the major storms coincide both at offshore and nearshore area. This indicates that the highest storms offshore are also the highest storms nearshore. Once the offshore/nearshore wave climate is understood, the study of the beach response to storms is described. For that, the general response and the response of the different sections of the beach are analysed. To that end, different storm scenarios are analysed and designed. The study was carried out by means of real data analysis as well as by the use of numerical modelling. Do the natural and engineered sectors of a hybrid pocket beach present the same morphology? A 2-year dataset of time exposure images was analysed in order to study the morphology of the beach of Zarautz. The beach morphology was classified by Wright and Short [1984] method. At the engineered sector of the beach the most common and stable shape was the lowest energy intermediate state (LTT). It appeared 61% of the time, followed by TBR (25%), RBB (11%) and LBT (3%) states. On the other hand at the natural sector, the LTT state was observed 88% of the time. The TBR and RBB states were less observed ( %) and the presence of an alongshore-uniform bar (LBT) was never observed. Overall, the outer bar control over the inner bar seems to be less pronounced on the western side of the beach. In general, the beach intertidal slope at the natural side is steeper than in the engineered zone. Furthermore, the width of the backshore increases from the western to the eastern side, hence the sand reservoir increases from west to east. In conclusion, the two sections of the beach are morphologically different. Yet, these differences do not occur dramatically in the limit of separation between the engineered area and the natural area but they occur gradually along the beach.

154 Chapter 6. Conclusions, recommendations and future perspectives 134 During a storm, do the natural and engineered sectors of a hybrid pocket beach respond in the same manner? After the analysis of the pre/post storm profiles the following conclusions were obtained: During high energy conditions erosive processes not only occur all over the beach, but also can occur at localized areas. It seems to exist a clear relation between the location of rip currents and the erosive area. This finding is consistent with previous studies (Wright [198]; Short and Hesp [1982]) were the maximum erosion of the beach was observed in the lee of the rip creating mega-cusps on the system. On the other hand there are cases where the limit of the seawall plays an important role on the beach evolution. In case of spring tides events, it seems that this promotes the erosion of the backshore and dunes of the beach, transporting the sand to the foreshore. In those cases the dune and backshore become important as they act as a buffer, preventing the foreshore erosion of the beach. Finally, when neap tides coincide with the presence of a high energetic event, the evolution of the foreshore might be sensitive to the wave characteristics rather than to the tidal range as those are decisive in the maximum level reached by the water layer. After the analysis of numerical model simulations the following conclusions were obtained: The volumetric changes at the engineered and natural sectors occur at the same time and following the same trend (loss or gain). However, by the end of the record, the engineered zone losses more volume (in relation to its initial volume) than the natural zone. During a storm, what is the tidal and wave height sequence order influence on the beach response? It was demonstrated that the beach evolution is altered both by inverting the wave height signal (storm sequence) and by inverting the tidal signal. Note that during these tests, the total energy is conserved; hence, the same energy distributed in a different way or reaching the coast at a different water level may have different consequences on the beach. The beach differences by the end of the simulation between the original storm and the tide inverted storm were larger than between the original storm and the wave inverted storm. This reveals the high relevance of the water level on the beach evolution. In addition, the analysis of the volume evolution throughout the storm shows that the erosion episodes are driven by tides more than by high powered events. Hence, it can be concluded that the

155 Chapter 6. Conclusions, recommendations and future perspectives 135 beach erosion is a compromise between the energy sequence order and the water level, being this last term relevant for the backshore and dune erosion. During a storm, what is the initial bathymetry influence on the beach response? If the response of two different bathymetries to the same storm is compared, it can be seen that the rate of change at the end and during the simulation is different. This shift is greater the larger the differences between the initial bathymetries are. On the other hand, the evolution of the beach follows a similar behaviour. That is, the erosion/accretion of the different sections of the beach is given at the same time, although they produce different magnitude changes. Which role plays the distance of the seawall to the mean water level on the beach response? This question is not directly addressed by the present study, but can be inferred from the field and numerical tests realized during it. The numerical model simulations show that the proportion of erosion/accretion of the natural and engineered sections are not significantly different. But they do indicate that the absolute loss of dry beach area can generate a complete loss of the intertidal zone. The complete loss of dry beach at the natural section is highly improbable, since the loss of dune volume mitigates the erosion of backshore and intertidal zones; however it can occur at the engineered section. The presence of a seawall itself should not be a problem as long as its position relative to water level at high tide is sufficiently large to allow the accumulation of the sand. This study supports the hypothesis stated by Weggel [1988] where it is stated that the impact of the seawall is a function the seawall s location on the beach and on the water depth at the seawall s base. Is the storm power representative of the beach erosion? The storm power integrates the power of a series of different sea states. Different combinations of H s, T p and storm duration can lead to a same storm power (e.g. a short storm with high H s and T p values can be of same magnitude as a long storm with low H s and T p values). Here it is demonstrated that the same storm magnitude formed by different H s and T p combinations can lead to a different beach response. Furthermore, a low return period storm power with high H s -T p values can generate greater beach changes than a high return period storm with low H s -T p values. In previous studies it was suggested that the small variations in wave period ( T p < 5 sec) between the storms do not significantly influence upper beach erosion (Carley et al. [1998]). Also it is stated that the use of the

156 Chapter 6. Conclusions, recommendations and future perspectives 136 wave integrated power (eq. 2.3) or the use of wave integrated energy to represent a storm (with similar wave periods) gave analogous results when linking them to the beach erosion (Splinter et al. [214]). This is not the case for the present study, where increasing the wave period ( T p = 4 sec) clearly increases the erosion of the dry and dune zone. Similar to the conclusions found here are discussed in Van Thiel de Vries [29], where it is mentioned that the dune erosion volume and the dune retreat increases for a larger wave period. The amount of energy that reaches the dune face is expected to increase as the wave period increases. 6.2 Numerical modelling recommendations XBeach-Beach Wizard: The use of XBeach-Beach Wizard model revealed that the model is sensitive to the initial beach morphology. Yet, it is assumed that this can be compensated improving the image quality and adding a series of images with a wide range of tidal and wave climate conditions. The value of Tr parameter affect the final result. Changes in the depth level are observed but the main features of the final bathymetry are preserved. This value should be tuned according to the wave climate of the study site. Moreover, the Tr should be variable throughout the study domain. The Tr fitting could be performed by either carrying out a field campaign, where the morphological change rates with respect to the beach zone and wave conditions are analysed or by obtaining a general value from the literature. A new boundary condition was implemented in the model (alongshore non uniform boundary). The model shows a better performance using alongshore non-uniform boundary conditions than using an averaged value. XBeach calibration: A calibration step is needed before any simulation is performed since results can vary significantly depending on the model parameter values. Parameters such as short wave run-up, γ ua, γ, eps and h min seem to be relevant for the model calibration. 1D cases help to infer a first set of parameter values and save time in the 2D tests. Despite the fact that 2D cases take longer computational time, these tests are necessary in alongshore non-uniform environments. The model skill varies depending on the beach section (dune section, seawall section). There is no optimal parameter set that satisfies a perfect model result; however it can be achieved a reasonable model skill at both sections of the beach.

157 Chapter 6. Conclusions, recommendations and future perspectives 137 The model tends to overestimate the erosion of upper part of the profile (at the engineered section) and also tends to locate incorrectly the position of the pivotal point. Regarding the spectral parameter calibration, if the real spectrum is used an error improvement of 25-5 % is obtained at the engineered zone; however at the natural section the error is lower using a parametric spectrum (1-5 %). Greater changes are detected when varying the directional width than the frequency width. 6.3 Future perspectives Detailed investigation of the storm parameters In the present work the impact on the beach erosion that is forced by the factors conforming the storm (H s and T p ) has been investigated. After the analysis it is highlighted the great importance of the intra storm parameters on the beach erosion. A future research line would analyse in more detail what are the physical processes affected by these parameters and why these physical processes are relevant for the beach erosion. In addition, this study would help to: 1. Better understand the physical processes that drive the erosion of the different sections of the beach. 2. Quantify the relative importance of each parameter on the beach erosion. 3. Improve the existing or create a new storm impact index factor. A numerical approach (i.e. XBeach) would be used to achieve the objective. As in the present work, a series of synthetic cases would be designed; but instead of using a time varying water level, a fixed water level would be implemented as boundary condition. Thus, the problematic would be simplified and the water level variations would be driven only by the wave forcing interactions (i.e. infragravity motions). Also, a wider range of H s and T p would be used to quantify the relative importance of each parameter on the beach erosion accurately. Find a suitable impact index for meso-tidal environments The estimation of the beach erosion through the storm magnitude parameter seems not to be accurate enough. The combination of the water level together with the wave height and the wave period are determining factors when estimating the beach erosion.

158 Chapter 6. Conclusions, recommendations and future perspectives 138 Previous studies dealing with the link between the storm magnitude parameter and beach erosion has been carried out so far (i.e. Harley et al. [29]; Splinter et al. [214]). In fact, these studies show that the storm magnitude and the beach erosion follow a power law relationship. In this thesis it is shown that the erosion of the beach also follows a power law-like function. However, it is also shown that the intra storm parameters and the water level are a key factor to estimate the erosion of the different cross-shore sections of the beach. For meso-tidal environments the water level variations need to be taken into account in the formulation. This might be carried out by adding a filtering parameter, which activates or deactivates the erosion of the different cross-shore sections of the beach in function of the water level recorded during the storm. On the other hand, the greater the wave period during the storm is; the greater is the dune and backshore erosion. Therefore, the beach response to two storms of similar magnitude but different wave period will not be the same. The addition of a weighting factor (corrector factor) for the wave period would improve the estimation of the beach erosion. Study of the hard structures on beach morphodynamics During this study the response to storms of a particular beach with a seawall has been studied. However, there are different types of seawalls. The variety of the seawalls type is related not only to the shape of the seawall, but also, related to the distance between the mean water level and the location of the structure. In fact, this seems to be the determining factor when estimating the impact of a storm in the engineered area. If the beach has enough sand between the seawall and the high tidal level, then, the beach will respond as if it were a natural beach. An interesting line of research would study which is the optimal location required to maintain its functionality during storms as well as causing a minimal impact on the beach behaviour. For that, a series of numerical tests with different seawalls locations and types of storms would be designed. However, if the short wave energy is not dissipated by the time that it reaches the seawall, the XBeach model should be optimized since the short wave reflection is not implemented in the code yet.

159 Appendix A Appendix A: Estimation of the directional spreading The directional spreading (σ) is defined as Kuik et al. [1988]. θ = arctan ( b1 a 1 ) (A.1) σ 2 = 1 a 2cos(2θ) b 2 sin(2θ) 2 = f max f π π sin2 (θ θ)e(f, θ) dfdθ f max π f π E(f, θ) dfdθ (A.2) where, directional moments are defined as: a 1 = f max π f π cos(θ)e(f, θ) dfdθ f max π f π E(f, θ) dfdθ (A.3) b 1 = f max π f π sin(θ)e(f, θ) dfdθ f max π f π E(f, θ) dfdθ (A.4) a 2 = f max π f π cos(2θ)e(f, θ) dfdθ f max π f π E(f, θ) dfdθ (A.5) b 1 = f max π f π sin(2θ)e(f, θ) dfdθ f max π f π E(f, θ) dfdθ (A.6) 139

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161 Appendix B Appendix B: Wave dominated beach types 1. Dissipative (D): Dissipative beaches are likely to appear on low energetic environments composed by fine sand. They present a low gradient surf zone with shore-parallel bars. The wave type of breaking is spilling. The swash zone of the beach is wide and it presents a low slope. The shoreline tends to be relatively straight and uniform alongshore with no rip currents. 2. Longshore bar and trough (LBT): These beaches are characterised by presenting a near continuous longshore bar. The beach face is straight alongshore and depending on sand size may have a low tide terrace (fine sand) and/or a reflective beach with beach cusps (medium sand). The bar is usually crossed by rips. Sometimes longshore bar and trough occurs as an outer second bar. 3. Rhythmic bar and beach (RBB): Rhythmic bar and beach are characterized by their relatively fine-medium sand and the more exposure to waves in contrast to dissipative and Longshore bar and trough beaches. They are characterised by an outer bar which is separated from the beach by a deep trough. The bar varies in width and elevation alongshore, and it is rhythmic. Waves break more heavily on the shoreward-protruding rhythmic bar sections. 4. Transverse bar and rip (TBR): They occur primarily on beaches composed of fine to medium sand. The bars are transverse or perpendicular to and attached to the beach, separated by deeper 141

162 Appendix B. Appendix B 142 rip channels. The bars and rips are usually regularly spaced. The shoreline is rhythmic forming the megacusp horns and embayments. The surf zone has a cellular circulation pattern. 5. Low tide terrace (LTT): They are characterised by a moderately steep beach face, which is joined at the low tide level to an attached bar or terrace. The terrace has a central crest, and may be cut every several tens of metres by small shallow rip channels. 6. Reflective (R): Reflective sandy beaches are representative of low energy systems. They are usually composed of coarse sand. They present a steep and narrow beach and swash zone. Beach cups may be present in the upper high tide swash zone. They have no bars and waves collapse at the beach front.

163 Appendix B. Appendix B 143 Figure B.1: Schematic illustration of the six wave dominated beach types with their general physical characteristics and patterns of wave breaking, bars troughs and currents (from Short [1999]).