Beach Nourishment Behavior Modeling of Beach Nourishment Planform Evolution: a Case Study of the Coast of North Zealand

Beach nourishment behavior Modeling of beach nourishment planform evolution: a case study of the coast of North Zealand

UNIVERSITY OF COPENH AGEN FACULTY OF SCIENCE

Master’s thesis Sofie Kamille Astrup and Serena Pilunnguaq Sørensen

Beach nourishment behavior Modeling of beach nourishment planform evolution: a case study of the coast of North Zealand

Main academic supervisor: Troels Aagaard, IGN

External co-supervisor: Nils Drønen, DHI

Submitted: February 8, 2016 Number of characters: 185,760

Department of Geosciences and Natural Resource Management

Chapter 1 / Introduction

Tak til alle

Chapter 1 / Introduction

Abstract

Beach nourishment is an important method for future protection of the Danish coastline. However, the modeling of beach nourishment behavior and estimates of predicted life-span and efficiency is associated with large error margins. This present thesis considers beach nourishment behavior, shape, symmetry in transport gradients and evolution in time. The 20-year planform evolution of beach nourishments in simplified settings is examined using the shoreline evolution model in the Littoral Processes FM framework. 15 schematized nourishment schemes were constructed in order to investigate the influence of various wave parameters on life-span and sediment diffusion pattern. This included variations in the angles at which the waves approach the shoreline. A simulation of the behavioral pattern of nourishments on a natural coastline is exemplified by a case study of potential nourishment scheme behavior at Tisvildeleje, Raageleje and Udsholt Strand, all located along the receding coastline of North Zealand. In order to evaluate qualitative assessments of potential longshore sediment transport produced using LITDRIFT, the actual erosion rates were determined using the GIS shoreline analysis tool DSAS. Recent research has shown that migration and formation of shoreline perturbations is related to the angles at which the waves approach the shoreline. Beach nourishments can be perceived as a sudden unnatural perturbation along a shoreline and therefore this study has investigated the possibility of recreating downdrift migration of beach nourishments. As the linear model has limitations with respect to modeling the morphological response to high incidence wave angles, migration of beach nourishments could not be modeled using the applied shoreline evolution model. The study of erosional patterns along the nourishments fostered the idea that a nourishment introduced on a sediment deprived beach will migrate in the downdrift direction if the littoral drift potential upstream of the nourishment is not satisfied. Since it was found that the examined coastline of North Zealand suffers from a chronic sediment deficit and a drift potential which exceeds the observed erosion rates, it is suggested by this study that migration of beach nourishment could occur on the coast of North Zealand.

Keywords: Beach nourishment; Planform evolution; Shoreline undulations; Coastal erosion; Coastal protection; Soft engineering methods; Historic shoreline change; North Zealand, LITLINE; Littoal drift

Chapter 1 / Introduction

Dansk resumé

Strandfodring er en vigtig del af den fremtidige beskyttelsesstrategi for de danske kyster. Imidlertid er simuleringer af kystfodringers udvikling, herunder projektets levetid og effekt, forbundet med store fejlmargener. I denne rapport undersøges kystfodringers morfologiske udvikling over tid, form og symmetri i transport gradienter. Den 20-årige udvikling i planform for sanddepoter er undersøgt for simplificerede forhold ved brug af kystlinjeudviklingsmodellen, som indgår i modeleringsværktøjet Littoral Processes FM. Der blev opstillet 15 skematiserede kystfodringsscenarier, med henblik på at undersøge indflydelsen af forskellige bølgeparametre på strandfodringens levetid og sedimenttransportmønstre. Simuleringerne inkluderede variation af bølgeindfaldsvinklen. Simulering af en strandfodring på en naturlig kyststrækning er eksemplificeret ved et casestudie af to mulige kystfodringsscenarier for strækningerne Tisvildeleje, Rågeleje og Udsholt Strand, som er beliggende på den eroderende kyststrækning mellem Hundested og Gilleje på Sjællands Nordkyst. For at kunne vurdere den potentielle langsgående sedimenttransportrate fundet ved brug af LITDRIFT, blev de faktiske erosionsrater bestemt på baggrund af en analyse af historiske flyfotos, foretaget ved brug af GIS-værktøjet DSAS. Nyere forskning har påvist, at dannelse og migration af kystlinjeundulationer kan relateres til skævtindfaldene bølger. En strandfodring kan opfattes som en kystlinjeundulation, og derfor er det i dette studie undersøgt, om migration af en sådan undulation kan genskabes ved brug af LITLINE. Da denne lineære model er begrænset i forhold til at kunne modellere det morfologiske respons i situationer med meget skævtindfaldende bølger, kunne migration af kystlinjeundulationer ikke simuleres i dette studie. På baggrund af observerede erosionsmønstre, er der udviklet en hypotese om, at migration af kystfodringer kan forekomme, i tilfælde hvor kysten lider af et kronisk sedimentunderskud. I tilfælde hvor den potentielle langstransportrate opstrøms for et kystfodringsdepot ikke er opfyldt, vil der blive eroderet langs den opstrøms side af depotet og aflejret langs den nedstrøms side, hvilket vil resultere i at depotet forflyttes i nedstrøms retning. Da det blev konstateret, at Nordsjællands kyst lider af et generelt sedimentunderskud, fordi den potentielle langstransport overstiger den faktiske erosionsrate, foreslår denne undersøgelse derfor, at der er mulighed for, at fremtidige kystfodringer på strækningen vil vandre i den dominerende langstransportretning.

Keywords: Strandfodring; Morfologisk udvikling; Kystlinjeundulationer; Kysterosion; Kystbeskyttelse; Historisk kystlinjeudvikling; Nordsjælland, LITLINE; Langstransport

Chapter 1 / Introduction

Contents

Abstract ...... 2 Dansk resumé ...... 3 1 INTRODUCTION ...... 7 1.1 Coastal zone management ...... 8 1.2 Scope of thesis ...... 9 1.3 Structure of thesis ...... 10 1.4 Erosional problems at the coast of North Zealand ...... 10 2 GENERAL THEORY ...... 14 2.1 Causes of beach erosion ...... 14 2.2 Responses to beach erosion ...... 15 2.3 Wave processes ...... 17 2.3.1 Wave characteristics ...... 17 2.3.2 Wave energy ...... 17 2.3.3 Wave transformation ...... 18 2.4 Sediment transport ...... 20 2.5 The cross-shore profile ...... 21 2.6 Longshore currents and littoral drift ...... 23 2.7 Application of numerical modeling for prediction of beach nourishment evolution ...... 25 3 STUDY AREA ...... 27 3.1 General description ...... 27 3.2 Geological setting ...... 28 3.3 Wind, waves and tides ...... 29 3.4 Local sediment budget ...... 30 3.5 Selected beach sections ...... 32 3.5.1 Tisvildeleje ...... 33 3.5.2 Raageleje ...... 36 3.5.3 Udsholt Strand ...... 38 4 METHODS ...... 40 4.1 The Littoral Processes FM framework ...... 40 4.1.1 Transport at a point ...... 40

Chapter 1 / Introduction

4.1.2 Littoral drift ...... 41 4.1.3 Table generation ...... 41 4.1.4 Coastline evolution ...... 42 4.2 Model predictions of beach nourishment planform evolution ...... 44 4.3 GIS-based shoreline and volume change analysis ...... 46 4.4 Wave transformation ...... 47 4.5 Nourishment predictions at selected shoreline subsections ...... 50 4.6 MIKE 21 FM Shoreline Model ...... 50 5 Evolution of schematized nourishments ...... 52 5.1 Single nourishment scenarios - comparison of initial shapes ...... 52 5.2 Multiple nourishment sites - effect of initial spacing ...... 53 5.3 Multiple nourishment sites - asymmetry ...... 54 5.4 Longshore sediment transport patterns ...... 55 5.5 Variation of incidences wave angle ...... 56 6 Shoreline change rates ...... 61 6.1 General observations ...... 61 6.2 Tisvildeleje ...... 63 6.3 Raageleje ...... 65 6.4 Udsholt Strand ...... 66 7 Nearshore wave modeling and equilibrium orientation...... 69 7.1 Wave modeling ...... 69 7.2 Model sensitivity to incoming wave angles and equilibrium orientations ...... 73 8 Coastline evolutions ...... 75 8.1 Tisvildeleje ...... 75 8.2 Raageleje ...... 79 8.3 Udsholt Strand ...... 82 9 Discussions ...... 86 9.1 Shoreline change and potential longshore sediment transport ...... 86 9.2 Beach nourishments and shoreline perturbation evolution ...... 88 9.2.1 Migration of nourishment deposits ...... 88 9.2.2 Beach nourishment evolution at the coast of North Zealand ...... 90 9.2.3 Nourishment migration on a starving coastline ...... 92 9.3 Evolution of a sand engine for beach nourishment ...... 93 9.4 Uncertainties of the performed shoreline change analysis ...... 95

Chapter 1 / Introduction

9.5 Model calibrations and considerations ...... 96 10 Conclusions ...... 98 References ...... 100

Appendix A ...... 103 Appendix B ...... 104 Appendix C ...... 105 Appendix D ...... 106 Appendix E...... 114 Appendix F ...... 115 Appendix G ...... 117 Appendix H ...... 119 Appendix I ...... 121

Chapter 1 / Introduction

1 INTRODUCTION

Beach erosion and shoreline recession are major problems along a large part of the sandy shorelines. Natural processes and human-induced changes of environmental forcing pose a significant threat of extensive erosion or frequent flooding of low-lying coastal regions in the 21st century. Beaches fringe about 40 percent of the world’s coastline, and many are directly exposed to the oceans or stormy seas. It is estimated that 70 percent of the world’s sandy shorelines are eroding, suggesting that eustatic sea-level rise is an underlying factor, although many other processes contribute to the problem (Davison et al., 1992). The coastal areas are of large socioeconomic importance, 10 percent of the global population, and 13 percent of the urban population lives within 10 meters of the current sea level (McGranahan et al., 2007). The coastal zone is highly dynamic and minor natural changes can have large socio-economic consequences, furthermore, human activities in the coastal areas can be a driving factor of change in local beach dynamics. Sandy shorelines are of vital importance as they decrease the force of incoming waves and have the ability to dissipate wave energy and protect the backshore in high energy situations.

Successful coastline management including coastal protection projects presupposes an understanding of the issue at hand and its cause as well as the temporal and spatial scale on which action is needed. In order to design a management strategy that corresponds to the problem, knowledge about the morphological and hydrodynamic processes affecting the management area is necessary. Many factors must be combined in order to create a sustainable site-specific protection plan, and therefore models play a fundamental role in any coastal management strategy. Shoreline evolution models allows for comparison of alternative designs with quantifiable evaluations of relative advantages and disadvantages and provide a methodology to summarize available knowledge and optimize project design.

The Danish Coastal Authority has with their Coastal Protection Strategy from 2011 specified nationwide criteria for future coastal protection, the strategy aims at a holistic sustainable effort where beach nourishments are the preferred method (Danish Coastal Authority, 2011). Beach nourishment is an attractive method of erosion control due to several factors; (1) the desire to reside along shorelines is increasing, and although the costs of beach nourishment is higher than hard construction solutions the recreational value of the beach is maintained and often improved by beach widening and the natural expression of the beach environment is retained; and (2) nourishments have beneficial effects beyond the particular shoreline in question. Groins and breakwaters may trap sand in one area starving adjacent beaches, but nourishments will in many cases result in adding to the sediment budget of adjacent coastlines (Dean, 1992).

Beach nourishment as a mean of protecting and improving a stretch of sandy beach was first carried out in USA in the beginning of the 1900’s and have over the last three decades increased in use, when compared to the practice of building hard structures. Beach restoration along eroding developed beaches is commonly practiced by combinations of periodic nourishments with or without coastal structures to stabilize a beach over the long term. The use of beach nourishment is favorable because of its less invasive means of fixating the coastline.

Within recent years the attention has been turned towards a new type of beach nourishment: the mega- nourishment. The Sand Engine which is the first of its kind, is a Dutch pilot project testing the efficiency of localized mega nourishments. Many questions arise from this project. How will one large deposit be redistributed along the coast? Will future nourishment projects carried out as mega nourishments reduce the economic and environmental cost of traditional beach nourishment schemes where frequent renourishments are required? Understanding and optimizing the coast and efficiency of beach nourishment project is of vital importance to engineers as well as policy makers.

Chapter 1 / Introduction

1.1 Coastal zone management In the decades following the Rio Earth Summit in 1992 and the adoption of Agenda 21, a new line of development and management focusing on sustainability was installed within the UN (Moksness, 2009). This also led to a change towards sustainable development in coastal areas, which was manifested in the policy framework of Integrated Coastal Zone Management (ICZM). The World Bank defined the overall concept of ICZM as stated below:

ICZM is a process of governance and consists of the legal and institutional framework necessary to ensure that development and management plans for coastal zones are integrated with environmental (including social) goals and are made with the participation of those affected

(Post and Lundin, 1996)

As Agenda 21 was not a binding agreement the legislative incorporation of ICZM is found in individual national legislations.

In Danish legislation the principals of ICZM can be found in the objective clause of the coastal protection law of 2006. It states that all individual applications for coastal protection should be evaluated according to the following eight criteria:

 the need for coastal protection  economic considerations  the coastal protection schemes technical and environmental qualities  the conservation and recovery of the coastal landscape  the continued free evolution of nature  recreational use of the coast  maintenance of current access to the coast, and  other significant factors of importance to coastal protection.

(Ministry of Environment and Food of Denmark, 2016)

The Danish coastal protection strategy was published in 2011, and its objective states that a national strategy should promote a coordinated, long-term and comprehensive approach to the management of the Danish coastline. Coordinated development of the coastal areas including coastal protection projects, is the basis of sustainable use of the coastal area (Danish Coastal Authority, 2011).

The overall approach presented in the protection strategy is holistic in the sense that measures of coastal protection should consider the value of the open and natural coastal landscape as well as socioeconomic values of the protected area. This aims at ensuring that the coastal area is not impaired in any respect. A corner stone in achieving this goal is to work with the natural processes and dynamics of the coast, and the balance between humans and the natural environment is therefore important. The strategy promotes the following main guidelines for future coastal protection projects:

 Large-scale solutions; the issues at hand should be handled on the scale on which they act; this will ensure better coastal protection.  Long term solutions taking technical optimization; usability and environmental issues into consideration.  Less invasive soft solutions such as beach and shoreface nourishment are preferred because they are easier to optimize and will adapt into the natural environment.

Chapter 1 / Introduction

 Coastal protection should not be performed at any cost, in some cases protection of private property should not be carried out because erosion is too advanced and the needed protection measures will be too invasive.  Redevelopment of the natural coastlines should be included as an active part of coastal protection projects, i.e. removal of old inefficient and scarring coastal protection.

As a follow-up to the coastal protection strategy, the Danish Coastal Authority published a paper concerning the specific need for future beach nourishment, stating that beach nourishment is the only method that can halt further erosion of the Danish coastline (Danish Coastal Authority, 2013).

Shoreline management is the subset of the broader coastal zone management which focuses on the management, maintenance and the continued development along a coastline. Shoreline management deals with the interaction between land and water, as it aims to manage and control the influences of erosion and flooding trough flood and coastal defence (Mangor, 2004). Understanding the natural system and its processes is of importance in all levels of planning.

In order to assess and design a suitable coastal protection plan, Mangor (2004) provides a set of guidelines that breaks up the process of establishing a coastal zone management plan into three; identifying the problem, identifying the cause and identifying the future risk for the shoreline in question. Based on the findings, the right technical solution and method for implementation can be selected.

According to Mangor (2004) a so called shoreline master plan is useful in the planning of implementation of possible coastal development projects. The master plan aims at describing appropriate project schemes, and schemes should consist of 5 main parts:

(1) Account of the assets and natural resources within the management area. Collection and mapping of data from regional and national databases including stakeholder interests. (2) Description of the meteomarine settings, field surveys and modeling of wind, currents and wave action. (3) Analysis of the morphological setting and the shoreline development, establishment of historic shoreline evolution and predictions of future shoreline development, often carried out by numerical modeling and sediment budget calculations. (4) Identification of sustainable protection measures. The suggested coastal protection should take both natural and socioeconomic interests into account, and identification of problems between projected coastline evolution and development is the key, as it should guide the protection design. (5) Publishing of the master plan, including a hearing of the stakeholders.

1.2 Scope of thesis The focus of the present thesis is beach nourishment behavior and the main mechanisms controlling this. Beach nourishments are in line with the coastal management strategy of maintaining the coastlines in Denmark with soft engineering solutions rather than hard structures. The general planform evolution of beach nourishments placed along a straight coastline as well as a case study of selected sections located along the northern coast of Zealand in Denmark will be studied.

The study is inspired by the new concept of mega-nourishment currently studied in the Netherlands and Denmark. The idea is that instead of placing sand along an entire stretch of shoreline subject to erosional problems, sand is placed at the upstream end of the shoreline, and from here it is redistributed downstream by the wave induced longshore current.

Chapter 1 / Introduction

Whilst the overall purpose of this study is to investigate beach nourishment behavior, it is at the same time centered around the third item of the shoreline master plan provided by Mangor (2004). The evolution and effect of beach nourishments is exemplified with the incorporation of the retreating coastline of North Zealand. In order to provide insight into the effect of the site specific nourishments, analysis of the sediment budget, morphological setting, historic shoreline evolution and erosional patterns is provided.

To understand the potential impacts of beach nourishments the effects on local coastline evolution is investigated through use of numerical models. Planning of nourishments in the context of a multi-year management strategy requires significant prediction skills, and for this purpose numerical shoreline models is an important instrument. The significance of initial nourishment design and the effect of wave incidence angle on nourishment lifespan and evolution are investigated through the construction of schematized nourishment scenarios by use of the Littoral Processes FM, developed and provided by DHI. This model framework will also be applied for simulating transport patterns and planform evolution of nourishments placed at three sites along the North Zealand coast, in this case a naturally varying wave climate is used in the simulation.

The local changes in erosion and accretion patterns induced by beach nourishments are analyzed in order to determine if downdrift migration of the nourishment can be detected and should be incorporated into future nourishment projects.

1.3 Structure of thesis After the introductory part of the thesis (this present chapter) which also includes an outline of the erosional problems of northern Zealand in section 1.4, the remaining part is structured as follows:

Chapter 2 gives provides an outline of theoretical subjects found essential for this study. Chapter 3 provides an area description of the North Zealand coastline and the sections selected for beach nourishments. In chapter 4, the applied methods are described. Chapters 5 to 8 contain the presentation of results obtained during this study. Chapter 5 is a description of the results obtained from using LITLINE for simulations of different nourishment shapes and spacing using constant wave forcing. Chapter 6 is concerned with a shoreline erosion analysis of the North Zealand coastline. In chapter 7 results from a MIKE21 spectral wave simulation used for generating a nearshore wave climate applied in the site specific nourishment scenarios is presented. Chapter 8 contains the results of the modeled shoreline evolution after implementing the three shoreline subsections and simulated wave climates into the LITLINE model. Finally, discussions and conclusions of the study are given in chapters 9 and 10.

1.4 Erosional problems at the coast of North Zealand Over the past century, the coast of northern Zealand has become an area dominated by human activity, resulting in denser development near the coastal zone. Prior to this, naturally eroding sections of the coastline provided the beaches with sand, and these sandy beaches have contributed to the attractiveness and the areas recreational value. The protection of the natural erosional areas, has generally led to a deterioration of the existing beaches and erosion of hinterlands that were previously protected by anterior beaches. Along some sections of the coast, the erosion has been so severe that the beach has been completely eroded. At these locations, only the cliff protection measures protect the coastline, prompting for further action due to the risk of cliff collapse. Figure 1.1 shows an example a coastline section in such a state.

Figure 1.2 shows an example of a coastal section, where there is no pronounced need for action, but the requirement of some level of continuous maintenance is still present.

Chapter 1 / Introduction

Figure 1.1 Section of the north Zealand coastline with pronounced erosional challenges. Exact location is unknown. (Photograph: Hasløv and Kjærsgaard, 2014)

Figure 1.2 Functioning section of the northern Zealand coast, where the need for action is not pronounced. Exact location is unknown. (Photograph: Hasløv and Kjærsgaard, 2014)

During the past decades the coastline of Northern Zealand has been subject to attention, especially from local authorities, due to significant erosional challenges.

In 1971 the local councils of five adjacent municipalities along the coastline, set up at joint committee, with the objective to undertake the planning of a balanced approach for protection of the northern Zealand coastline. The committee was joined by researcher from the department of coastal morphology, University of Copenhagen and engineers J. Hostrup-Schulz & Sørensen cooperating with the DHI. The committee has published several reports, throughout the years, including an overall assessment of the coastal conditions including historical development.

As part of the work for the committee a beach nourishment pilot project was carried out at Hald Strand, located between Hundested and Tisvildeleje. A beach nourishment sediment deposit of ~23,000 m3 was placed at the beach and monitored during the following years. In conclusion the nourishment project was a success; the sediment was contained in the inner part of the beach profile. A downdrift effect was observed, as sand was accumulated on the adjacent beaches. The sediment transport took place in bands along the bars. Furthermore, a longshore migration of sand was set off in extreme weather situation as larger volumes of sediment was released from the nourishment site; generating migrating perturbations (Fællesudvalget for Kystpleje og Kystsikring af Nordkysten, 1987).

Chapter 1 / Introduction

In a report published in 1989, shoreline change from 1897 to 1983 along the coastline from Hundested to Gilleleje was assessed from cartographical material, and it was concluded that the beaches had recessed due to lack of sediment availability. The following average recession rates were found; 1897-1949: 0.35 m y-1; 1949- 1967: 0.75 m y-1; 1967-1983: 0.45 m y-1 (Fællesudvalget for Kystpleje og Kystsikring af Nordkysten, 1989).

In 2009 COWI published a report suggesting two different nourishment schemes as a means of protecting the coast of North Zealand. The evaluation of nourishment possibilities was carried on behalf of the municipality of Gribskov. The first suggestion only comprised nourishments and suggestion two a combination of nourishments and replacements of old ineffective structures with new strategically placed structures. The recommended nourishment schemes were based on historic shoreline analysis and calculations of gradients in transport capacity based on the CERC method. Their findings suggest that yearly longshore sediment transport increases along the north coast from zero in the West at Kikhavn to ~50.000 -70.000 m y-1 near Gilleleje (COWI, 2009).

In 2013, Danish Coastal Authority published the results of a nationwide screening performed to uncover the future need for nourishment of the inner Danish coasts within the next 25 years. The long-term risk level was assessed based on the historic erosion rates, which was determined by researchers form University of Copenhagen (Kabuth et al., 2014). Projections of future coastal retreat were calculated using the Bruun Rule and projections of sea level rise. The screening took criteria such as the coastal situation and governing trends of erosion based on historic shoreline retreat, changes in external forcings, as well as a qualitative valuation of the hinterlands into account. The project concluded that nourishment should only be performed where significant societal values are at stake i.e. shorelines where joint developments or infrastructure is in the immediate vicinity of the coast. Expected frequency and intensity of storm activity was not taken into account. On the basis of this screening, possible future nourishment sites were determined, one of which was the shoreline along the western part of North Zealand (Danish Coastal Authority, 2013).

In 2013 the municipalities of Gribskov and Helsingør had DHI and Hasløv and Kjærsgaard perform an investigation into the general climate adaption of the northern coast of Zealand, with focus on reusing dredged sediment from Gilleleje Harbour and Hornbæk harbour as a source for nourishment of the coastline. In this study it was estimated that the longshore sediment transport just west of Gilleleje is in the order of 65,000 m3 y-1 (DHI and Hasløv&Kjærsgaard, 2013).

In 2013 DHI developed a method for evaluating the erosion pressure along Danish coastlines, in order to classify coastlines according to following classes; accretional, stable, subject to little, moderate or high erosion. This included a pilot project which focused on the coastline along northern Zealand. It was found that the coastline can be classified as subject to moderate erosion based on expected erosion rates. The study found the potential drift based on observed erosion rates to be in the order of 100,000 m3 y-1 at Gilleleje (DHI, 2013).

The local interest in beach protection has increased within recent years, especially set off by the erosion that took place during the storm in December of 2013, Bodil. This event made it clear that the current beach protection was not dimensioned to counter extreme weather situations. Figure 1.3 shows the flooding and destruction of the seaside road at Raageleje, resulting in severe damage despite the concrete seawall.

Chapter 1 / Introduction

Figure 1.3 Top: Photograph of the flooding of a seaside road in Raageleje during the severe storm, Bodil, which raged 4-7 December 2013. Bottom: Photograph of damages suffered by the seaside road, taken during the storm aftermath. (Photographs: Eriksen, L., 2013)

Direct damages caused by the storm amounted to 85 million DKK only on the coast of northern Zealand (Region Hovedstaden, 2014). In the spring of 2014, following the damages caused by the storm in December, a cooperation between the three affected municipalities Gribskov, Helsingør and Halsnæs was sparked. This led to the publishing of a conceptual design, compiled together with Hasløv and Kjærsgaard, addressing the future management and protection of the entire stretch of coastline.

The report assumes a general potential drift for a typical profile along the coastline to be 40,000 m3 y-1, whilst the actual transport is estimated to be 25,000 m3 y-1, due to shortage of available sand (Hasløv&Kjærsgaard, 2014).

In 2015, The Capital Region of Denmark donated 2.2 million DKK towards the initiative, and the municipalities continue the cooperation with stakeholders in order to prepare comprehensive future management plan, including possible financials models.

Chapter 2 / General theory

2 GENERAL THEORY In order to describe the effects of beach nourishments a basic understanding of coastal morphology and dynamics is required. This chapter gives a brief outline of theories concerning this present study.

2.1 Causes of beach erosion During the past century, many of the world’s beaches have been depleted by erosion. Where beaches are eroding, this is most likely to continue and even increase due to predicted global sea level rise and increased storm frequency (Bird & Lewis, 2015). Beach erosion occurs when the sediment outputs from a system exceed the sediment inputs and a deficit in sediment budget is created. Erosion on a particular beach is generally due to more than one driver, although one cause if often dominant. Below, the most common causes for beach erosion are listed:

 reduction of sediment supply from eroding cliffs  reduction of fluvial sediment supply to the coast  reduction of sediment supply from the sea floor  reduction of sand supply from inland dunes  submergence and increased wave attack  increased wave energy because of increased storminess  losses of beach sediment alongshore  a change in the angle of incidence of waves  interception of longshore drift by breakwaters or groynes  increased loss of beach sediment to the backshore  beach weathering, including erosion of beach sediment  a rise in the beach water table  removal of beach sediment by runoff  increased scour by wave reflection from an artificial structure  extraction of sand and shingle from the beach. (Bird & Lewis, 2015)

Erosion can be long-term, resulting in a net retreat of the coastline, or temporary, reversed by following periods of accretion. Useful terms for these two types of erosion are (1) chronic erosion and (2) acute erosion.

Chronic erosion along exposed coastlines is typically induced by variations in the longshore sediment transport, and is caused by gradients in morphological controlling factors along the coastline. These factors include changes in coastal orientation, sediment availability and/or wave direction or energy. In cases where the sediment transport increases in the direction of transport, a coastline will receive less sediment upstream than what is lost. This deficiency leads to erosion of the coastal profile causing the coastline to gradually move in the landward direction (Hasløv and Kjærsgaard, 2013). The rate of chronic erosion is difficult to quantify, because beaches are dynamic in both the special and temporal scale and long term monitoring is rare and costly.

Acute erosion takes place during extreme weather events when large waves and higher water level cause erosional processes to take place on the back beach, eroding sediments from dunes or escarpments. During a high water level event a beach will adjust towards a new equilibrium profile that matches the short term forcings;

Chapter 2 / General theory

this leads to a flattening of the profile where sand from the beach is moved offshore (this is further explained in section 2.5).

The littoral sediment budget is a calculation based on the volume of sediment inputs (sources) and sediment outputs (sinks) to and from a given beach and nearshore system. The most common sources and sinks are schematized in Figure 2.1.1.

Figure 2.1.1 Schematization of the most common sources and sinks for a littoral sediment budget. (Figure adapted Davidson-Arnott, 2010)

If the sediment budget along a given coastline is positive i.e. the amount of sediment entering the system exceeds the amount of exiting sediment, deposition will occur and the shoreline will prograde. Contrary, if the above is reversed, coastal erosion will occur.

Quantification of a sediment budget for a coastline or subsection is difficult, and is therefore often merely informed guesses (Davidson-Arnott, 2010). However, supply of sediment from coastal erosion is one of the easiest sources to quantify as estimates of the annual volume supplied from the coastline to the littoral system can be calculated from the recession rate.

2.2 Responses to beach erosion A commonly applied response to beach erosion has been to build solid structures designed to protect and maintain existing beaches in order to prevent further coastline recession. By building structures such as sea walls or boulder rampers along an eroding beach, retreat of the coastline can be haltered. However, reducing the natural supply of sediment from the backshore, often leads to depletion of beaches in front of the structure due to wave refraction (Bird and Lewis, 2015).

As described in section 1.1, a widely recognized paradigm shift in the approach to coastal management has occurred during the last decades (Stive et al., 2013a). Alternatives to hard structures have become increasingly popular. These methods are usually termed soft engineering methods and are intended to work with the existing coastal processes along a given coast. The most widely applied method of soft engineering is beach nourishment. Other methods in this category include dune restoration using vegetation, managed coastline retreats and beach scraping (Bird and Lewis, 2015).

Along eroding developed beach fronts, protection is commonly practiced by combinations of periodic nourishments with or without coastal structures to stabilize a beach over the long term (Benedet et al., 2007). Although beaches can be restored in many ways, beach nourishment has become the most commonly practiced method of shore protection in both the United States and Europe (Bird and Lewis, 2015).

Chapter 2 / General theory

Hard structures Revetments are generally introduced to prevent wave attacks on eroding coasts, usually in front of receding cliffs or dunes with a beach in front that has not been sufficient enough to prevent wave energy from eroding the back beach.

Modern revetments are usually large stone or concrete walls designed to protect the coast from the incoming breaking waves. When the incoming waves meet the sea wall they are reflected seaward, which may then cause scouring away of the beach. Construction of revetments on a particular section of a coast to protect housings or infrastructure is usually followed by continued recession of adjacent coastlines.

Another response is to introduce breakwaters, which are designed to retain a beach by protecting it from wave attack. Breakwaters are detached structures parallel to the coastline, designed to interrupt and reduce wave action in order for beach accretion to occur on the landward side, and at the same time shelter the existing beach from erosive waves. Offshore breakwaters are built 50-200 m offshore, and wave breaking here cause the energy to be diffracted before reaching the beach (Bird and Lewis, 2015).

Groynes offer the same effect; inserting multiple groynes along a coastline help retain the longshore drift and in that way stabilize the coastline. Sediment drifting alongshore is trapped in the compartments between the groynes, and accumulates here until sediment starts to bypass. Interception of the longshore sediment drift causes reduction in sediment supply to downdrift beaches, causing the erosion problem to transfer along the coastline.

Beach nourishments Beach nourishment is the method where sand is placed on a beach to advance it seaward. This can be perceived as an artificial source of sediment introduced in order to counter erosion caused by a negative sediment budget (Dean, 2002). Nourishments have been used for preventing the undermining of solid structures built as means of beach protection, but recent studies show that using nourishments alone to maintain or increase beach width can mitigate many hazards (eg. Yoshinda et al., 2014).

Generally, nourishment methods can be categorized according to the placement of the nourishment sediment: (1) traditional beach nourishment, where sediment is placed mainly in the subaerial beach and/or the dunes (Figure 2.1 a); (2) shoreface nourishment, where submerged nearshore bars are created. The main impact of shoreface nourishment is to feed the shoreface with sediment, with the objective of modifying the surf zone processes to result in a non-eroding beach (Figure 2.2.1 b) (Stive et al., 2013a).

Figure 2.2.1 Conceptual diagram displaying beach nourishment methods. a) traditional beach and dune nourishment where sand is placed directly on the beach and dunes. b) Shoreface nourishment, where natural marine processes redistribute the sand that is placed under water to gradually protect the beach over time. (Stive et al., 2013a)

Chapter 2 / General theory

Beach nourishments may be considered as shoreline perturbations. If placed along a somewhat straight coastline, beach nourishments will under the action of waves spread out along the shoreline and within the nourishment project area there will be a loss of sand. The process where sediment is removed from the nourishment and deposited in adjacent coastal areas is referred to as “spreading out” (Dean, 2002).

In order to predict the process of spreading out, it is necessary to relate the longshore sediment transport to the nourishment planform perturbation, as the gradients in longshore sediment transport is determined by the angle between the incoming waves and the shoreline. This will be elaborated in section 2.6.

2.3 Wave processes The inner Danish coasts are wave dominated and micro tidal, which means that the main factor driving coastal change, is the incoming waves. The energy input from waves drives currents and create gradients in energy along the coastline. As waves approach a coastline, the wave shape is transformed as the wave is influenced by the bathymetry and the decrease in water level. When waves begin to interact with the seabed, several processes are induced. In the following, wave characteristics, wave transformation and the main processes influencing shoreface morphology and sediment transport are explained.

2.3.1 Wave characteristics In nature, waves of different height, period and celerity interact creating an irregular wave field and any representation of actual wave action by one set of parameters is a simplification. A simplification of natural waves is needed, and commonly a statistical wave analysis is applied in order to determine representative values. The most important wave representation parameters are:

Hs significant wave height, the highest 1/3 of the wave record (m) H12 the wave height that is surpassed 12 hours a year (m) Hrms root mean squared wave height (m) Hb breaking wave height (m) T wave period (s) α wave angle (degrees) αb breaking wave angle(°) C wave celerity (m s-1) L wave length (m)

An alternative approach to statistically classifying a wave record is spectral analysis, where the dominant wave in a wave record is selected. The selection is based on the proportion of wave energy contained within different frequencies. When using spectral analysis it is evident that averaging wave properties can be a misrepresentation of the actual wave conditions (Masselink et al., 2011). It is often necessary to apply statistically determined wave parameters because the total wave record may not be available.

2.3.2 Wave energy Waves are efficient carriers of energy, which is transferred from the wind. Wave energy is proportional to H2 and L, and the total wave energy, or wave energy density, (E) expressed as the energy per unit area (N/m) can be calculated as follows:

1 퐸 = 휌𝑔퐻2 equation 1 8 in which 휌 is the density of water.

Chapter 2 / General theory

Since the wave energy is proportional to H2, an increase in wave height yields a large change in wave energy. The wave energy flux (P) expresses the rate at which the energy is being translated along with the wave:

푃 = 퐸퐶𝑔 equation 2 where Cg is the wave group celerity, the group celerity and wave celerity is related trough the parameter n:

퐶𝑔 = 퐶푛 equation 3 In deep water the waves travel twice as fast as the wave group and n = 0.5 but in shallow water the wave celerity becomes the same as the wave group celerity and the parameter n = 1 and Cn is equal to C, this means that the energy flux is given by

푃 = 퐸퐶 equation 4

Wave energy and the conversion of energy are important parameters when considering the wave parameters as they are affected by shoaling and refraction. The level of wave energy reaching the shoreline determines the strength and rate of sediment transport and erosion.

2.3.3 Wave transformation As the wave propagates into intermediate and shallow waters, the wave is affected by bottom contours, and this induces shoaling, refraction, breaking and swash. These wave transformation processes are separately described below.

Shoaling Wave shoaling takes place outside of the surf zone up until the point of wave breaking. During shoaling the wave shape, height, celerity and length is transformed due to interaction with the seabed. The only property that is not affected by shoaling is the wave period, which is usually assumed constant.

As water depth decreases, the wave is slowed down by bottom friction, and C and L decreases. Because of the difference in water depth under the crest and trough, the effect of bottom friction is more pronounced in the trough, and wave orbital velocity skewness develops such that the onshore directed orbital velocity becomes larger than the offshore directed orbital velocity.

When assuming that the wave energy is constant, disregarding loss of energy due to bottom friction and growth in energy from continued influence of wind, the change in wave height during shoaling can be described by the following equation:

1/2 퐶푔1 퐻2 = 퐻1 ( ) equation 5 퐶푔2 where the suffixes represent two successive points going in the direction of wave propagation. As the waves translate, the wave height increases up until the point of breaking, where the energy arriving with the wave is dissipated.

Refraction Refraction is the bending of waves due to varying water depths. When waves approach the coastline and bottom contours at an angle, the transformation of the progressing wave is affected. Refraction is an important factor in determining the magnitude of wave erosion, impacts on harbor and shore protection structures and the direction and magnitude of longshore sediment transport. Refraction allows wave energy to reach parts of complicated shorelines that face different directions from that of the incident wave (Davidson-Arnott, 2010).

Chapter 2 / General theory

Assuming a relatively straight coastline with shoreline parallel bottom contours, waves approaching the coast at an angle will be aligned. As the wave progresses towards the coast, the influence of the bottom will vary with depth.

The parts of the wave that reaches shallow water first will be influenced by friction slowing down the wave and creating a gradient in wave celerity along the wave front; the part of the wave that is not influenced by the bottom will catch up to the part that has already reached shallow water. The wave will rotate and gradually become parallel with the bottom contours and the coastline. The change in wave direction can be described applying Snell’s law, implicating that the relation between wave angle and bottom contour is constant: sin 훼1 sin 훼2 = = 푐표푛푠푡푎푛푡 equation 6 퐶1 C 2 where α is the angle between wave crests and bottom contour. The subscription refers to two successive points in the direction of wave propagation.

Assuming shoreline parallel contours the wave angle can be directly related to the depth using the deep water angle:

퐶 푠𝑖푛훼 = 푠𝑖푛훼0 equation 7 퐶0

C0 and αo are the deep water wave celerity and the deep water wave angle, respectively. Refraction along a straight coastline leads to a spreading of the wave orthogonals and from this follows a spreading of the wave energy density. Snell’s law cannot predict the transformation of waves passing over a complex bathymetry, and in cases where the coastline and the contours are not straight and parallel the refraction patterns will create zones of wave convergence and divergence, leading to gradients in wave energy along the coastline. Where waves pass over a localized area of shallow water, there will be a focusing of the wave energy; wave convergence, whereas local areas of deeper water will lead to spreading of wave energy; wave divergence.

Wave energy can also be spread along the wave crest; wave diffraction. Diffraction is the response to sudden change in bathymetry, a reef or a headland or constructions such as harbors and seawalls. When the wave encounters a sudden change in topography energy is passed along the wave crest instead of in the direction of wave propagation, which allows for waves to spread into the shadow area of the encountered obstruction (Masselink et al., 2011).

Breaking The most notable wave transformation process is wave breaking. Breaking occurs in the surf zone when the wave becomes unstable because of decrease in water depth. The instability occurs when the velocity of water particles in the wave crest exceeds that of the wave trough, causing water to leave the wave form (Short, 1999). Breaking is of large importance to the coastal morphodynamics, as the sudden release of energy drives currents, which transports sediment.

As the wave progresses onshore depth becomes a controlling factor of wave height. The relation between wave height and water depth is referred to as the breaker index (γ), and is expressed as:

퐻푏 = 훾h푏 equation 8 where hb is the water depth at breaking.

Chapter 2 / General theory

Several studies have been carried out in attempt to determine a general value for the breaker index. The most widely used value of γ is 0.78. Natural breaking conditions vary based on beach slope and wave type, and in general it has been found that the breaker index decreases with wave steepness and increases with beach gradient (Short, 1999).

The depth dependency of wave breaking causes a feedback between topography and wave processes. Understanding the wave climate and the breaking conditions is of large importance when investigating sediment transport; where and at which wave height the waves break is a controlling factor for the potential sediment transportation.

2.4 Sediment transport Sediment transport is the mechanism which translates the work of the hydrodynamic forcings and processes into morphological change (Aagaard and Hughes, 2003). Modification of the coast takes place through the erosion, transport and deposition of material that is either eroded by waves and currents or brought to the coast by for example rivers (Davidson-Arnott, 2010).

Morphodynamic changes of a beach can be considered as is a three dimensional, but in order to describe the overall changes it is functional to segregate between changes in planform; the changes in coastline position and form, and changes in profile; the cross-shore profile evolution. The dimensional changes are interdependent, but act and are observed on different timescales. In most cases the spatial gradients in cross-shore sediment transport is larger than those of the longshore transport. Sediment transport is generally simplified by separating the transport vector into cross-shore and longshore components relative to the orientation of the shoreline or the depth contours (Aagaard and Hughes, 2013).

The upper shoreface morphology is constantly evolving and adjusting to the in situ hydrodynamic conditions as it feeds back onto the processes that forced the morphological change. This constant change is referred to as morphodynamics, see figure 2.4.1.

Figure 2.4.1 Main components of coastal Fluid motion Topography morphodynamics and the feedback Waves & between morphology and process. Current Stratigraphy Waterlevel

∆t

Sediment transport

Mass, acceleration, velocity and stress are the fluid properties that are directly relevant for sediment dynamics. The sequence of processes that control localized sediment movements are (1) erosional entrainment of sediment into the flow via stresses and forces acting on the bed induced by the fluid; and (2) transport of sediment via momentum transfer from the fluid to the sediment, and (3) settling or deposition of sediment back on the bed via gravity (Masselink et al., 2011).

The total force that is exerted on a seabed is referred to as the total stress, consisting of normal stress and a shear stress component. The dynamic behavior of sediment moving in a fluid is strongly determined by the sediment grain size. When a given grain rests on the seabed experiencing no acceleration, the lift, drag (friction between

Chapter 2 / General theory

fluid and particle) and weight forces acting on the grain are in equilibrium. In order for the grain to be lifted from the seabed, the lift and drag forces must overcome the weight force.

Based on experimental data, Shields (1936) proposed a relationship between bed shear stress and grain size, causing the grain to move, and this critical bed shear stress was transformed into a non-dimensional parameter, known as the Shields parameter. The expression for prediction of the critical Shields parameter (and bed shear stress) is:

0.30 휃 = + 0.055[1 − exp (−0.02퐷)] equation 9 푐 1+1.2퐷 Once in motion, the mode of transport that a sediment grain takes is largely dependent on the grain size and the current speed and direction. In currents, sediment can be transported as either bedload or suspended load. As bedload, the grains are supported by continuous or sporadic contact with the seabed. This is a relatively slow mode of transport, and typically occurs when currents are weak or grain sizes are in the range of pebbles or boulders. The bedload layer is typically only a few millimeters high, and therefore it has proven difficult to measure grain velocities and concentrations for this transport mode. In suspended load, the grains are supported by turbulence within the water column, this mode typically occurs when strong currents are transporting sands or moderate currents are transporting silts (Masselink et al., 2011).

The sediment transport rate Q is the sum of suspended load and bedload, and is defined as the mass of transported sediments.

In coastal and nearshore areas, the capacity for sediment transport is not unlimited, and the volume of transported sediment is strongly influenced by the interrelationship between the hydrodynamic processes, bathymetry, coastline geometry and sediment supply. Sediment transport tends to take place within littoral cells, which are a specific geographic area of the coast within which the sediment is moved. Littoral cells are often delimited at the coast by bedrock headlands.

2.5 The cross-shore profile Different wave regimes dominate across the nearshore, resulting in different sediment transport characteristics. The shoreface is the upper part of the continental shelf that is affected by wave processes and extends from the landward limit of wave runup to the seaward limit for wave driven sediment transport.

The definition of the shoreface includes the lower shoreface, upper shoreface and the beach face encompassing the swash zone (Figure 2.5.1).

Figure 2.5.1 Schematic diagram of the nearshore as defined by Aagaard and Hughes (2013).

The lower shoreface is dominated by shoaling wave processes, and wind- and tide-generated currents are also significant contributors to sediment transport. The upper shoreface is the region where erosion and accretion

Chapter 2 / General theory

result in measureable changes in bed elevation on a yearly timescale, this is referred to as the active profile (Short, 1999). The changes in bed elevation are usually largest in the vicinity of the beachface and decrease progressively offshore.

During beach erosion, sand is not only transferred from the beachface to the surf zone bars, but also some distance beyond the surf zone. This results in a lowering of the inner part of the upper shoreface and accretion in the offshore part of the profile (Cowell et al., 1999). In phases of beach recovery this process reverses.

The depth of closure conceptually the limit between the upper and lower shoreface, and thereby the active profile, although movement of sand and bedforms does occur at greater depths. The definition of the closure depth rests upon the work of Hallermeier (1981) who analyzed the envelope of profile change on the upper shoreface during a typical year. The depth of closure reflects the largest storm waves, and it is predicted by the imperial equation provided by Hallermeier (1981):

2 퐻푠12 ℎ푐 ≈ 2. 28퐻푠12 − 68.5 ( 2 ) equation 10 𝑔푇12 where T12 is the wave period associated with H12 and g is the acceleration caused by gravity. The offshore limit of the shoreface is not distinguished by any sharp break in the topography, but there is often found to be a distinctive break in sediment characteristics. The upper shoreface is usually made up of well sorted sediment with decreasing grain size in the seaward direction until the closure depth (Cowell et al., 1999). On the lower shoreface, the sediment size distributions are complicated. Firstly, the offshore limit of the lower shoreface and thereby the limit of on- and offshore exchange of sediment is not as clearly defined as the active depth, which delineates the nearshore limit. The actual limit of the lower shoreface corresponds to the depth at which wave action ceases to mobilize the sediment at the seabed.

The variation in transport rates and directions are responsible for zones of accretion and erosion in a given profile. In high-energy periods the sediment flux is directed offshore due to the dominant undertow driven by the high energy released from the incoming waves. This situation generates offshore bar migration, caused by a zone of erosion on the landward slope of the bar and a zone of accretion on the seaward slope. In low-energy situations, transport rates are lower and sediment fluxes will be mainly onshore directed, due to orbital velocity skewness. With no further factors added this skewness in velocity leads to a net onshore transport.

Beach erosion is usually marked by the evolution of a concave-upward cross-shore profile, whereas accreting beaches typically have convex-upward profiles. There is sometimes found an erosional scarp, where an upper convex beach is being undercut as a lower concave profile becomes established. Backshore dunes are often cliffed behind beaches that have been lowered and cut back by erosion.

Equilibrium profile Configuration of the coastline is a continued process where the initial landscape, structure and local geology adjust to the strength and character of the hydrodynamic forcing. In a given profile there is a constant complex change between periods of erosion and accretion, but seen over time the profile will converge towards an idealized state, where a dynamic equilibrium between the hydrodynamic forcings develops. The development of equilibrium profiles presumes relatively stable boundary conditions, such as wave climate and sediment availability (Aagaard et al., 2008).

Most beach profiles exhibit broad similarities: a) they are generally concave upwards; b) beaches composed of coarser sand tend to be steeper than those of fine sand; and c) storm waves tend to transport sand seaward, cause beach recession and a reduction in the profile slope (Dean, 2003).

Chapter 2 / General theory

The concept of an equilibrium profile assumes that on a beach with continued existence of sand an idealized concave beach profile can be used as a representation of the actual profile. The equilibrium concept provides insight into the morphodynamic coupling between the processes responsible for shoreface form and changes in this.

Brunn (1962) proposed the following expression for the shape of an equilibrium profile:

ℎ(푦) = 퐴푦2/3 equation 11 where h is the water depth at distance y from the shoreline. The coefficient A is the profile scale parameter. Based on the assumption that sediment characteristics is a controlling factor of beach slope, Dean (1987) fitted the profile scale parameter to the settling velocity (ws) for a given mean grain size:

0.044 퐴 = 0.067푤푠 equation 12 Equilibrium profiles are used extensively in the engineering field as an input to predict the form of nourished beach profiles where little field data available (Davidson-Arnott, 2010).

Theoretical conditions for equilibrium profiles and shoreface theory provide useful references for comparing shoreface morphology observations in nature, but the observed morphology cannot be expected to mirror the theoretical equilibrium (Cowell et al., 1999). The effect of local geological make-up further complicates these predictions. The theoretical equilibrium is highly simplified as a matter of necessity, and therefore cannot be expected to represent real-world conditions.

Sudden changes due to severe storms are normally viewed as a temporary distortion of the upper shoreface (Short, 1999). Storm conditions can produce a section of the upper shoreface, where the profile is displaced landward and the point on the profile corresponding to the closure depth is moved seaward.

The concept of an equilibrium profile validates assuming a constant profile over time, but the preservation of sediment within the active beach profile disregards an offshore loss of sediment. The difference in orientation and incoming wave angle will serve as a reference for system stability.

2.6 Longshore currents and littoral drift In contrast to cross-shore sediment transport, littoral drift, is typically unidirectional over large spatial and temporal scales, and is driven by wave-induced longshore currents due to the arrival of waves at an angle to the shoreline or bottom contours (Bird and Lewis, 2015). Along coasts composed of mobile, non-cohesive sediments, relatively small gradients in alongshore sediment transport can locally cause great changes in shoreline positions.

The alongshore sediment flux, QS, is a nonlinear function of the local shoreline angle relative to the wave crests, hence, the magnitude of alongshore sediment transport is a function of the relative angle between wave crests and the local shoreline orientation (Slott et al., 2010).

The process of waves arriving at an angle to the shoreline producing the longshore transport of sediment can be described by two main mechanisms: (1) waves generate a longshore current within the upper shoreface that transports the sediment that is already suspended above the seabed; (2) swash transport, can be described as the saw-tooth mechanism, where sediment is moved onto the beach at an oblique angle under the action of breaking waves and swash followed by a seaward transport of the sediment normal to the shoreline due to gravity-driven return flow (Komar, 1971).

Chapter 2 / General theory

It has been demonstrated that longshore currents generated by waves can be related to the longshore component of radiation stress.

Shoaling and breaking of waves causes a translation of water mass shoreward driving an excess flow of momentum towards the shoreline, which causes a residual stress on the water column (Masselink et al., 2011). Radiation stress measures the excess momentum associated with waves and the gradient of this in the surf zone leads to wave set-up. When waves break at an angle to the coastline the longshore-directed radiation stress is given by:

푆푥푦 = 퐹푚 sin(훼) cos(훼) equation 13 in which Fm = ECg , which is is given by:

1 퐿 2푘ℎ 퐸퐶 = ρh퐻2 + [1 + ] equation 14 𝑔 8 푇 sinh (2푘ℎ

By balancing the alongshore-directed momentum flux with seabed friction forces and eddy viscosity, the steady longshore current velocity can be predicted. The velocity will increase from wave breaking until it is balanced by the opposing forces of bed friction and bed shear stress.

For irregular waves, an empirical estimate of the mean longshore current on planar beaches is given by Komar (1979):

푉 = 1.0√𝑔퐻푏푠 sin(훼푏) cos(훼푏) equation 15 where 훼푏 is the angle of the breaking wave to the shoreline. The presence of bars in the nearshore zone complicates the task of predicting longshore current velocity because of variations in wave set-up, breaking and topography. The maximum current speed tends to occur just landward of the bar crest or in the trough landward of the bar (Davidson-Arnott, 2010).

At shorelines where waves do not arrive at an angle to the coast, there is no driver for the longshore current, and where the waves are parallel to the coastline, no breaking occurs, and thereby no energy for driving the longshore current is released. The longshore flux exhibits a maximum when the deep water wave angle relative to the coast approximately equals 45°, assuming that the shore-parallel contours reflect the shoreline orientation (Slott et al., 2010). Figure 2.6.1 illustrates the relationship between the incidence wave angle and the alongshore sediment transport, referred to as a Q/ 훼-curve.

Figure 2.6.1 Schematic relationship between alongshore sediment transport, QS, and relative wave angle showing that the maximum in QS occurs at wave incidence ~45 degrees. (Kærgaard, 2015)

Chapter 2 / General theory

Various expressions relate wave-induced alongshore sediment transport to its driving forces; wave height and angle. The most common of these relationships, is referred to as the CERC (Coastal Engineering Research 3 -1 Center) equation, which relates the volumetric alongshore sediment transport (Ql, m day ) to the breaking wave height and wave angle:

5/2 퐾 퐻 √𝑔/(퐻 /ℎ ) sin2(훽−훼 ) 푄 = 푏 푏 푏 푏 equation 16 푙 8 (1−휌)(푠−1) 2 where K is the sediment transport coefficient, which is a function of sediment size, 휌 is the sediment porosity and β is the angle of the outward beach normal.

There is uncertainty about the correct value of K, which in the original CERC formula is assigned the value 0.39, but later studies values down to 0.2 have been applied for sandy beaches (Bayram et al., 2007).

In nature, the longshore currents are not unidirectional, and therefore the total littoral drift is likely to exceed the net rate many times.

Natural coastlines will vary in orientation, resulting in longshore variation in wave incidence angle and wave energy causing changes in the longshore wave energy flux. The littoral drift rate is proportional to the wave energy flux, and therefore orientation of coastline with respect to the incidence waves controls changes in the coastline. Where the littoral drift rate increases, progressively more sediment will be entrained. This sediment will have to be provided by erosional processes, and over long timescales a coastline subject to increasing littoral drift rate is expected to retreat (Masselink et al., 2011).

Planform equilibrium orientation In a costal cell the shoreline orientation will converge towards an equilibrium orientation determined by the wave climate. The response time and adjustability is higher in areas where the coastal zone is made of up unconsolidated material, such as the Danish coastline (Aagaard et al., 2008).

The equilibrium orientation is the orientation at which the net longshore littoral transport is zero; this is also referred to as the main incident wave angle (Mangor, 2008, DHI and Hasløv & Kjærsgaard, 2013). If the coastal orientation is different from that of the equilibrium, the coastline is unstable and the direction of littoral sediment transport can be determined based on the difference between actual and equilibrium orientation.

For a natural wave climate the equilibrium orientation can be determined as the orientation at which the long- term longshore sediment transport rate is zero. The orientation can therefore be useful as an indication of the overall littoral drift direction and shoreline stability.

2.7 Application of numerical modeling for prediction of beach nourishment evolution A beach nourishment project causes an abnormality that alters the preexisting longshore sediment transport patterns (Work and Dean, 1995). Therefore there are many details in the design of a beach nourishment project to consider, where one is which coastal morphodynamic numerical model to apply in order to predict the performance of the project and the evolution in both cross and longshore directions a given number of years into the future.

Numerical modeling has been much used by engineers as a basis for computational simulations of coastal processes (hydrodynamics and sediment transport). Models are used to study the effects of the integrated processes of waves, tides and currents on nearshore sediment flow, and the ways in which these processes and responses are modified by coastal protection initiatives (Bird and Lewis, 2015).

Chapter 2 / General theory

The general approach to models of shoreline change involves the division of the coastline into a large number of compartments, and equations relating the alongshore sediment transport rate to the wave parameters and to velocities of alongshore currents are employed to calculate the shift of sand from one cell into its neighbor. The application of a continuity equation allows for the conversion of volumes of sand entering or exiting a particular cell into resulting shoreline changes. A geometric assumption is that sand is transported alongshore between two well-defined limiting elevations on the profile. The shoreward limit is located at the top of the active berm, and the seaward limit is located at the depth of closure. Restriction of profile movement between these two limits provides the simplest way to specify the perimeter of a beach cross-sectional area by which changes in volume, leading to shoreline change, can be computed.

Numerical models have become increasingly numerous and sophisticated in recent years. First-generation models used regular wave inputs, had very simple topographical extrapolation algorithms and did not allow for diffraction or wave-current interaction (Davidson-Arnott, 2010). Newer models such as the MIKE suite models developed by DHI Water & Environment (DHI), combine wave prediction of random wave fields with sophisticated modeling of nearshore bathymetry, refraction and diffraction. These newer and more sophisticated models offer the potential for better modeling of the natural system and assessment of the impact of coastal alterations such as beach nourishments or structures.

There does, however, follow a large number of uncertainties along with the modeling of the highly dynamic coastal zone, as for any other dynamic natural system. There are many parameters to take into account, for which reason model outputs always require careful and critical analysis against a range of coastal indicators (Davidson- Arnott, 2010).

Chapter 3 / Study area

3 STUDY AREA

The areas of interest are located along the western coast of North Zealand, Denmark. The summary of findings in previous studies with regards to longshore transport and historic erosion rates was provided in section 1.4. These will serve as a basis for comparison of the findings in this present study. This chapter provides descriptions of the coastline sections in question and the governing hydrodynamic conditions.

3.1 General description The entire coastline along the northern part of Zeeland faces the marine sub area of Kattegat with a relatively long fetch towards northwest. This study will focus on subparts of the coastline between Hundested and Gilleleje. The sections are shown in Figure 3.1.1.

Figure 3.1.1 Aerial photographs from 2014 showing the coastlines of interest. Top left: The entire coastline between Hundested and Gilleleje. Top right: Tisvildeleje. Bottom left: Raageleje. Bottom right: Udsholt Strand. Based on overall orientation, the coastline of the entire northern Zealand can be divided into two; the western stretch of coast between Hundested and Gilleleje is orientated towards northwest, whereas the eastern coastline from Gilleleje to Helsingør is orientated northeast.

Chapter 3 / Study area

Overall, the coast is a moderately exposed littoral dune and cliff coast, generally with barred profiles (see aerial photographs in Figure 3.1.1). In previous observations and sediment sampling in the area, the sediment size has been found to vary between 0.2 and 0.5 mm. The occurrence of sand and pebbles along the coast can vary on a yearly basis, but overall, there is a continuous sand transport zone from southwest to northeast.

As the results of the shoreline analysis will show in section 5.2, the beaches along the coastline are retreating. Along several subsections, the former sandy beaches have completely eroded, causing the coastline to lose its scenic, recreational and touristy qualities. Gilleleje harbor is located at the northernmost part of Zealand, and here, the sediment is transported northeast along the coastline from Hundested causing recurring navigational problems at the harbor, as the harbor entrance acts as a sediment sink. Approximately 15,000 m3 sand is being dredged from the harbor entrance and an additiona l4,000 m3 of gravel is being sourced for commercial purposes from the accreting beach section west of Gilleleje Harbour (DHI and Hasløv & Kjærsgaard, 2013).

3.2 Geological setting Since the Danish landscape is primarily a glacial landscape, the coasts are predominantly composed of loose sediments, which can be degraded, transported and redeposited by waves and currents. The glacial deposits at northern Zealand initially resulted in the formation of a 25-50 m wide rampart consisting of large rocks and stones along most of the coastline. Over the past 500 years, the effect of the coastal protection provided by this reef has been lost, due to the removal and use of these rocks for large building projects such as the foundation of Kronborg Castle and the fortification of Copenhagen (Petersen, 2016).

The study area consists of a range of different landscapes, and thus the sediment types, hinterlands and beach types vary. A coastal cliff rises along large parts of the coastline, in several places rising as high as 20-30 m above sea level (see elevation map in Appendix A).

The modern landscape was covered by the Weichselian Ice Sheet, and therefore displays a variety of depositional landforms (Figure 3.2.1). The coastline consists of semi-hard moraine sections (till), with marine deposit shorelines in between. Land sediments are shown in the sediment map found in Appendix A.

Figure 3.2.1 Chart of the northern coast of Zealand, Denmark, showing seabed sediments and landscape elements. For land sediments, see Appendix A.

Chapter 3 / Study area

The hard sections of the coastline have provided material for building up the sedimentary shorelines, as the loss of material from the protruding areas has created marine forelands (Figure 3.2.1). When waves reach an undulating coastline they will refract and converge; the wave energy will be higher at protruding sections and lower in the bays. As a result, the protruding sections erode and part of the sediment is transported along the coastline and deposited in the bays, and thereby an undulating coastline smoothens, converging towards an equilibrium orientation. The orientation of the coast between Tisvildeleje and Gilleleje varies between 315 degrees and 340 degrees, approximately perpendicular to the dominating wave direction.

This process of erosion and straightening has caused the forming of a straight shoreline, where the moraine landscape has been cut back to nearly a straight line with marine dune landforms in between. As the straightening by erosion continues, the initially accumulative parts of the coastline will begin to erode back (Mangor, 2004).

The off shore water depth along the coast is 15-20 m. However, at Gilleleje Flak located seaward from the harbor, the off shore water depth is as shallow as 6 m (COWI, 2009).

3.3 Wind, waves and tides The governing wind directions are from directions south-southwest to west-northwest. The wind rose in Figure 3.3.1 shows the directional distribution of the observed wind speeds from 1993 to 2008.

Figure 3.3.1 Wind directions at Anholt Station (1993-2008), north of the study area in Kattegat (COWI, 2009).

The largest wind speeds occur during storms from western and northwesterly directions. The governing wind directions are reflected in the overall wave climate, as the height, length and period of wind waves increase with increasing wind speed and with the length of time and distance over which the wind is in contact with the sea surface. The combined effects of the wind pattern, site specific fetch lengths and the orientation of coastline produces a wave climate, where around 50 % of waves reaching the area approach with angles from 270-360 degrees (COWI, 2009).

Available hindcast wave data, extracted at offshore locations along the coast are shown in Figure 3.3.2. The wave roses show that there is an increase in the proportion of the waves from west-southwest along the coast towards Gilleleje.

Chapter 3 / Study area

HS12 is between 1.9 m and 2.7 m, with the largest HS12 beteween Tisvildeleje and Udsholt, and smallest at Hundested, signifying that the wave height increases with fetch length. According the exposure classification scale provided by Mangor (2004), this classifies this coast as a medium exposed coastline (HS12 = 1-3 m). Along the coastline east of Gilleleje, the shores less exposed to waves from the westerly directions.

By use of equation 10, an active depth of 6 m was determined and is used for calculations of volumetric sediment calculations in following sections.

Figure 3.3.2 Alongshore variability of 1993-2012 wave roses at selected locations off northern Zealand.

In the inner Danish seas, the water level is almost exclusively controlled by local weather conditions. Strong north and northwesterly winds generate sea level rises in southern Kattegat. Conversely, strong winds from southeast will cause a lowering of the sea level along the northern coast of Zealand.

The 1-year extreme water level event at Hundested is +1.08 m, whilst the 20, 50 and 100 years events are +1.48 m, +1.57 m and +1.64 m, respectively (COWI, 2009). The storm in 2013, Bodil, caused the water level to exceed the 100-year event by almost 0.6 m because of its long duration of winds from northwest pushing water from Skagerrak into Kattegat (mean wave direction was 334 degrees with a significant wave height of 3.3 m (Danish Coastal Authority, 2014)).

3.4 Local sediment budget The difference between the actual coastline orientation and the equilibrium orientation is an expression of how far the coast is from being oriented normal to the dominant wave incidence angle. Therefore, the potential

Chapter 3 / Study area

erosion rates are higher along sections of the coastline where the difference between the coastline orientation and the dominating wave direction is larger. At Hundested, the average coastline orientation is in equilibrium with the dominating wave direction, causing longshore sediment transport here to be at a minimum. Due to changes in coastline orientation and increase in the fraction of waves from westerly directions and increasing wave height, the longshore sediment transport increases from west to east along the coastline. Since a comprehensive survey of the coastal profile along the coast of North Zealand does not exist, the estimates of littoral drift rates are based on knowledge available.

The actual erosion rates cannot be expected to equal the potential littoral drift. The sediment transport depends on the availability of sediment and is also affected by the existing coastal protection structures, which causes the actual littoral drift to be lower than the potential drift. As outlined in section 1.1, the littoral drift estimates vary greatly. However, multiple sources have stated that a maximum littoral of 50.000-70.000 m3 y-1 near Gilleleje is realistic. Figure 3.4.1 shows where the study conducted by DHI and Hasløv & Kjærsgaard (2013) estimates the potential littoral drift to exceed the actual drift.

Figure 3.4.1 Potential and actual observed littoral drift in northeasterly direction along the coastline between Hundested and Gilleleje. (DHI and Hasløv & Kjærsgaard, 2013).

There are two main sand deposits along the coastline which supply the downstream adjacent subsections with sediment; one is at Tisvilde Hegn, and the other is at Heatherhill.

In the past 100 years the natural sediment input to the beaches have decreased, due to the geological stage; the coastline is overall in the late stage of simplification, erosion is taking place along an increasing part of the coastline (Mangor, 2004; Fællesudvalget for Kystpleje og Kystsikring af Nordkysten 1987).

In order to counter beach erosion from the areas with high potential erosion rates, beach protection structures have been implemented to protect and maintain the existing beaches and prevent further recession of the

! !! !! !!! !! !!! !!!!!! !! !!!!! !!!!! !!! !!! !!!!! !!!! !!! !!!!!!!!!!!! !!! !! !! !! !! !! !!! !!! !!! !!! !!! !!! !!! !!!! !!! !!!! !!!! !!!! !!!! !!!! !!!! !!!!! !!!! !!!!! !!!!! !!!!! !!!!! !!!!! !!!!! !!!! !!!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!!! !!! !!!! !!!! !!!! !!!! !!!! !!!! !!!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !! !!! !!! !!! !!! !! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !! !!! !! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!!! !!!! !!!! !!!! !!!! !!!! !!! !!! !!! !! !! !! !! !! !! !! !! !! !! !!! !! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!!! !!! !!!! !!! !!!! !!!! !!!! !!!! !!! !!!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! ! !!!!! !!!!!!! !!!!!!!!!!! !!! !! !! !! !!! !!! !!! !!! !!! !!!! !!!! !!!! !!!!! !!!!! !!!!! !!!! !!! !!! !! !! !! !! !! !!! !!! !! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !! !! !! !! !! !! !! !! !! !!! !!! !!! !!! !!! !! !!! !! !!! !!! !! !!! !! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!!

Chapter 3 / Study area

coastline. The purpose of the constructions is to reduce the mobilization of sediment in the inner part of the profile, but erosion can still take place in the parts that are not secured. Constraining sediment at the coast increases the erosion rate of downstream neighboring sections. Therefore the sediment deficiency continues despite the presence of the hard structures. Along large parts of the coastline there is protection of the hinterland; cliffs and dunes have been secured by use of revetments as well as groynes and wave breakers. This limits the natural input of sediment that would have been supplied into the system during periods of acute erosion.

Figure 3.4.2 shows an example of the problem caused by hard structure protection measures. The coastline at Heatherhill has been protected in order to maintain the coastline position; however, just east of the structures, there is active erosion of the cliff, signifying that the interception of the longshore sediment drift causes reduction in down-drift sediment supply, transferring the erosion along the coastline. ¯

0 60 120 240 m

Figure 3.4.2 Aerial photograph from 2015 showing the coastline at Heatherhill, illustrating the erosional problems caused down-drift from a protected area.

3.5 Selected beach sections Three specific locations along the coastline have been selected (see Figure 3.1.1). The two locations Tisvildeleje and Raageleje, have been selected as hotspot areas for potential nourishment projects in the recent climate adaption plans proposed by DHI and Hasløv & Kærsgaard, 2013. With respect to Udsholt Strand, the previous studies do not agree on a suitable choice of protection measures. DHI and Hasløv & Kjærsgaard (2013) question whether Udsholt Strand is a suitable site for beach nourishment due to two main reasons; the higher incidence angle, and the proximity to Gilleleje Harbour. Preliminary studies conducted by COWI (2009) did however appoint this location as a main nourishment site.

Recent cross-shore profiles from the three locations have been made available for use in this study. Data was collected by the Danish Coastal Authority in 2011 and Mette Lundov, Department of Geoscience and Natural Resource Management, in late 2013 and early 2014.

The sites are partly assessed on the basis of aerial photos and partly on the basis of geology, geomorphology and historical observations.

In general, there are one or two bars present in the nearshore profile (50-200 m from the beach), but there are also locations along the coastline where no bars are present in the profile. At several subsections the erosion has

Chapter 3 / Study area

exposed the more resistant sediments and in some locations the natural seabed therefore consists of pebble and cobble sized sediments.

In high-energy wave situations the waves break across the outer bar first, and then reform and break again across the inner bar. The longshore current and therefore sediment transport will be at a maximum at breakpoint locations. As described, profiles may in some places not consist solely of readily mobile sand, which limits the sediment transport in these areas.

3.5.1 Tisvildeleje The extent of the Tisvildeleje subdomain is shown in Figure 3.5.1. The Tisvildeleje shoreline subsection covers a densely developed stretch of the coast, with housing bordering the cliff. The breakwater, in the western part of the domain, was originally constructed to provide shelter for coastal fishermen. Today, the breakwater is partly covered by sand which has been transported along the coast from southwest. Large amounts of sediment passes by the breakwater and is transported further along the coast.

As seen in Figure 3.5.1 (and in Appendix B), a chain of groynes have been implemented along the entire coastline in lee of the large breakwater. It is likely that these, have been implemented after the breakwater in order to counter the leeside erosion (COWI, 2009). The structures are relatively short and not very efficient seen from a technical point of view; in aerial photos it is evident that the structures are very closely spaced and allows for very little transport on the inner part of the profile. In the middle part of the shoreline subsection, also protected by a concrete seawall, breakwaters have been constructed in-between the groynes.

Figure 3.5.1 Aerial photograph from 2014, showing the extent of the coastline at Tisvildeleje, as well as locations for available profile data and coastline protection measures. Profiles 1 and 3 collected by Mette Lundov, 2013-2014, and profile 2 by The Danish Coastal Authority, 2011

Chapter 3 / Study area

The beach has been almost completely eroded away in front of the concrete seawall, which has been implemented as slope protection (Figure 3.5.2). Erosion here is a natural consequence, as waves are reflected causing erosion of the anterior beach. East of the concrete seawall there are some larger and more efficient groynes, effectively maintaining a wide sandy beach. The cliff is here protected by the placement of large boulders along the foot of the cliff.

Figure 3.5.2 Photograph of the concrete seawall shown in Figure 4.3.1. (Photograph from COWI, 2009)

The general coastline normal orientation for the Tisvildeleje shoreline subsection is 322 degrees. The three profiles available are shown in Figure 3.5.3.

Figure 3.5.3 Cross shore profiles available for Tisvildeleje. Locations are shown in Figure 3.5.1. The distance on the x-axis relates to MWL.

Profile 2 includes the elevation of the cliff backing the sparse beach and reflects the topography seen in the photo shown in Figure 3.5.2. Profile 1 is located downstream from the breakwater, and it is evident that there is more sand available in the profile due to the presence of a pronounced bar.

West of the breakwater, where no protection measures have been implemented, recent storms have depleted the dunes and backshore areas, exposing a parking area. Figure 3.5.4 shows the impacts of the storm in December 2013; frontal dune scarping, and in one location, the dunes have been breached, resulting in a dune breach. Figure 3.5.5 shows the result of two subsequent storms approximately two years later. Due to the initial

Chapter 3 / Study area

breaching in 2013, the storm resilience has decreased, causing the storms in 2015 to completely inundate and destroy the dune in front of the parking area.

Figure 3.5.4 Depleted dunes and flooded backshore area in the western part of the Tisvildeleje shoreline subsection, just after the storm in December 2013. (Petersen, 2016)

Figure 3.5.5 Same location as Figure 3.5.4. Depleted dune field after two subsequent storms in the fall of 2015. (Petersen, 2016)

Chapter 3 / Study area

3.5.2 Raageleje The Raageleje coastline is shown in Figure 3.5.6. There is a large breakwater located at Raageleje, referred to as the pier, which similar to the Tisvilde breakwater, was constructed in 1918 to provide shelter for local fishermen.

Figure 3.5.6 Aerial photograph from 2014, showing the extent of the coastline at Raageleje, as well as locations for available profile data and coastline protection measures.

After its construction, the pier caused significant leeside erosion which resulted in the construction of coastline protection along the lee side. There is a series of old groynes partly covered by sand or submerged. The pier has not been maintained since 1928, and has a top elevation below MWL. As seen in the photograph shown in figure 3.5.7, waves breaking across the submerged breakwater can be observed.

Figure 3.5.7 Photograph showing the submerged breakwater at Raageleje. (Hasløv and Kjærsgaard, 2014)

Chapter 3 / Study area

East of the breakwater a concrete seawall has been constructed, functioning as a waterfront promenade, as well as protection of the seaside road (Figure 3.5.8). In front of the seawall remainders of original wooden groynes are found. They were originally constructed to protect the downstream shadow area from erosion.

Figure 3.5.8 Photograph of the concrete seawall/beach promenade protecting a seaside road at Raageleje. Original wooden groynes front the seawall. Locations shown in Figure 4.3.4. (COWI, 2009)

The promenade is exposed to high wave energy, and in some high energy situations, the road is flooded despite the seawall protection. The construction of the seawall underlines that protection of the infrastructure is of high importance along this specific location. As the case in Tisvildeleje, housing is built neighboring the beach.

The general coastline normal orientation for the shoreline subsection is 320 degrees. In Figure 3.5.9, the profile data available for Raageleje is visualized. The upper shoreface of profile 5 is the steepest; from 0 m to -100 m the elevation decreases with 5 m, and a depth of 3 m is reached only 100 meters offshore. Bar development is evident in all three profiles.

Figure 3.5.9 Cross shore profiles available for Raageleje. Locations are shown in Figure 4.3.4. The distance on the x-axis relates to MWL.

Chapter 3 / Study area

3.5.3 Udsholt Strand Udsholt Strand is located further northeast within the study area and has a general coastline normal orientation of 337 degrees. The selected shoreline subsection is located just after an overall shift in coastline orientation, see Appendix B. Especially noticeable are the pronounced perturbations located in the western part of the shoreline subsection, where the beach is approximately 30 m wide, and in 2014 four sand waves were present (Figure 3.5.10). The perturbations are migrating towards east due to the wave and current conditions and they guard the area where profile 8 was measured from the direct impact of the most westerly waves. There are only a few breakwater present along this shoreline subsection.

Figure 3.5.10 Aerial photograph from 2014, showing the extent of the coastline at Udsholt, as well as locations for available profile data and coastline protection measures.

The sediment is coarser than at Tisvildeleje and Raageleje; the backshore consists mainly of pebbles, but sand is present at the beachface (Figure 3.5.11). The perturbation mainly consists of pebble sized sediment, which is less mobile under moderate wave conditions. This suggests that the perturbations will only evolve and migrate during high energy conditions from westerly directions. As seen in Figure 3.5.1, the potential littoral drift at Udsholt Strand is estimated to be twice that of the actual drift, but as it is shown in Figure 3.5.10 far fewer structures are present along this coastal section than in the previously examined cases of Tisvildeleje and Raageleje.

Figure 3.5.11 Photograph of the perturbation located in the western part of the Udsholt shoreline subsection. (Abrahamsen, 2014)

Chapter 3 / Study area

The profiles located in this subdomain are shown in Figure 3.5.12 below. In Profile 9, an onshore migrating bar is present.

Figure 3.5.12 Cross shore profiles available for Udsholt Strand. Locations are shown in Figure 4.3.7. The distance on the x-axis relates to MWL.

Chapter 4 / Methods

4 METHODS The computer model used in this study is the Mike Zero framework created by DHI. In order to firstly correlate model results with observations of the actual sediment transport rates, and then to further investigate and appreciate the results provided by the models, several preliminary steps have been undertaken using a range of methods.

An initial approach to the investigation conducted within this study, was to apply the coastline evolution model in order to study the change in longshore sediment transport when placing perturbations along an initially straight coastline. Furthermore, the shoreline retreat rates at the study areas were determined by applying the GIS based shoreline analysis tool Digital Shoreline Analysis (DSAS). This method provided insight into the sediment budget and specific transport rates for the three subsections selected for further study. The MIKE 21FM framework was used for computing a nearshore wave field, which could be used for the modeling of beach nourishment behavior at the three locations. The final coastline evolution setups were calibrated against the site specific erosion rates, found in the DSAS analysis in order to obtain site specific nourishment behavior predictions.

In this chapter, firstly a model description of the Littoral Processes FM is provided, and in the subsequent sections detailed methodical descriptions of setups and other procedures are provided.

4.1 The Littoral Processes FM framework The Littoral Processes (LP) FM module is a numerical model capable of simulating littoral drift and coastline evolution in areas with non-cohesive sediment and quasi-uniform beaches in which the flow and transport can be assumed to be primarily in the longshore direction.

The LP FM package contains several model types that can be used alone or together as a model complex. The core of the sand transport calculations in the LP FM is the quasi-3D sediment transport module STPQ3, which is a deterministic description of non-cohesive sediment transport in a single point. Applying the STPQ3 in a series of points in a profile and using actual hydrodynamic data allows for the calculations of the littoral drift and annual net and gross sediment transport which can then be used for predicting coastal profiles and coastline evolution.

In the following subsections, the integrated calculation models contained within the LP FM elaborated.

4.1.1 Transport at a point The basic sediment transport module calculates the instantaneous and time-averaged sediment transport for two opposing directions by use of the STPQ3 model. Prior to the sediment transport calculations, the hydrodynamic flow conditions are calculated. The hydrodynamic model is based on the solution of the force balance across the water column from which the averaged flow velocity is found. The force balance includes contributions from near bed orbital motion and the forces associated with wave breaking. The interaction of undertow, longshore current and wave motion are also automatically taken into account in the time-averaged vertical flow velocity distribution. Wave data properties are defined by the user for the outer depth of the profile (preferably the outer grid point of the profile). From here, the model shoals and refracts the waves across the profile onto the coast and calculates the resulting longshore current across the profile.

Chapter 4 / Methods

For a given longshore position, the waves are refracted and shoaled towards a break point until the specified breaking condition,훾, is satisfied. The values for the wave height, wave period, wave angle and water level at the breaking point are used to interpolate sediment transport and then the coastline evolution.

The model discriminates between bed load and suspended load in the transport calculations. The deterministic bed load transport model by Engelund and Fredsøe (1976) is used for calculations of bed load. The criterion for grain sizes that can be brought into suspension by the current is a sediment fall velocity less than a value given as a function of the seabed friction. The vertical suspended sediment concentration is calculated from the vertical diffusion equation for suspended sediment according to Fredsøe et al. (1985) (DHI, 2012). The instantaneous sediment concentration is calculated as the product of the instantaneous flow velocities and the instantaneous sediment concentration:

1 푇 ℎ 푞 = ∫ ∫ (푢푐) 푑푧푑푡 equation 17 푠 푇 0 2푑 where u is the current velocity and c is the sediment concentration.

The calculations of the concentration varying in time and over depth is iterated over several wave cycles until a periodic solution is found.

4.1.2 Littoral drift The littoral drift module (LITDRIFT) calculates the littoral transport by combining hydrodynamic input parameters and the transport model STPQ3D, for one or several cross-shore profiles assuming longshore uniformity. The calculation of the littoral transport consists of longshore current and sediment transport calculations. The parameters considered in describing the incoming waves are refraction, shoaling, breaking and directional spreading. The angle between the wave front and the coastline is given by Snell’s law. The annual littoral drift is found by contributions of transport from each of the wave incidents occurring during the simulation period. The wave climate is described in a time series file, and the duration of each of the individual wave incidences are considered. The total annual drift is found as the sum of the contributions from all wave incidents:

푁 푄푎푛푛푢푎푙 = ∑𝑖=1 푄푆(𝑖) ∙ 퐷푢푟푎푡𝑖표푛(𝑖) equation 18 where N is the total number of incidents and Duration(i) is the duration of the wave incident.

4.1.3 Table generation The sediment transport information used in the coastline evolution model is derived from transport tables pre- generated in the table generation model. During the simulation of coastline evolution, the transport rates are found by interpolation of pre-generated transports in the table, rather than calculation of the instantaneous transport for all locations along the coastline. The inputs necessary for creating a transport table include the varying hydrodynamic parameters which are specified by the minimum and maximum values. The maximum and minimum values entered reflect the interval of conditions that are expected to occur during the simulation period, and the number of values in the table defines the total number of values in the resulting transport table. The combined effect of the wave properties, mean water level and regional current will determine the maximum

Chapter 4 / Methods

values of wave conditions at the breaking point. The wave breaking point for a wave progressing towards the shore is defined as the grid point where the wave height and water depth meet the wave breaking criterion. The table generation also includes the input of a cross-shore profile, which defines the cross-section position where the transport conditions are derived from. The transport rates in points along the coast are interpolated from the specified locations and associated cross-sections. Based on the inputs, the total transport rates and the cross-shore distribution of these are organized in a table for varying hydrodynamic and bathymetric conditions. These customized sediment transport tables enables the coastline evolution calculations to be done faster than calculations of the instantaneous rates (DHI, 2012).

4.1.4 Coastline evolution The coastline evolution model (LITLINE) calculates the movements of the coastline position based on a coordinate system where the x-axis is a baseline that runs parallel to the overall coastline orientation and the y- axis is the distance from the baseline in the off-shore direction (Figure 4.1.1)

Figure 4.1.1 Schematization of the co-ordinate system used in the coastline evolution model. yC is the distance from the baseline to the coastline. ( DHI, 2014b)

The model calculations are based on a one-line theory, where the input cross-shore profiles are assumed to stay the same during erosion or accretion. Therefore the morphological changes at the coast due to sediment transport are expressed as changes in coastline position. The coastal evolution can be calculated using up to five different profiles in the longshore direction. The main equation in the coastline evolution calculation is the continuity equation for sediment volumes expressed by:

휕푦 (푥) 1 휕푄(푥) 푄 (푥) 푐 = − + 푠표푢 equation 19 휕푡 ℎ푎푐푡(푥) 휕푥 ℎ푎푐푡(푥)∆푥 in which the variable yc(x) is the distance from baseline to coastline, t is time, Q(x) is longshore transport of sediment, x is the longshore position, ∆x is the longshore discretization, Qsou(x) is the the supply of sediment from sources, including dune erosion and hact(x) is the active height of the cross-shore profile.

The model is a useful tool for shoreline evolution over long time scales. The 2D effects are parametric formulations, which work well in simple cases but not so well in complex cases, e.g. where nearshore bathymetry is very complex.

Structures The transformation of wave angle and height at breaking is altered by the presence of coastal structures, and this leads to alterations in predicted transport rates. The coastline evolution model includes the option of including four types of hard coastal protection structures; groynes, jetties, offshore breakwaters and revetments. Breakwaters and revetments span in the longshore direction whilst jetties and groynes extend from the shoreline in the cross-shore direction.

Chapter 4 / Methods

As previously explained, groynes and jetties influence the coastline evolution by blocking the longshore sediment drift, which causes areas of accretion and erosion on the coastline around the structure. The position of these structures is defined by the position of the tip. Figure 4.1.2 illustrates the definition of a groyne and jetty in the LP FM setup.

Figure 4.1.2 Schematization of groyne and jetty in the LP FM setup. (DHI, 2014b)

The setup also requires information about bypass length, which defines the section of the structure where some sediment may pass despite the presence of the structure. The model assumes that the longshore current and thereby the littoral transport will be back to full equilibrium at a distance 10 times the length of the structure in the longshore direction. Not all natural effects of the structures are included in the model (DHI, 2014b). The coastline evolution model setup assumes long and uniform coastlines, and the placing of structures violates this assumption, and large numbers of structures may cause modeling difficulties. The impact of each structure is basically modelled with the assumption that it is the only structure along the coastline. Therefore, in setups with many groins, it may in some cases be an advantage to model this as one revetment.

Revetments are defined as structures on the beach and are defined in the LP FM setup by points (Figure 4.1.3). Revetments act as a seawall by preventing the coastline from eroding along structure, but erosion may still take place in front of the revetment.

Figure 4.1.3 Schematization of groyne and jetty in the Littoral Processes FM setup. (DHI, 2014a)

Chapter 4 / Methods

4.2 Model predictions of beach nourishment planform evolution In this analysis, one or more nourishment deposits (perturbations) were placed on an initially straight shoreline, and the change in longshore sediment transport was then studied to evaluate the effect of different constant wave parameters. To also analyze the effect of spacing between several nourishments, perturbation size and shaping, the study comprised a total of 15 nourishment schemes. The objective was to provide a basic understanding of the evolution of beach nourishments, and this serves as a basis for predicting nourishment behavior in a natural dynamic setting.

The shorelines were created using MATLAB, and consisted of a straight 20 km coastline, with the perturbation schemes at the center. In 12 of the schemes, the nourishment planforms are bell-shaped, and the shapes were created using the Gaussian function. In three of the single-deposit scenarios, the nourishment planform is squared, and here the perturbations were creating by shifting the shorelines seaward at certain sections.

The LITLINE shoreline evolution model was used for modeling the perturbation behavior for a variety of wave incidence angles and wave heights. A sediment grain size similar to that of the average native sand of the northern Zealand was used (~0.3 mm), and for the sake of simplicity, a straight gently sloping cross-shore profile (slope: 0.01 m m-1) was assumed for these simulations. Both slope and sediment size was uniform across the entire coastline and wave conditions were assumed constant in time and space. The nourishment volume was calculated using trapezoidal rule and an active depth of 5 meters was presumed.

Table 4.1 shows the modelled combinations of constant wave heights and incidence wave angles (the degrees are given as the anti-clockwise direction relative to the shore normal).

Table 4.1 Combinations of wave height and incidence angle relative to the coastline for scenarios shown in Figure 4.2.1

Wave height, H Wave angle S (m) (degrees) 10 0.75 20 30 10 1 20 30 10 1.25 20 30

Variations of wave angle were introduced to investigate the nourishment scenarios’ response. The LITLINE model suffers some limitations in modeling the shoreline evolution when incidence wave angles approach 45 degrees. To ensure model stability incoming wave angles of 10, 20, and 30 degrees were therefore applied. In scenario S3 the model became unstable when applying an incidence wave angle above 25 degrees and in order for a better comparison between the rectangular nourishment evolutions, a maximum wave incidence angle of 25 degrees was used for all the rectangular nourishment simulations.

In order to compare the predictions of morphological development, all nourishment volumes total to an amount of 175.000 m3 sand, and a simulation period of 20 years was selected. The 15 deposit scenarios are shown in Figure 4.2.1, and characteristics are described in the table found in Appendix C.

Chapter 4 / Methods

Figure 4.2.1 Definition sketch showing initial nourishment planforms with the same volumetric amount of sediment. Note non-identical cross-shore distances.

The study includes five nourishment configurations with one deposit, three scenarios with two deposits, four scenarios with three deposits, and three scenarios with four deposits. Apart from the number of nourishments, the variations within the scenarios include deposit spacing, asymmetry and initial planform shape.

For future reference, the point of maximum seaward extension of a given shoreline perturbation is termed the peak position.

Chapter 4 / Methods

4.3 GIS-based shoreline and volume change analysis Shoreline change was estimated from the annual average recession rates determined from comparison of historical aerial photographs. From the shoreline change observations, the transport rates were found by assuming that the profile is constant over time, and that there is no change in the cross-shore distribution of sediment.

The tool DSAS is provided by the U.S. Geological survey as a plug-in for ArcGIS. The shoreline analysis tool compares the positions of the shorelines as ArcGIS polyline features along cross-shore transects cast from a straight baseline. Transects were cast with an alongshore spacing of 20 m. The shoreline displacements were defined as the distance between the intersections of the different shorelines with the transect lines (Figure 4.2.1). The shoreline polylines were created using digital aerial photographs for the years 1954, 1995, 1999, 2002, 2010 and 2014, which have been produced and rectified by COWI. A default uncertainty of 2 meters was used for the coastline positions.

Figure 4.3.1 Workflow of shoreline change computation in ArcGIS and DSAS

The shoreline movement distances allowed for calculations of the quantitative volumetric changes along the coastline. The volume of sand was found assuming an equilibrium profile:

푄 = ℎ푝∆푥∆푦 equation 20 where ℎ푝is the total active height of the profile, ∆푥 is the coastline movement in meters and ∆푦 is the transect spacing.

For this purpose, the depth of closure was assumed uniform along the entire coastline at -6 m, and the active beach height was assumed to be 2 m.

Chapter 4 / Methods

4.4 Wave transformation In order to obtain a better outcome in the 1D modeling of the shoreline evolution using the non-uniform local wave fields, the available offshore wave data is modified locally obtain a better representation of the wave data after the refraction processes. Therefore wave transformation was carried out in order to produce suitable nearshore non-uniform wave series for each of the shoreline subsection. The MIKE 21 SW spectral wind-wave area model was used for wave transformation. The model simulates the growth, decay and transformation of wind-generated waves and swells offshore and in coastal areas.

To produce the nearshore wave series, offshore wave data extracted from a hindcast model was used. The hindcast data originates from DKBS, a national wave model produced by DHI. The data covers the time period 1994-2011 for all Danish seas. From these results wave data for ten points along the outer boundary of a domain specified along the North Zealand coast has been extracted and made available as dfs1 files. Seabed bathymetry and offshore wave extraction points are shown in Figure 4.4.1.

Figure 4.4.1 Seabed bathymetry describing the depth at specific geographical positions (50x50m) shown with wave extraction points from the nationwide hindcast model DKBS. Depths at extraction points are 11.5-15 m.

The wave parameters provided were:

(6) significant wave height (7) spectral peak period (8) mean wave direction (9) directional standard deviation

Chapter 4 / Methods

An initial step in the wave simulation process was to draw up the model domain. The mesh file was generated in the MIKE Zero Mesh Generator, which is a tool for generation and handling of unstructured meshes, including the definition and editing of boundaries.

A computational mesh representing the bathymetry from the coastline to the wave extraction points was created. The land/water boundary was digitized from aerial photos. The data necessary for the mesh creation were scatter data, defining the bathymetry values, and boundary outlines, which defined the model domain. A section of a 50x50 m grid of the Danish seabed bathymetry provided by the Danish Coastal Authority, was used as scatter data for the bathymetry mesh. The arcs defining the model domain and the bathymetry scatter is shown in Figure 4.4.2.

Figure 4.4.2 Defined domain area shown with aerial photograph and bathymetry scatter data.

Each boundary was given a code in order to specify different wave conditions at each boundary. The eastern boundary was kept closed as it was assumed that waves from this direction are not significant for the domain. The western boundary was given the boundary conditions corresponding to the wave data from extraction point 1. The inner part of this boundary was, however, kept closed because transformation must take place some distance from the coast. A file containing wave data from all ten extraction points was used as boundary condition for the shore parallel offshore boundary, so that the wave data varies along this line. As a final step in the mesh generation, the scatter data was interpolated onto the mesh. The final mesh representing the bathymetry in the study area is shown in Figure 4.4.3.

Chapter 4 / Methods

Figure 4.4.3 The mesh as it appears after interpolating the bathymetry data.

In the MIKE SW module, the wave boundary information for each code (boundary section) was specified as wave parameters (Version 2), which required specification of the four wave parameters provided with the DKBS wave data. For the offshore boundary, the wave parameters were specified as varying along line as well as in time. For the western boundary the waves were specified as constant along line.

The SW module includes two different formulations: (10) Directionally decoupled parametric formulation (11) Fully spectral formulation

The directionally decoupled parametric formulation is computationally less demanding, and is considered sufficient at spatial scales less than ~50 km, which is why this model formulation was applied. The quasi stationary formulation was used as time formulation, as it is also generally less computationally demanding.

Outputs were specified with a time step of 3 hours, as both an area series within the total domain, a line series along boundaries at the three sub-domains and point series at 9 m, 7 m and 5 m at locations just offshore of Tisvildeleje, Raageleje and Udsholt Strand.

In order to select the most suitable wave series to apply in the LITLINE simulation of the nourishment scenarios at each of the shoreline subsections, Q/α-curves were modeled using LITDRIFT. The differences in predicted littoral drift rates when using the offshore wave time series and the extracted nearshore wave data from the wave transformation, provided insight into the effect of wave transformation on littoral drift simulations. Comparing the Q/α-curves to the observed erosion rates allowed for identification of a best fit the wave climate for further calculations.

Chapter 4 / Methods

4.5 Nourishment predictions at selected shoreline subsections For the purpose of studying the effect of placing nourishment deposits at the three selected shoreline subsections,

Three model setups were created in order to predict and simulate the coastline behavior at each location. Similarly to the setups used for the predicted evolution of the schematized nourishments, planform evolutions and littoral drift patterns were simulated using the LITLINE module.

Setting up the model comprised the task of creating a simplified representation of the sites and transforming the available data into a format which could be understood by the model.

In order to model the littoral drift and coastline response the basic inputs produced for each of the study sites were:

 Coastlines; digitized from 2014 aerial photographs using MIKE Zero Mesh Generator, rectified using the DHI rectification tool, Image Rectifier, and regridded to obtain even grid spacing using MATLAB  Overall orientation of the shoreline subsections  Profile lines of equidistant spacing, smoothened and regridded using MATLAB, which included information of the determined hc of 6 m.  Time series containing non-uniform wave climates, represented by H0, α0, T and reduction factor Before modeling the effect of placing beach nourishment deposits at the three study sites, the model setups were calibrated according to the annual observed littoral drift obtained from the GIS-based shoreline analysis. Several parameters were initially calibrated, including the bed resistance and sediment properties. Even though the general coastline orientation is specified in each set up, the endpoint orientations were manipulated as these angles control the flux of sediment in and out of the model domain.

At Tisvildeleje, profile 1 was used as a representation of the bathymetry, at Raageleje, profile 5 was selected as bathymetry representation and at Udsholt Strand, profile 9 was selected. The profiles were related to individual transport tables. The sediment properties were defined in the grid points of the cross-shore profile(s). COWI (2009) found that the best fit equilibrium profile was found by using a mean grainsize of 0.3 mm, and therefore for the sake of simplicity this grain size was assumed at all sites.

After calibrations, the best fit set ups were selected for simulating the coastline evolution over a 20-year period when placing nourishment deposit on the beach. The scenarios were modelled by displacing the shoreline 20 m in the cross-shore direction along a 400 m section and along an 800 m section. Based on the assumed active profile, the scenarios correspond to nourishment volumes of ~64,000 m3 and 128,000 m3. Wave data for the period 2002-2011 was used for all simulations, as it was assed that the variations in the wave climates for this period offered a representation of the wave energy in the area good enough to represent any future wave climate.

4.6 MIKE 21 FM Shoreline Model For coastlines with coastal structures or where an assumption of alongshore uniformity is not valid, MIKE 21 Coupled Model FM provides a more detailed and robust method than what is offered by the Littoral Processes FM.

MIKE 21 Coupled Model FM is comprised of seven modules; a hydrodynamic module, a transport module, ECO LAB/oil spill module, mud transport, particle tracking, sand transport and spectral wave module. The hydrodynamic module and the spectral wave module act as the basic computational components of the MIKE 21 Coupled Model FM.

Chapter 4 / Methods

The spectral wave module simulates the growth, decay and transformation of wind generated waves and swell waves. The module can be used in isolation if the aim alone is to generate a particular wave field, or it can be coupled to the other modules.

The shoreline model is comprised within the sand transport module, and is used in cases where the focus of the simulation is shoreline evolution. The model calculates the bed level change rates and related volume change in the domain, and during each time step the change of sediment volume is integrated across the shoreface for each coastline point. The morphology is then updated for the shoreline using a predefined coastal profile, and redistributed in the mesh, producing morphological feedback between the bathymetry and hydrological forcings.

The model includes dynamic coupling of waves and currents, and provides full feedback of bed level changes on waves and currents. The model concept is illustrated in Figure 2.6.4.

Figure 2.6.4 Concept of the MIKE21 FM modules relevant for the Shoreline Model, including model input files

Chapter 5 / Evolution of schematized nourishments

5 Evolution of schematized nourishments The initial approach to the study of shoreline response to beach nourishment was a simple setup of schematized nourishments. In the previous chapter the 15 different nourishment scenarios were presented, and in the present chapter the simulated evolution over a 20-year period is elaborated.

First, in sections 5.1 - 5.4, a presentation of planform evolution, focusing on the effects of the initial shape of the nourishment as well as the effects of varying deposit size and placement along the coastline. Secondly, in section 5.5 the difference between the initial shape and their corresponding transport patterns will be further analyzed in order to understand the difference between a bell-shaped nourishment and a rectangular nourishment. In addition, the nourishment sensitivity to wave angle will be investigated in order to determine nourishment response to waves approaching the shoreline with higher wave incidence angles.

5.1 Single nourishment scenarios - comparison of initial shapes The evolution of the five single-nourishment scenarios is presented in figure 5.1.1. Over time, the rectangular scenarios morph into bell-shaped perturbations similar to the initial shape of the other scenarios. This change signifies the smoothening and spreading of the nourishment due to the initially strong gradients in shoreline orientation.

The perturbations are spread out along the shoreline under the action of waves and current. The rate, especially within the first year, depends on the initial width and height of the nourishment. Within the first year, the most rapid change in peak position is observed in the scenarios with the highest initial peak positions: 1A, 1B and S3.

The initial peak position in scenario 1A is 70 m, and after one year, the peak position is at 35 m, corresponding to a retreat of 50 % in initial beach width. The corresponding change in scenario 1B where the initial peak position is 35 m is 26 %. In scenario S3, the peak position is 25 m after one year, corresponding to a retreat of 35 % (see Appendix D).

In the widest of the rectangular scenarios, S1, the initial beach width is maintained within the first year; changes have only occurred on the shoulders of the deposit, but the nourishment has not yet become bell-shaped. In scenario S2 the beach width has decreased with 2.4 % within the first year of modeling (Figure 5.1.1).

The results also show that on a longer time-scale, all nourishments converge towards the same planform. After 20 years, the 5 single- nourishment scenarios exhibit similar planform shape; the peak position of all the single- deposit scenarios are within 1 m, and 1A, 1B, S2 and S3 within 0.2 m (see Appendix D).

Chapter 5 / Evolution of schematized nourishments

Figure 5.1.1 Planform sketch of single nourishment evolution after 1, 5, 10, 15 and 20 years. From top: scenario 1A, 1B, S1, S2 and S3. Wave height: 1m, wave period: 6 seconds, wave incidence angle: 10 degrees.

It is observed that increasing the longshore width of the initial nourishment planform has a stabilizing effect on the rate of spreading out; this is evident from the evolution of scenarios S1, S2 and S3. A strong diffusional phase is observed within the first year, this diffusion rate increase with cross-shore perturbation width and decreases with long-shore perturbation length.

5.2 Multiple nourishment sites - effect of initial spacing The effects of varying the distance between neighboring deposit sites was examined in the scenarios with four deposits (Figure 5.2.1).

Chapter 5 / Evolution of schematized nourishments

Figure 5.2.1 Planform evolution of multiple-deposit nourishments with dissimilar spacing. From top: scenarios 4A, 4B and 4C. Wave height: 1m, wave period: 6 seconds, wave incidence angle: 10 degrees.

Similar to the evolution of the single -deposit scenarios, the perturbations are smoothened out over time and the initial individually placed deposits join together to form one bell-shape perturbation.

In scenario 4A; after the initial diffusional phase, the beach width only recedes 1 m for the remainder of the simulation period. When considering the entire stretch of coast, which the deposits cover, the spreading out of the individual perturbations has a stabilizing effect. The initial peak positions of the nourishments in scenarios 4A, 4B and 4C is only 25 % of the initial extent of nourishment A1, however, the difference in beach width after 20 years of modeling is only 1.6 m.

As the distance between the deposits is increased, so is the time it takes for the nourishments to join. The four deposits of scenario 4C have only completely levelled out by the end of the simulation period. In scenario 4B the deposits form a single perturbation after only one year. In scenario 4C the deposit becomes very stable with minimum retreat in coastline from year 5 to year 20. This emphasizes the stabilizing effect of nourishing a long stretch of coast, as noted for the single-deposit scenarios.

5.3 Multiple nourishment sites - asymmetry In the scenarios with 3 deposits, the effect of varying the sizes alongshore was explored in order to investigate if a larger deposit could shelter the downstream deposits from the waves and current.

The evolution of scenarios 3B and 3C with inverted asymmetric positioning of three deposits did however not show any difference in overall planform evolution. The initial asymmetry is detectable throughout the entire 20-

Chapter 5 / Evolution of schematized nourishments

year period, as the peak position is displaced in the direction of the largest deposit (Figure 5.3.1 and Appendix D). The sheltering effect of having one larger nourishment is not detected in this set up.

Figure 5.3.1 Planform sketch of asymmetrically placed multiple-deposit nourishments with equal spacing. Wave height: 1m, wave period: 6 seconds, wave incidence angle: 10 degrees.

5.4 Longshore sediment transport patterns The above described differences in shoreline evolution can be explained by the differences in longshore transport patterns which are caused by gradients in the angle between the incoming waves and the coastline at a given position along the coast. In figure 5.4.1, the temporal changes in transport patterns along the single-deposit scenarios of 1A, 1B, S1, S2 and S3 is visualized.

Figure 5.4.1 Plots of the alongshore sediment transport rates for the five single-peaked deposits. From left: 1A, 1B, S1, S2 and S3. Wave height: 1m, wave period: 6 seconds, wave incidence angle: 10 degrees.

Chapter 5 / Evolution of schematized nourishments

It is observed, that as the planform evolves and the initial perturbations spread out, the rate and gradient in longshore sediment transport is in turn reduced. In scenario 1A and S3 the rapid recession of the cross-shore peak during the first year corresponds to high initial transport rates and gradients (Figure 5.4.1).

Zones of erosion are located across the distance where the sediment transport increases, and the rate of erosion is determined by the gradient in transport. All single-deposit scenarios have two accretion zones located on either side of the perturbation. In the case of scenarios 1A, 1B, S2 and S3, the initial shape leads to one continuous erosion zone along the crest of the perturbation. In scenario S1, the widest of the rectangular nourishments, the erosional zone is separated into two, as the perturbation is stable along the shoreline parallel crest.

This pattern is recurrent for each of the deposits of the multiple-deposit scenarios (Figure 5.4.2). Of the scenarios comprising of four deposits, it is only in scenario 4C that the distance between the individual nourishments are large enough for the beach segments between the nourishments to become unaffected by the nourishment.

Figure 5.4.2 Plots of the alongshore sediment transport rates for the five multiple-deposit scenarios. From left: 4A, 4B, 4C, 3C and 3B. Wave height: 1m, wave period: 6 seconds, wave incidence angle: 10 degrees.

When the nourishments morph together so do the zones of erosion, the shorter distances with high gradients evolve into longer stretches with smaller constant gradients in sediment transport rate. There is no effect of the asymmetric positioning of the nourishment; there is no lee effect, the transport pattern is reversed when 3C and 3B is examined.

5.5 Variation of incidences wave angle The results presented above show that nourishment shape and the following gradients in longshore-sediment transport along the perturbations determine the in situ erosion and accretion patterns. In order to further examine the in situ longshore transport patterns induced by the nourishments, scenarios 1A and S1 will serve as examples when varying the wave incidence angle.

The effect of varying the wave angle on littoral drift across the initial shape for scenario1A and S1 is shown in Figure 5.5.1, where the effect 10, 20 and 30/25 degree incidence wave angles are shown. The angles yield baseline transport rates of 0.003, 0.006, 0.008/0.007 m3 sec-1, respectively. In Figure 5.5.1 the in situ littoral drift rates have been normalized using the baseline transport rates, and this shows that the transport pattern is

Chapter 5 / Evolution of schematized nourishments

displaced downdrift when the incoming wave angle is increased. Furthermore, it is evident that that the gradient in transport capacity is higher in 1A then in S1. When the incoming wave angle is increased the transport capacity is span narrowed.

Figure 5.5.1 Alongshore variation of normalized littoral drift for varying incidence wave angles. Left: Scenario 1A. Right: Scenario S1. Wave height: 1 m and wave period: 6 seconds.

In figure 5.5.2 the zones of accretion are marked with a green overlay, while the red areas refer to zones of erosion. These zones correspond to the areas where transport capacity is decreasing and increasing. In scenario S1, erosion takes place at the crest of the perturbation and deposition along the edges, whereas there is a broad zone with no gradient in transport rate along the crest and shorter zones of accretion and erosion on the edges in the initially rectangular deposit (figure 5.5.2).

The maximum transport rate in scenario 1A corresponds to an increase of 56 % from the baseline drift for an incoming wave angle of 10 degrees, whereas the minimum transport rate is 61 % lower than the baseline drift. For scenario S1, both the minimum and maximum transport rates correspond to 16 % of the baseline drift.

Chapter 5 / Evolution of schematized nourishments

Figure 5.5.2 Top: Scenario 1A, bottom: Scenario S1. Snapshot of the first modelled time step. Top panel of both figures is shoreline planform. Solid line: angle between incidence waves and shoreline. Dashed line: littoral drift. Red overlay: erosion zones. Green overlay: accretion zones.

Chapter 5 / Evolution of schematized nourishments

The difference in the erosional and accretional response is explained by the nonlinear relationship between wave angle and potential littoral drift, which was presented in section 2.6. This means that even though the shoreline perturbation is symmetric the sediment transport response to incoming waves is asymmetric. This can be explained by the Q/α-curve, which becomes less steep closer to the maximum transport capacity at the orientation of 45 degrees (Figure 5.5.3).

Figure 5.5.3 Q/α-curve for wave incidence angles of 10, 20 and 30 degrees respectively. Dark green overlay marks the active transport capacity span produced by scenario S1, light green overlay marks the active transport capacity span produced by scenario 1A.

Considering the first year of modeling it is evident that that the erosion of the peak in scenario 1A is much more rapid when waves approach from an angle of 10 degrees than when they approach from 20 and 30 degrees (Figure 5.5.4). The same effect is observed in respect to scenario S1, but is less pronounced. This is due to the fact that erosion and accretion is controlled by the longshore gradient in littoral drift not by the actual drift rate.

Figure 5.5.4 Left: Scenario 1A: Planform evolution within the first year of simulation for incoming wave angles of 10, 20 and 30 degrees. Right: Scenario S1: Planform evolution within the first year of simulation for incoming wave angles of 10 degrees, 20 degrees and 30 degrees.

Chapter 5 / Evolution of schematized nourishments

As the effect of the nourishment is spread out along the coast, transport patterns become similar, and as the gradients in coastline orientation decreases so does the overall transport gradients. In general it has been observed that the nourishments experience exponential cross-shore decay under the influence of wave energy (Figure 5.5.5).

Figure 5.5.5 Decay of the nourishment over the 20-year modelled period. Left: cross-shore position of nourishment peak of A1. Right: cross-shore position of nourishment peak of S1.

This analysis suggests that the lifespan of beach nourishments is prolonged when the sediment deposit is placed as a shoreward displacement of the shoreline forming a rectangular planfrom. Furthermore, the study shows that stability of the nourishment increases with longshore width of the nourishment. The joining of neighboring sediment deposits trough smoothening is also a factor which can contribute to maintaining sediment within the nourishment area since sediment is deposited in between the individual deposits. The decay of beach nourishments is related to the active span of the Q/α-curve, underlining the importance of knowledge about wave climate and changes in orientations along a potential nourishment area.

Chapter 6 / Shoreline change rates

6 Shoreline change rates The historical shoreline changes along the entire coastline of northern Zealand as well as the changes along the shoreline subsections at Tisvildeleje, Raageleje and Udsholt Strand was performed using the GIS-tool DSAS. In this section, Firstly, estimates of the general shoreline change trends are presented, and subsequently results of estimated shoreline change rates for the three shoreline subsections is presented. Furthermore, the varying rates of change in separate time periods are examined.

6.1 General observations The observed change from 1954 to 2014 is presented in figure 6.1.1. For the entire 32.8 km of coastline between -1 Hundested and Gilleleje the results of this analysis show that the average shoreline recession rate is ~0.16 m y , corresponding to a total of ~9.5 m for the period of 60 years. This corresponds to an average erosion rate of ~0.06 3 -1 3 m m per year, equal to ~41,440 m per year, with a total loss of sediment during this period amounting to 3 ~2,072,032 m .

Figure 6.1.1 Changes in shoreline position (m yr-1) and annual drift (m3 yr-1) along the entire coast between Hundested and Gilleleje. The distance shown in the diagrams corresponds to distance shown the bottom aerial photograph from 2014.

The largest shoreline retreat rate was found at Raageleje, where a total retreat of >50 m was observed at the pier, which over time has become submerged, and therefore no longer maintains its intended purpose. Another example of the evident chronic erosion is found at Liseleje, where the shoreline east of a large breakwater has been cut back (Figure 6.1.2).

Chapter 6 / Shoreline change rates

Figure 6.1.2 Examples of retreating shorelines at structures. Left: Wave breaker at Raageleje. Right: Liseleje, ~11 km along coastline shown in Figure 6.1.1.

Another example of the erosion and the attempt to halter the erosion of the beach by implementation of coastal structures is found along the coastline between Raageleje and Udsholt (Figure 6.1.3).

Figure 6.1.3 Erosion of coastline between Raageleje and Udsholt Strand.

From 1954 to 1995 the beach recessed approximately 30 m, despite of installation of smaller groynes in the western part of the coastline section. The 2002 photograph shows the installation of breakwaters in the eastern

Chapter 6 / Shoreline change rates

and middle part which caused the development of 30 m long tombolo formations every 40-60 m in lee of the breakwaters. By 2014 a chain of breakwaters along the entire stretch has been implemented in an attempt to prevent further recession. There is little evident effect of the installed groynes.

Figure 6.1.4 shows the average annual coastline retreat and littoral drift, for the entire time period as well as for three sub periods; 1954-1995, 1995-2002 and 2002-2014. Largest shoreline retreat is observed from 1995-2002, with an average of ~0.25 m per year. This rate is similar to that of 1954-1995, whilst the rates of the total period are evidently smaller. Conversely, an annual coastline advance of ~0.1 m is observed from 2002 to 2014, 3 -1 equivalent to a total accretion rate of ~32,300 m y .

Figure 6.1.4 Shoreline change statistics for the periods 1954-2014. Left: average shoreline change, m y -1, for the three periods. Right: Littoral drift m3 y-1.

The positive shoreline changes in the latter 12 years, may be a reflection of the storm event Bodil, where water levels reached 2-3 m above MWL and wave heights of ~3 m. Extremes like this causes sand and gravel to be eroded from the cliff, and delivered to the beach profile, which causes a shoreline advance, but not necessarily an increase in total sediment amounts. The DSAS tool can therefore be a misleading tool in cases of acute erosion, where new sediment is released from the cliff and enters the profile.

In accordance with general knowledge presented earlier in this work, the findings presented here validate that the coastline of northern Zealand is subject to chronic erosion.

6.2 Tisvildeleje -1 The average yearly coastline retreat rate from 1954-2014 for Tisvildeleje is ~0.2 m y , amounting to an erosion 3 -1 rate of ~5200 m y . The largest retreat in coastline is observed around the breakwater (Figure 6.2.1). For the 3 -1 more current period 1995-2014, an erosion rate of ~6200 m y is found.

Chapter 6 / Shoreline change rates

Figure 6.2.1 Changes in shoreline position (m yr-1) and annual sediment transport (m3 yr-1) along the Tisvildeleje The distance shown in the diagrams corresponds to the bottom aerial photograph.

Figure 6.2.2 shows the shoreline movements for the periods 1995-1999, 1999-2002, 2002-2010 and 2010-2014. The corresponding erosion rates are shown in Appendix E. There is a slow decrease in the retreat rate from the wave breaker towards east, with the exception of a section around 2250 m, where retreat has been especially significant in the period between 1954 and 1995, prompting construction of the chain of breakwaters and a revetment which are present today, and have produced a slight advance of the overall shoreline here.

Figure 6.2.2 Annual shoreline movement in different time periods within the last two decades.

The largest variations are observed during the periods 1999-2002 and 1995-1999, with a peak annual retreat rate -1 from 1999-2002 of ~3.5 m y at distance 1200 m.

Chapter 6 / Shoreline change rates

6.3 Raageleje The annual shoreline recession rate at Raageleje for the period 1954-2014 is 0.2 m, with the total sediment loss 3 -1 amounting to ~5200 m y . Figure 6.3.1 shows the annual coastline movement as well as the annual volumetric change in sediment along the entire coastal subsection.

Figure 6.3.1 Changes in shoreline position (m yr-1) and annual sediment transport (m3 yr-1) along the Raageleje. The distance shown in the diagrams corresponds to the bottom aerial photograph.

Along the first half of the coastline the recession rate is larger than at the downstream part, except for the area in lee of the breakwater at approximately 600-850 m. At some places, the beach in front of the seawall has completely eroded despite of the groyne field, leaving only a narrow sediment starved beach.

Figure 6.3.2 shows the shoreline movement for the overall period, as well as for the three sub-periods. An advance of the coastline at the groyne field, approximately 1100-1200, in the period 1995 to 1999 m is followed by a large retreat in the following period, 1999-2002. In the period 1995-2010, the annual sediment loss is ~6200 m3 y-1.

Figure 6.3.2 Annual shoreline movement in different time periods within recent years. Corresponding sediment transport rates are shown in Appendix E.

Chapter 6 / Shoreline change rates

6.4 Udsholt Strand Conversely, to findings in the two previously analyzed shoreline subsection, it was found that at Udsholt Strand the overall coastline subject to investigation had advanced during the 60 year period from 1954-2014. The perturbation described in Chapter 3 (section 3.5.3) is located approximately 400 m along the shoreline. The shoreline analysis revealed that it had advanced some 50 m over the 60-year period, inflating the entire sediment budget so that the overall budget becomes positive (see Figure 6.4.1). The perturbation has developed just downstream of a significant change in shoreline orientation from northwest to north-northwest (see photograph Appendix B).

Figure 6.4.1 Top: Aerial photograph from 1954. Bottom: Aerial photograph from 2014.

The advance at Udsholt Strand results in a distortion of the overall sediment budget along the coastline. The -1 3 -1 average shoreline advance was found to be ~0.02 m y corresponding to an accretion rate of ~2900 m y . From the shoreline movement and annual transport it is evident that erosion is occurring along the shoreline east of the perturbation (Figure 6.4.2).

Chapter 6 / Shoreline change rates

Figure 6.4.2 Shoreline change from 1954 to 2014. The bottom aerial photograph of the coastline in 2014 is scaled and fitted to the distance shown in the top panels.

As seen in Figure 6.4.3, the shoreline west of Udsholt Strand has suffered erosion, despite attempts to maintain the beach, and this is likely the source of the sediment deposited at the perturbation. Discarding this perturbation, -1 3 the rest of the shoreline has retreated at an average rate of ~0.3 m y corresponding to a sediment loss of 2600 m y-1. Figure 6.4.3 shows the observed coastline retreat from 1954-2014 east of the perturbation (approximately from distance 600 m).

Figure 6.4.3 Shoreline change immediately east of the perturbation shown together with aerial photograph from 2014, black dotted line: coastline 1954

A closer look at the recent time periods reveals that the perturbation advanced significantly seaward from 1999 to 2002, and then increased just east of the peak in the following two periods (Figure 6.4.4), verifying the observations mentioned in the area description in section 3.5.3.

Chapter 6 / Shoreline change rates

Figure 6.4.4 Annual shoreline movement in different time periods within recent years. Corresponding littoral drift rates are shown in Appendix E.

Chapter 7 Nearshore wave modeling and equilibrium orientation

7 Nearshore wave modeling and equilibrium orientation In order to produce a nearshore wave climate, which could be used for further site specific simulations, MIKE21 spectral wave model was used for modeling the wave propagation of the available offshore wave data (DKBS). The nearshore waves obtained by use of this model are used in the LITLINE simulations of the coastline evolution at the three specific shorelines.

7.1 Wave modeling The nearshore waves were computed for the 19-year period from 1994 to 2013 within the entire study area domain. The locations of the data selected for creating the boundary conditions to the coastal wave model are shown in Figure 4.4.1. To see the effect of the wave transformations performed by the MIKE 21 spectral wave model, waves were extracted in points at 5, 7, and 9 meters depth off the coast at the three shoreline subsections, Tisvildeleje, Raageleje and Udsholt Strand.

An example of the effect of the wave transformation across the nearshore bathymetry is visualized in Figure 7.1.1, which shows the offshore wave height and the wave height at 5 m depth off the coast at Tisvildeleje. The mean significant wave height at 9 m is 0.56 m, whilst the mean significant wave height at 5 m is 0.49 m, corresponding to an average decline in significant wave height of 11 %. The seasonal variation is as expected; months with higher significant wave heights are generally November to February, whilst the months with a calmer wave climate are April to August.

Figure 7.1.1 Comparison of significant wave height at offshore location (DKBS) and the simulated nearshore significant wave height at 5 m depth, serving as an example of the wave transformation performed by the MIKE 21 spectral wave module (SW model). Top: years 2002-2011. Bottom: year 2002.

Chapter 7 / Nearshore wave modeling and equilibrium orientation

To further illustrate the wave transformation, figure 7.1.2 shows a snapshot of the wave conditions from January 3, 2003 at Udsholt Strand where the offshore significant wave height at the model boundary is ~2.1 m. The wave simulation shows the wave height transformation and directional change. The waves are initially approaching from 260 degrees, and refraction of the waves and alignment with the coast is evident. The vectors illustrate the divergence of the wave orthogonals as the waves propagate towards land, which causes a decrease in energy and ultimately the observed decrease in significant wave height.

Figure 7.1.2 Wave simulation results for Udsholt Strand, January 3 2003. Example of the change in significant wave height as the offshore waves propagate towards the land.

Figure 7.1.3 shows the change that has occurred in wave direction. Waves with offshore mean directions of ~265 degrees have a mean direction of ~311 degrees or more in the nearshore area, corresponding to a change in direction of >45 degrees.

Chapter 7 / Nearshore wave modeling and equilibrium orientation

Figure 7.1.3 Example of change in mean wave direction, as the offshore waves propagate towards the land. Wave simulation results for Udsholt Strand, January 3 2003.

From the wave transformation results, wave parameters have been extracted at 5, 7, and 9 m depth off the coastlines at Tisvilde, Raageleje and Udsholt Strand

The wave roses in Figure 7.1.4 show the directional distribution of significant wave heights offshore as well as in the nearshore points off the coast at each of the locations.

The wave roses show that the waves with significant wave heights of >1.5 m have all been bent towards an angle more normal to the shoreline orientations, and waves of this size are no longer present in the high incidence angle intervals. This transformation is not only evident when comparing the offshore waves to the nearshore simulations, as the change in directional distribution is also evident across the nearshore from 9 m depth to 5 m depth.

Chapter 7 / Nearshore wave modeling and equilibrium orientation

Figure 7.1.4 Directional distribution (mean wave direction) for significant wave heights. Top row: Tisvildeleje (coastline orientation is 322 degrees), middle row: Raageleje (coastline orientation is 320 degrees, bottom row: Udsholt Strand (coastline orientation is 337). From left: Offshore waves (DKBS), predicted directional distributions at 9, 7 and 5 m.

At all locations, the peak offshore wave directions are between 250 and 260 degrees (see wave sorting details in Appendix F). It can however be noted, that the waves at Raageleje approach from slightly more westerly directions than Tisvildeleje, and at Udsholt even more waves are from westerly directions and the wave heights are also slightly larger than observed at the other locations.

The directional distributions clearly reflect the effect of the refraction process simulated by the SW model; the high angle offshore waves have been aligned, eliminating any wave approaching from shore parallel angles.

Chapter 7 / Nearshore wave modeling and equilibrium orientation

7.2 Model sensitivity to incoming wave angles and equilibrium orientations As described in chapter 2, the equilibrium orientation is a valuable parameter for the assessment of shoreline sediment budgets. Q/α-curves show the variation in the potential littoral drift for a given set of wave conditions as a function of shoreline orientation.

For each of the three locations, the annual sediment drift was calculated using the sediment transport model LITDRIFT and Q/α-curves were constructed. In order to also compare the effect of the wave climate on equilibrium orientation, the littoral drift rates were calculated for the three wave conditions in the nearshore as well as for the offshore wave data.

The transport rates for each of the locations with the four different wave climates are presented in Figure 7.2.1. These also provide information about the equilibrium orientation, as zero sediment transport is obtained when the resulting wave energy approaches normal to the shore. Negative values indicate that the integrated drift is directed westward and positive an eastward direction.

Figure 7.2.1 Q/α-curve for the simulated littoral drift potentials for differing wave cliamtes at all three locations. The arrow mark the shoreline orientation at each of the shoreline subsections. From left: Tisvildeleje, Raageleje and Udsholt Strand.

At Tisvildeleje the shoreline normal is 322 degrees, and from the Q/α-curves it is seen that the corresponding annual littoral drift is significantly different depending on which wave climate is used to generate the potential drift. The non-modified offshore waves result in a potential drift of ~350,000 m3 y-1, whilst the SW-nearshore wave climates at 5, 7 and 9 m depth, result in an annual drift of ~ -40,000 m3 y-1, ~-22,000 m3 y-1 and ~19,000 m3 y-1, respectively.

The orientation at Raageleje is 320 degrees and the potential littoral for the offshore wave data corresponds to ~260,000 m3 y-1, whilst, the model predicts a drift of ~ 12.000 m3 y-1 for nearshore waves extracted at 9 m and ~ - 650 m3 y-1 and ~ 3,500 m3 y-1 for waves at 7 and 5 m.

At Udsholt Strand, the predicted littoral drift was significantly larger than at the two other locations. This can mainly be explained by the fact that the shoreline orientation has shifted to 337 degrees, resulting in a more significant disequilibrium between the dominant wave direction and the coast (See section 3.5.5). Due to this fact, and because the wave direction along this part of the coast is subject to more energy directly from western directions, the simulated drift is very high. The offshore waves result in a potential drift of ~390,000 m3 y-1,

Chapter 7 / Nearshore wave modeling and equilibrium orientation

whilst applying the SW-nearshore wave climate for 5, 7 and 9 m depth, results in an drift rates ~100,000 m3 y-1, ~125,000 m3 y-1 and ~190,000 m3 y-1, respectively.

Equilibrium orientations for each wave climate identified from the Q/α-curves are listed in table 7.1.

Table 7.1 Equilibrium orientations for varying wave climates. Equilibrium Location Wave extraction orientation Tisvildeleje DKBS 297⁰ SW 9m 320⁰ SW 7m 324⁰

SW 7m 326⁰ Raageleje DKBS 297⁰ SW 9m 319⁰ SW 7m 320⁰

SW 7m 319⁰ Udsholt DKBS 296⁰ SW 9m 320⁰ SW 7m 323⁰

SW 7m 326⁰

For modeling of the nourishment evolution at the three coastline sections, the waves extracted at 9 m depth were selected. The Q/α-curves as well as the derived equilibrium orientations highlights that small variations in the shoreline orientation can result in a steep change in littoral drift, indicating that the calculations of potential littoral drift rates is highly sensitive to changes in coastline orientation. This implies that selection of the coastline orientation and input wave parameters are a prerequisite for successful modeling of a littoral drift.

Chapter 8 / Coastline evolutions

8 Coastline evolutions In the previous chapter the littoral drift rates for the three study sites were calculated using LITDRIFT in order to evaluate the effect of different wave climates. In the following section, nourishments are placed along each of the three shoreline subsections, and the evolution is modelled using LITLINE. At all locations, the nourishments were placed in the upstream parts of the coastline just downstream of a littoral barrier.

The evolution of an initially rectangular perturbation subject to constant wave conditions has been reviewed in the study of the schematized nourishment scenarios. The placing and shapes of the nourishments in this case study are similar to that of scenario S1.

Two cases are studied in the present chapter for each of the locations where perturbation evolutions are simulated for 20 years at each of the shoreline subsections. For yearly time steps not presented in this chapter, see Appendix G.

The nourishments are placed along the shorelines by displacing the coastline seaward. In the first case, the shoreline is displaced 20 m along 400 meters, corresponding to an added sand volume of ~64,000 m3. In the second case, the shoreline is also displaced by 20 m but along 800 m sections amounting to a total volume of ~128,000 m3.

Several other parameters in LITLINE and LITTABL were calibrated thoroughly, but changes in the angles between the two endpoints both upstream and downstream was found to have the most significant effect on the domain sediment budgets. Therefore, prior to simulating the evolution, the LITLINE setups were optimized independently for the three sites by calibrating the littoral drift in and out of the model domain against the observed erosion rates in order to replicate erosion rates corresponding to the historical observations and thereby a reproduce realistic shoreline change rates in the simulation period.

The input and output of sediment in the model domains were controlled by adjusting the coastline orientation at the first and last 10 m of the coastline sections according to the Q/α- curves presented in the previous chapter. The edges of the model domain have been disregarded since the manipulation of orientations here produces an unviable evolution.

8.1 Tisvildeleje At Tisvildeleje, the nourishments were placed on the shoreline just downstream of the breakwater (at approximately 600 m), and the effect of the attached breakwater as a littoral barrier was found difficult to simulate using LITLINE. Simulating the coastline evolution with a breakwater or revetment at this location did not produce good results, and instead the best model fit was found by inserting a long jetty at the location of the breakwater. Furthermore a revetment was inserted along the coastline east of this jetty, where the beach is actually kept in place by chains of breakwaters as well as revetments. The simulation was run for a warm up period in order to stabilize the effect of the jetty, so the planform development would not be skewed.

The LITLINE simulation yielded an erosion rate of ~10,000 m3 y-1 corresponding to an average recession rate of 0.47 m y-1. The evolution of the 64,000 m3 nourishment is shown in Figure 5.4.1 and Figure 5.4.2, shows the evolution of the larger deposit of approximately ~128,000 m3 sand. The nourished shorelines are shown together with the non-nourished coastline simulated for the same time period.

Chapter 8 / Coastline evolutions

Figure 8.1.1 Plan views of the model domain at Tisvildeleje after a 20 m seaward displacement of a 400 m section of the beach east of the breakwater (from top: yr. 0, 1, 2, 3, 5, 10, 15 and 20. Dotted line represents the nourished shoreline, and black represents the shoreline evolution with no nourishment.

Chapter 8 / Coastline evolutions

Figure 8.1.2 Plan views of the model domain at Tisvildeleje after a 20 m seaward displacement of a 800 m section of the beach east of the breakwater (from top: yr. 0, 1, 2, 3, 5, 10, 15 and 20. Dotted line represents the nourished shoreline, and black represents the shoreline evolution with no nourishment.

Chapter 8 / Coastline evolutions

The Figures above show that the cross-shore beach width of the perturbation decreases while alongshore length increases as a function of time. Within the first year, the shape of the deposit changes quickly from rectangular to a low bell-shape, and a rapid recession is observed at the shoulders of the deposit. The Figures also show that the shoreline upstream from the jetty has accreted, since this is not due to the nourishment, but the effect of the jetty which blocks the upstream input of sediment into the domain, this accretion is disregarded.

The effect of the littoral barrier is evident in both scenarios; it is evident that the spreading out is blocked by the jetty. This effect is illustrated in Figure 8.1.3 where zero is the modelled shoreline position with no nourishment, shows the shoreline position in the two nourishment cases, around the jetty. The Figure show no migration of the peak or downdrift displacement of the nourishment. The littoral barrier does however cause the maximum cross- shore extent of the perturbation after 20 years to be located slightly upstream from the initial center of the initial rectangular perturbations.

Figure 8.1.3 Plan views of simulated shoreline evolution at Tisvildeleje. Cross-shore distance 0 represents the un-nourished coastline after 9 years. Left panel: smaller nourishment (initial nourishment 400 m along the shoreline). Right panel: larger nourishment (nourishment along 800 m of the shoreline). Top panel: years 0-10, bottom panel: years 12-20.

After 20 years, the alongshore extents of the nourishments are 1300 m and 1600 m for the smaller and larger nourishment, respectively. By the end of the simulation period the maximum gained beach width is 10.5 m and 14.5at the peak of the bell-shaped planforms.

Chapter 8 / Coastline evolutions

8.2 Raageleje The shoreline Raageleje is closer to its equilibrium orientation than Tisvildeleje. In the shoreline change analysis presented in chapter 6, it was found that the annual erosion rate at Raagelege is similar to that of Tisvildeleje (~5,200 m3 y-1), and the LITLINE model domain was therefore calibrated in order to produce an erosion rate within a reasonable range of this. It was chosen to implement an offshore breakwater in the model setup at the location corresponding to the submerged breakwater as well as a revetment along the entire coastline east of the breakwater which is fronted by groynes.

This domain produced a littoral drift of approximately 10,000 m3 y-1, corresponding to an annual recession rate of ~0.43 m3 y-1. The two nourishments were placed approximately 600 m from the upstream boundary, where it has been observed that the beach has suffered severe erosion in front of the concrete seawall. The planview of the nourishments and the 20-year predicted coastline evolutions for both nourishment cases are shown in Figures 8.2.1 and 8.2.2. Since no barrier obstructs the littoral drift in this domain, the spreading out is significantly different than the pattern observed at Tisvildeleje, where the directional spreading was limited in the upstream direction. Within the first year of modeling the nourishment with an initial alongshore length of 400 m has spread out covering an additional 200 m in both the upstream and downstream direction and the initial maximum cross- shore width of 20 m has already decreased with 1 m. The larger nourishment does not decrease its maximum cross-shore width until 3 years modeling, and by then the nourishment has spread out 400 m in both directions.

In both scenarios, the nourishments spread out beyond the upstream boundary of the model domain. By the end of the simulation period, the smaller deposit has spread out across approximately 2100 meters, with a peak cross shore distance of 5 m, whilst the bigger deposit has spread out across the entire model domain and has maintained a peak cross-shore distance of 11 m (Figure 8.2.3).

Chapter 8 / Coastline evolutions

Figure 8.2.1 Plan views of the model domain at Raageleje after a 20 m seaward displacement of a 400 m section of the beach east of the breakwater (from top: yr. 0, 1, 2, 3, 5, 10, 15 and 20. Dotted line represents the nourished shoreline, and black represents the shoreline evolution with no nourishment.

Chapter 8 / Coastline evolutions

Figure 8.2.1 Plan views of the model domain at Raageleje after a 20 m seaward displacement of a 800 m section of the beach east of the breakwater (from top: yr. 0, 1, 2, 3, 5, 10, 15 and 20. Dotted line represents the nourished shoreline, and black represents the shoreline evolution with no nourishment.

Chapter 8 / Coastline evolutions

Figure 8.2.3 illustrates the spreading out of the nourishments. Here, it is clear that both the updrift and downdrift coastline sections accrete and benefit from the sand deposit, and no migration in the downdrift is detected even though the annual drift is ~10,000 m3. The disturbance 700 meters into the domain is ascribed to the presence of the wave breaker.

Figure 8.2.3 Plan views of simulated shoreline evolution at Raageleje. Cross-shore distance 0 represents the un- nourished coastline after 9 years. Left panel: smaller nourishment (initial nourishment 400 m along the shoreline). Right panel: larger nourishment (nourishment along 800 m of the shoreline). Top panel: years 0-10, bottom panel: years 12-20.

8.3 Udsholt Strand The nourishments at Udsholt Strand were placed downdrift from the perturbation, which was described in detail in previous sections, because it is evident from the shoreline analysis in chapter 6, that this shoreline section is receding. Reproducing an accumulation of sediment along the perturbation proved difficult since the gradients in sediment size was not accounted for in the LITLINE simulations, and the model setup will straighten the shoreline if these natural undulations are not represented with a mechanism of fixating the coastline position. With no structures present along the perturbation, the shoreline was smoothened out within a relatively short time period due to the angle between the incoming waves and the undulation. Therefore a 250 m revetment in the eastern section served as a mean of keeping the perturbation in place. Revetments may in some cases advantageously be implemented in order to simulate the effect of a shortage of mobile sediment. Furthermore, a revetment was placed along the locations protected by breakwaters. This LITLINE setup produced an annual drift of 4,000 m3 y-1. The plan views of the shoreline evolution of the two nourishment cases shown in Figure 8.3.1 and 8.3.2.

Chapter 8 / Coastline evolutions

Figure 8.3.1 Plan views of the model domain at Udsholt Strand after a 20 m seaward displacement of a 400 m section of the beach east of the breakwater (from top: yr. 0, 1, 2, 3, 5, 10, 15 and 20. Dotted line represents the nourished shoreline, and black represents the shoreline evolution with no nourishment.

Chapter 8 / Coastline evolutions

Figure 8.3.2 Plan views of the model domain at Udsholt Strand after a 20 m seaward displacement of a 800 m section of the beach east of the breakwater (from top: yr. 0, 1, 2, 3, 5, 10, 15 and 20. Dotted line represents the nourished shoreline, and black represents the shoreline evolution with no nourishment.

Chapter 8 / Coastline evolutions

The nourishment spreads out in front of the seawall representing the perturbation; here a small bump of sediment can be observed in some time steps (Figure 8.3.2). This effect should be disregarded as an actual nourishment effect, but the observation does, however, underline, that the spread out effect of the nourishment does in fact bypass minor littoral barriers.

The shoreline displacement caused by the nourishments are shown in Figure 8.3.3 (the shoreline section in front of the seawall is disregarded). Like the nourishment evolution at Tisvildeleje, it is evident that littoral barrier limits a symmetric spreading out of the nourishment. Since the sediment cannot bypass the barrier, the planform becomes asymmetric. For both nourishment scenarios, the peak shifts upstream after three years, but as the nourishment decreases in cross-shore width, the peak is again translated in the downstream direction.

Figure 8.3.3 Plan views of simulated shoreline evolution at Udsholt Strand. Cross-shore distance 0 represents the un- nourished coastline after 9 years. Left panel: smaller nourishment (initial nourishment 400 m along the shoreline). Right panel: larger nourishment (nourishment along 800 m of the shoreline). Top panel: years 0- 10, bottom panel: years 12-20.

Interestingly, the cross-shore beach width grows beyond that of the initial nourishments in both scenarios. And it is not until 15 years of simulation that the maximum extent recesses significantly. Since the domain area is shorter than at Tisvildeleje and Raageleje, the nourishment spreads out of the downstream domain boundary.

Chapter 9 / Discussions

9 Discussions In this chapter the main findings of this study will be discussed in order to give an overall picture of the beach nourishment behavior uncovered throughout numerical modeling of the evolution of schematized beach nourishment scenarios as well as the complex task of replicating and predicting beach nourishment evolution in a natural setting. The discussion is divided into four main lines of enquiry: section 9.1 is concerned with the result of the shoreline change analysis and relations to the simulated littoral drift calculated using LITDRIFT. Section 9.2 discusses the projected beach nourishment planform evolution and explores the possibility of downdrift migration of beach nourishments analytically since this has not been possible to model using LITLINE. In section 9.3 the symmetric speeding of out of beach nourishments is compared to the monitored development of the Sand Engine. Lastly the methods applied in this study are discussed with regards to reservations, advantages and disadvantages in section 9.4.

9.1 Shoreline change and potential longshore sediment transport The coastline analysis of the historic shoreline positions and the derived recession rates since 1954 served as valuable insight into the sediment budget of the coastline of North Zealand as the findings provided a direct account of the actual erosion. In this section the differences and validity of the erosion rates determined using DSAS and the littoral drift rates simulated in LITLINE are discussed and compared.

It is important to distinguish between potential littoral drift and the amount of sediment that is actually eroded from a particular shoreline. The potential littoral drift is usually difficult to quantify, and literature has revealed that such quantifications does not exist for the North Zealand coastline.

The trend of a gradual increase in littoral drift from Hundested towards Gilleleje, which holds consensus with in literature, was observed in this analysis (Figure 6.1.1). The average shoreline recession rate during the past 60 -1 3 -1 years was found to be 0.16 m y , corresponding to a sediment loss of ~41,440 m y . This figure is similar to littoral drift rate estimates available in literature; e.g. Hasløv & Kjærsgaard (2014) suggest a potential littoral drift rate of 40,000 m3 y-1 and an actual erosion rate of 25,000 m3 y-1.

This study found that several kilometers of erosion along the shoreline from Hundested to Gilleleje in the time period between 1954 and 2014. In between the retreating sections suffering chronic erosion, the shoreline fluctuated between small advances and retreats. Further analysis of the trends in coastline recession rates in the recent decades showed that excluding the first 40 years from the analysis did not produce smaller recession rates. The highest annual recession rate for the periods 1954-1995, 1995-2002, 2002-2014 and 1954-2014 was found to be 1995-2002. The advance of the shoreline from 2002-2014 was ascribed to the storm event Bodil, which released large quantities of sediment into the littoral system from dunes and cliffs. When the shoreline positions are compared by using the land/water boundary, sediment transported seaward from the upper part of the profile is expressed as shoreline advance even though it is not due to an increase in the total amount of sediment within the profile, and the observed accretion is actually an expression of acute erosion.

Due to the long time period covered in this analysis, varying types of structures along the shoreline subsections have been constructed which to some degree hampers rational use of these results in some areas. Where groyne fields had been constructed or other protection measures had been taken, a reversal in trends and rates of shoreline evolution was observed. The gradual fortification of the coastline will in many cases cause a downdrift translation of erosional hotspots, which can also be observed along the coast of North Zealand. At some locations, the linear shoreline change rates in m y-1 might therefore not be a suitable measure due to the nonlinear nature of longshore sediment transport and shoreline changes. A more elaborate discussion the method used for historical erosional rate is found later in this chapter (section 9.5.1).

Chapter 9 / Discussions

The analysis of the entire coastline validates that the coast of North Zealand suffers chronical erosion, combined with the local analysis of each subsection; it provided insight into the dynamics and effects of the installed shoreline protection structures.

The easterly directed increase in recession rates was not detected along the individual subsections at Tisvileleje, Raageleje and Udsholt Strand. At Tisvildeleje and Udsholt Strand, the peak recession rates were observed just downdrift from the littoral barriers located in the western part of the selected coastlines creating a local transport pattern which is controlled by the sediment availability and not the overall potential transport capacity. As described previously, the formation of the perturbation at Udsholt Strand distorted the general sediment budget of this subsection. The sediment budget should be revised with respect to the geomorphological setting as well as the anthropogenic manipulations of the natural system.

The results of the simulated potential longshore sediment transport were presented as Q/α-curves in the sensitivity analysis, section 7.2. These results are in accordance with the observed trend of east-directed longshore sediment transport, as the potential drift rate at Udsholt Strand is much higher than at Tisvildeleje and Raageleje. In the cases of both Tisvildeleje and Raageleje, the actual shoreline orientation is so similar to the calculated equilibrium that the waves extracted at 5 and 7 meters depth produce a longshore sediment transport directed towards west. This is in direct discrepancy with the geomorphological shoreline features along the coast such as the described leeside erosion east of the wave breaker in Tisvildeleje, as well as in the multiple groyne fields within the area.

Within shoreline evolution modeling wave transformation is a key element of a meaningful calibration of the simulated littoral drift and the wave direction is extremely critical often more important than wave height. In this study, the offshore wave parameters from a national hindcast model were applied as forcing for the spectral wind-wave numerical model MIKE21 SW which was used for propagating the waves towards the coast. This nearshore wave climate was then used in LITDRIFT as a qualitative assessment of potential longshore sediment transport in the three study areas. The potential sediment transport is predicted using the general orientation of the subsections, and as exemplified by the Q/α-curves, small changes in orientation is of large importance to the calculation of potential sediment transport rates. The potential transport may therefore vary along a meandering coastline section.

The simulated potential drift at Udsholt Strand was found to be in the order of 190,000 m3 y-1 when applying the wave data extracted at 9 m depth and ~100,000 m3 y-1 when applying the wave data extracted at 5 m depth. The potential drift rate of ~190,000 m3 y-1 surpasses any estimates found in literature, but a drift rate of ~100,000 m3 y-1 at Gilleleje has been suggested by DHI (2013). This revokes the problem of quantifying the potential sediment transport, but in the presented literature there is agreement on the presence of an increasing sediment deficit from Hundested to Gilleleje, and this is reproduced in the littoral drift estimates produced in this study by use of LITDRIFT.

In the planning of beach nourishment projects the observed erosion rates should not be assumed to match the potential littoral drift for the particular shoreline. When a coastline section is suffering from sediment deficiency, the actual erosion rate may be much less than the potential transport capacity. Placing beach nourishments at a coastline will introduce large amounts of available sand to the littoral system; and in cases where the potential drift rate is higher than the actual erosion rate the erosion rate will increase within the littoral drift potential. This means that when estimations of nourishment lifespans are made, both the actual erosion rates and estimates of the potential drift should be considered.

Chapter 9 / Discussions

9.2 Beach nourishments and shoreline perturbation evolution This section will firstly discuss the possibility of beach nourishments migrating in the direction of the littoral drift. This discussion will include comparisons of elaborate studies of shoreline perturbation evolution and the erosional patterns determined from the study of schematized beach nourishment evolution presented in chapter 5. Secondly, the projected beach nourishment evolution at Tisvildeleje, Raageleje and Udsholt Strand are held against the idealized evolution of the schematized nourishment setups, and issues of modeling the natural variability of the shorelines as well as the effects of hard structures is discussed. Finally, the possibility of changes in patterns of nourishment planform evolution induced by sediment starvation is explored.

9.2.1 Migration of nourishment deposits When considering a beach nourishment as a shoreline perturbation, comparison with the evolution of natural shoreline undulations such as shoreline sand waves can provide further insight into nourishment behavior. Sand waves can occur as single features or as rhythmic patterns along a coast, and the alongshore width can be several kilometers. Studies have shown that such undulations tend to migrate downdrift whilst still maintaining their sand volume (van den Berg et al., 2010). Migrating shoreline sand waves have been observed at many locations, including the Danish North Sea Coast (Kærgaard, 2011). The catalysts and the morphodynamics of sand waves have been linked to large sediment discharges from rivers, welding of shoals and bars and finally, the emergence and migration of shoreline undulations have been linked to shoreline instability caused by waves approaching from high incidence angles (Kærgaard, 2011; van den Berg et al., 2010; Ashton et al., 2001 ). The following section is concerned with the mechanism driving the migration of shoreline undulations which will be discussed, in relation to the nourishment evolution modelled using LITLINE.

Ashton et al. (2001) were the first to model the shoreline instability created by high angle waves, and they found that in the case where a coast is continuously affected by waves from a single high-angle direction the waves induce instabilities in the shoreline. The continued erosion along the updrift flank of a perturbation will increase the local shoreline angle and eventually result in downdrift migration of the inflection point. This will ultimately cause the accreting peak to translate downdrift while growing seaward. As the amplitude of the crest increases, sediment flux just downdrift of the crest will approach zero leading to a spit like feature extending from the perturbation crest. Van den Berg (2010) found that if there is a dominant littoral drift the feedback between the changing coastal morphology and the general wave field will cause downdrift migration of a coastline no matter if they grow or decay.

The migration of a shoreline undulation is explained by the feedback between waves and bathymetry; when waves approach the coastline from high angles (>45 degrees) a reduction of the wave angle along the upstream flank of the perturbation will lead to increased transport capacity, whilst the opposite response is observed when waves approach at low angles (< 45 degrees).

Figure 9.2.1 Visualization of the instability of a shoreline perturbation subject to high angle waves. Left: Q/α-curve showing the corresponding response in sediment transport. Right: Angle between incoming waves and shoreline normal. (Kærgaard, 2011)

Chapter 9 / Discussions

From the transport pattern shown in Figure 9.2.1 it becomes clear that any small undulation of the shoreline will have a larger longshore sediment transport on the upstream side (qu) than on the downstream side (qd). This results in erosion on the upstream side of the perturbation and accretion on the downdrift side (Kærgaard, 2011).

Ashton and Murray (2006a) showed that in cases where sediment transport is driven by low-angle waves the shoreline will tend to smoothen out any undulations along an otherwise straight sandy coastline. In opposition to this, van den Berg (2010) found that a simplified nourishment perturbation with an alongshore length of 2,000 m and a cross-shore width of 100 m migrated noticeably in the downdrift direction when subjected to waves approaching the coast from angles larger than 30 degrees. During a simulation period of eight years, a migration rate of 56 m y-1 was found. The effect of high-angle waves (in this study determined 30-60 degrees) was also modeled, and this yielded a migration rate of 800 m within the first year. Long-term modeling with constant high-angle incidence waves lead to migration and the formation of rhythmic downstream undulations on the coastline, also termed sand wave trains (van den Berg, 2010). Both Ashton and Murray (2006a) and van den Berg (2010) successfully model migration of shoreline undulation but differ on the critical angle at which migration takes place.

In this present study, LITLINE was used for modeling the evolution of schematized perturbations along an otherwise straight coastline. LITLINE assumes a stable shoreline, and it was found that migration of the perturbations could not be modeled. The model became unstable and could not predict the shoreline response when the angle between the incoming waves and the shoreline orientation approached 45 degrees at any point along the shoreline. Due to this, the model was limited to a maximum input angle of 30 degrees and thus, none of the modeled scenarios showed signs of migration. The migration of a perturbation induced by high-angle wave instability observed in other studies could not be modelled using LITLINE.

The investigation clearly demonstrated that the erosional patterns change as a function of incoming wave angle, but for the stable angles applied in this study the diffusion patterns are highly symmetric. The smoothening of the shoreline perturbation observed in all schematized scenarios corresponds to earlier studies of perturbation planform evolution (e.g. Dean, 1992; Work and Dean, 1995). On the contrary to what was initially expected, the gradient in sediment transport capacity along the nourishments was found to be higher for incidence wave angles of 10 degrees than for the higher wave angles. This is however, explained by analysis of the Q/α-curve.

The rectangular nourishments yielded a more stable transport pattern and were less sensitive to variation is wave angle than the initially bell-shaped nourishments. Overall stability of the nourishment increased with width, and this was especially evident when comparing the three rectangular nourishment scenarios. These findings are supported by Dean (1992).

It is widely accepted that the wave angle at breaking drives the longshore sediment transport, but Ashton and Murray (2006a) question at which wave state this angle should be taken into account; in their investigation of spit and sand wave formations it was found that the offshore wave angle controls the shape of the coastline. In the study of nourishment behavior at Tisvildeleje, Raageleje and Udsholt Strand, offshore waves were transformed to produce nearshore wave climates. This had a significant effect on the amount of high-angle waves approaching the shoreline. In the offshore wave data, a large proportion of the offshore waves were actually within the high incidence wave angle interval, and modeling nourishment evolutions using these waves, would most likely have resulted in shoreline instabilities.

At Udsholt Strand, a natural shoreline undulation was observed along a change in coastline orientation. From aerial photographs it was observed that the perturbation had grown within recent years. Based on the study of the coastline, the governing hydrodynamic conditions and the study of perturbation behavior when subjected to high angle incidence waves, it could be suggested that the formation of the perturbation has been triggered by a storm event with waves approaching from high angles. It was found that a large proportion of the waves off shore

Chapter 9 / Discussions

from Udsholt Strand approach the coast from 280-290 degrees, and this angle corresponds to an offshore incidence wave angle of ~45 degrees (see Appendix F).

In the modeled evolution of nourishments the perturbations are all smoothened out quite quickly and symmetrically. The natural perturbation at Udsholt Strand does however not show any signs of smoothing out. An essential explanatory factor for this is the difference in sediment size. Because the grain size at the perturbation is larger than that of the neighboring beaches, the sediment may not be mobilized under normal wave conditions. This theory is supported by the observations made during the beach nourishment project at Hald Strand, where it was observed that extreme weather events formed sand waves migrating in the downstream direction. In this project, the sediment grain size of the nourishment was also larger than that of the surrounding native sediment (Fællesudvalget for Kystpleje og Kystsikring af Nordkysten, 1987).

Ashton and Murray (2006a) showed that for asymmetric wave climates, shoreline features migrate in the downdrift direction either as sand waves or as off-shore flying spits, depending on the proportion of high-angle waves. It was found that when shoreline perturbations are subjected to a higher proportion of waves approaching from high-angle directions than from low-angle directions, the perturbation will grow seaward because the wave angle will cause sediment flux to reach its minimum at the peak of the perturbation. Mangor (2004) suggests that the development of spits on beach nourishments could occur if a large nourishment is placed along a beach where a large proportion of the waves approach from high angles. It is proposed that the spit development will lead to increased erosion at adjacent beaches due to the shadow effect caused by this nourishment shape. Therefore Mangor (2004) proposes that areas of high incident wave angles are less suitable for beach nourishment projects, which could question the suitability of a nourishment project at Udsholt Strand.

9.2.2 Beach nourishment evolution at the coast of North Zealand The actual transport rates obtained from the GIS-analysis provided an indication of the drift rate which should be obtained in order to reproduce the actual shoreline states at Tisvildeleje, Raageleje and Udsholt Strand. It was beyond the scope of this study to reproduce the exact variations of shoreline change trends for each location, as this would have required more time dedicated to fine tuning and detailed calibration of the model. Therefore the littoral drift rates for each of the shoreline subsections were reproduced by calibrating parameters to fit the overall sediment budget of each individual shoreline subsection.

The overall goal of simulating the shoreline response to placing large sand deposits at the eroding beaches of Tisvildeleje, Raageleje and Udsholt Strand was to predict the diffusion of the supplied sand in the years after the nourishments had been placed along the coast.

From the shoreline change analysis, it can be inferred that the amount of sediment supplied in the two nourishment cases simulated for each of the locations, is equivalent to the amount of sediment lost downstream over the course of 13 years for the smaller nourishment (400 m) and 26 years for the larger nourishment (800 m) in the cases of Tisvildeleje and Raageleje, and 22 and 44 years in the case of Udsholt Strand, respectively. However, by the end of the 20-year shoreline simulation period, none of the shorelines have reached the level equivalent to the baseline scenario. For the cases of the smaller nourishment scenarios at Tisvildeleje and Raageleje, additional beach width is still detected after 20 years.

The planform evolution of the initially rectangular nourishments where similar to the schematized evolutions despite of varying wave climate. Even though the littoral drift rates were reproduced in each individual setup, the distribution of the actual littoral drift along the coastlines was not replicated completely. In all setups, the sediment volume entering the domain was smaller than the amount of sediment exiting, but the drift was not evenly distributed across the domain.

Chapter 9 / Discussions

In the schematized nourishment scenarios, it was observed that the nourishments on a long straight beach evolve similarly despite a 30 degree change in mean wave direction. The nourishment deposits placed along the three shoreline subsections displayed the same trends in diffusivity as the schematized scenarios. Even at Udsholt Strand where the coastline is further from its equilibrium orientation, the spreading out of the nourishment is similar to the observation at Tisvildeleje and Raageleje which are closer to their equilibrium orientation.

However, the prediction of nourishment evolvement when coastal structures are present adds some difficulty and many uncertainties and Dean (1992) estimates the predictability of shoreline changes and volumetric losses where structures are present to be ±60 %.

The results of the shoreline evolution are limited by the fact that LITLINE assumes that the entire sections are covered by a veneer of mobile sediment even in areas where the shoreline is eroding. At Udsholt Strand, the modelled shoreline evolution may have been limited by the fact that in reality the sediment is coarser, and the produced coastline evolution is therefore not an accurate representative. It was however, attempted to keep the shoreline in place by the use of revetments.

Figure 9.2.2 serves as an example for showing the gradients in alongshore transport. In the scenarios with natural non-uniform wave conditions, the pattern established in the examination of the schematized nourishments was replicated. The gradients in longshore sediment transport were found to be most significant near the shoulders of the deposits, and it was also observed that as the planform evolves and the deposit spreads out, the gradient in longshore transport at the critical points was reduced.

Figure 9.2.2 Gradients in longshore sediment transport at the nourishment placed along the coastline of Tisvildeleje. Top: 800 m nourishment deposit. Bottom: 400 m nourishment deposit.

Chapter 9 / Discussions

Before any conclusions are drawn from these simulations, the limitations of the model and its calibration should be taken into consideration. The natural morphological and geological restraints should be carefully integrated into the evaluation of the model performance.

9.2.3 Nourishment migration on a starving coastline As described in this study, the entire coastline of northern Zealand has over a long period of time experienced sediment starvation, which over time has led to the implementation of large amounts of more or less efficient small scale beach protection measures. Groynes, breakwaters and slope protection of varying quality have shifted the areas of erosion leading to the implementation of more hard structures, which has led to erosion of sediment in the outer profiles, creating a starving seabed and a coastline that is not in equilibrium in the cross- shore and longshore directions. This is expected to alter the erosional and depositional response to a beach nourishment, as large amounts of available sediment is introduced into the littoral system.

In the investigation of schematized nourishment scenarios, it was found that the transport capacity decreases at the upstream flank of the nourishment, resulting in symmetric accretion characterizing the process of spreading out (chapter 5). This nourishment behavior presupposes that sediment is transported from the upstream area of the domain and is available for deposition once the shoreline perturbation is reached.

On a sediment starved coastline sediment availability will control the sediment transport rate, and the pattern of erosion and accretion where longshore transport is present, could lead to downdrift migration of an imposed shoreline perturbation. This is sketched in Figure 9.2.3.

Figure 9.2.3 The sketch shows the erosion and accretion pattern along a beach nourishment on a sediment starved beach, where potential sediment transport exceeds actual sediment transport. The resulting transport pattern is the outcome of gradients in transport capacity as well as the availability of sediment. Continuous line: initial beach nourishment planform shape. Dashed line: projected planform shape. Dashed arrow: potential sediment transport. Red arrow: potential sediment transport rate is not fulfilled. Blue arrow: actual sediment transport equals the potential littoral drift. Yellow zone: non-fulfilled littoral drift: local patterns of erosion are controlled by the availability. Red zone: erosion, where the sediment transport capacity is fulfilled by the nourishment sand. Green zone: accretion.

Along the upstream beach section, lack of available sediment limits the sediment transport so that the decrease in sediment transport capacity on the upstream flank of the nourishment is surpassed by the effect of sand available for transport. Along the crest of the perturbation, sediment will also erode, and a depositional zone will follow on the downstream flank due to decrease in transport capacity. This process will lead to downdrift migration of the shoreline perturbation.

Chapter 9 / Discussions

This suggests that the effect of beach nourishment at a starved shoreline will translate downdrift benefitting adjacent beaches. This asymmetric behavior and downdrift migration of shoreline perturbations does not depend on a given interval of wave incidence angles, but is induced by the introduction of available sand into an otherwise sediment starved system. Sediment placed at the upstream end of a starving shoreline can therefore be redistributed along the downstream shoreline by the changes in littoral drift and sediment availability at the nourishment.

9.3 Evolution of a sand engine for beach nourishment In this section, the modeled beach nourishment evolution presented throughout this study is compared to the design considerations and evolution projections as well as the current evolution of the Sand Engine.

This thesis has been concerned with the placement and evolution of a large volume of sand in one particular area on a coastline. This approach to beach nourishment projects has gained attention within recent years, especially associated with the Sand Engine project implemented in the Netherlands in 2011. The project is a pilot project of a 21.5 million m3 mega-nourishment on the Delfland coast, designed to feed a wide stretch of coast and increase the time interval between nourishments in combination with adding recreational value.

The mega-scale nourishment was proposed as a promising alternative for traditional beach and shoreface nourishments (Stive et al., 2013b). The project is a test of the efficacy of local mega-scale nourishments as a counter measure for the anticipated enhanced coastal recession in the Netherlands. If the predicted volume of necessary sand for nourishment of the Dutch coast were to be provided in the form of traditional shoreface nourishments, it would result in significant widening of the beaches along the entire Dutch coastline, which means that beach user’s access to water would become less accessible (Stive et al., 2013a).

Figure 9.3.1 shows the evolution of the nourishment from just after construction until 18 months later. The mega-nourishment initially formed a hook-shaped spit, and the prediction is that the deposit will gradually change shape before it is ultimately transformed into a new dune landscape and a wider beach. The envisioned lifetime is in the order of 15-20 years. Figure 9.3.2 shows the expected morphological development of the nourishment in the 20-year period.

Since a nourishment project of this scale has never been executed before, the long- term morphodynamic predictions of the nourishment are linked to inaccuracies. The model predicted morphology shows that the nourishment will gradually diminish in Figure 9.3.1 its cross-shore width and extend alongshore by 8 km over the 20-year period. It is Photographs showing the evolution of the Sand Engine, interesting, that the predicted nourishment evolution in Figure 9.3.2 gives a visual 2011-2012. From top to bottom: impression of the nourishment developing into an asymmetrical bell-shape, with 5 july 2011, 13 October 2011, 30 the peak migrating in the downdrift direction. However, observations made 18 March 2012 and 4 September 2012. (Dutch Ministry of months after the construction indicate that the planform shape has become nearly Infrastructure and Environment, symmetric; the erosion and accretive sections have reshaped the nourishment such 2013) that it resembles a bell-shape (Schipper et al., 2014).

Chapter 9 / Discussions

Figure 9.3.2 Long-term model prediction of the morphological development of the Sand Engine. (a) The initial model bathymetry, (b- f) the prediction 3, 5, 10, 15 and 20 years after construction. (Stive et al., 2013b)

Figure 9.3.3 shows a normal distribution function fitted to the outer shoreline positions 18 months after construction. This visualizes to what extent the nourishment planform has become symmetric. The resemblance between the shoreline shape and the Gaussian shaped normal distribution implies that the nourishment has very quickly diffused into the classical bell-shaped perturbation discussed throughout this study. The evolution of the Sand Engine suggests that beaches in the downdrift as well as upstream vicinity of a beach nourishment will benefit from the sediment supplied into the littoral system. This is in accordance with the behavior predicted using LITLINE using both constant and naturally varying wave conditions.

The skewedness of the planform shape and future conjectures about the behavior of this is, however, still part of ongoing research, as it is unknown whether the skewness that has been observed to date is a remnant of the initial asymmetry or a result of obliqueness in the wave climate (Schipper et al., 2014). Long-term detectability of initial nourishment shape was also seen in this study; the simulation of asymmetrically placed nourishments in this study (section 5.3) showed that even as the overall shape of the three sediment deposits converged towards a bell-shape, the initial skewedness was detectable throughout the 20-year modeling period.

Figure 9.3.3 Observed change in planform shape of the Sand Engine mega-scale nourishment, shown together with a normal distribution in order to visualize the developed symmetry in the planform shape. (Schipper et al., 2014)

Chapter 9 / Discussions

9.4 Uncertainties of the performed shoreline change analysis In this study, the DSAS tool in ArcGIS was used for digitizing and comparing shorelines along the coastline from Gilleleje to Hundested in order to obtain shoreline change rates, which is a commonly used measure for analyzing erosion along a coastline. Historic shoreline change analysis is often applied as a guideline for planning and modeling of coastal evolution such as beach nourishment projects, and the uncertainties associated with the method should be kept in mind.

According to literature digitizing shorelines using GIS is the preferred method for estimating shoreline change rates (Davidson-Arnott, 2010) However, the method does not necessarily provide an exact portrayal of the transport along the coast. For one, the assumption of a cross-shore profile of constant height and shape is a simplification of reality (DHI, 2013). A large uncertainty for the results obtained from this method is the active height of the profile, which apart from wave conditions also depends on the shapes and types of landscapes, which vary greatly along the coastline.

The backshore along some subsections of the coastline may be low-lying, whereas other sections are cliffs, and this variety is not accounted for in this simplified method. Along sections of coastline with elevated cliff sections, this method will underestimate the amount of sediment eroded when the coastline retreats.

Furthermore, the method assumes that the eroded sediment is included in the longshore transport. Of the eroded sediments, only a part will be incorporated into the longshore transport. Typically, the longshore transport will consist of sand within the sizes of normal beach sand as finer sediments will be transported offshore, and not accrete in nearshore areas. Contrariwise, the wave conditions will rarely be capable of transporting cobbled sized sediments or larger. Moraine sediments, which are preset along the coastline of the North Zealand, will consist of a range of sediments of varying sorts and sizes, and therefore only a part of the eroded volume at a given coastline will be contained in the longshore transport.

Another challenge for this method is human interventions in the coastal morphodynamic systems. Human interventions included in this study were coastal protection structures such as breakwaters, groynes and revetments. Breakwaters and groynes intercept the longshore drift, and as presented in chapter 6, large amounts of structures have been built across the years to stabilize the coastline, and in some cases the structures resulted in local advance.

The historic coastline recession and sediment transport rates are based on an average over 60 years, and it is to be expected that present transport rates will be significantly lower along protected subsection and higher along unprotected subsections. Structures cause accretion upstream of a littoral barrier and thereby starvation at downdrift subsections.

Apart from human interference through coastal protection measures, seasonal beach-profile changes, acute erosion (i.e. erosional events under storm surges), raw data uncertainties as well as errors associated with digitizing were potential sources for sampling errors in the shoreline position (Kabuth et al., 2014).

Thieler and Danforth (1994) tested the DSAS cross-shore transect method with source data from historical maps and aerial photographs covering a time span of 36 years, achieving a resolution of shoreline-change rates of ±0.51 m y-1. Furthermore, Kabuth et al. (2014) conducted a multidecadal shoreline change analysis along 7000 km coastline around Denmark and found that the DSAS method was more robust and performed better in detection of local extremes than a Nearest Neighbour search method also tested. The shoreline change resolution obtained in the study was ±0.2 m y-1.

Chapter 9 / Discussions

Smith and Zarillo (1990) quantified the error due to short-term variations by combining long-term variations in shoreline positions with short term beach profiling. It was found that short-term variability in shoreline position was the largest source of errors in quantifications of long-term shoreline changes.

The findings of this study proved robust as the trend of chronic erosion could be independently detected in the analyzed time periods, with exception of the most recent period that include the 100-year storm event of 2013. An additional assessment of the effects of short-term changes on the results was beyond the scope of this study.

9.5 Model calibrations and considerations Before modeling beach nourishment behavior at Tisvildeleje, Raageleje and Udsholt Strand, the model was calibrated in order for the littoral drift rates to represent those found in the shoreline change analysis. Some of the parameter calibrations will be discussed in this section.

Alongshore sediment transport driven by waves is generally assumed to smoothen a coastline, and this notion has been demonstrated in the application of LITLINE in this study. The LITLINE model simulates development towards equilibrium conditions, where gradients in the littoral drift disappear.

It proved difficult to prevent the natural undulations of the shoreline from smoothening, as the shoreline converged towards an equilibrium orientation. Digitized shorelines was used as model inputs, however, a simplification of the shorelines may have provided a better fit for simulating the evolution of the individual coastlines since the LITLINE is a tool meant for modeling the evolution of coastlines more uniform that those modeled in this study. It was also found that the predicted shoreline behavior depended greatly on the orientation used as model input. Changing the overall orientation of the shoreline sections by just a few degrees resulted in altered evolutionary prediction of the shoreline behavior.

The geological conditions, shoreline protection measures and other controlling factors for the coastline position are therefore important but rather difficult to replicate in the model setup.

LITLINE is a simple one-line model, which assumes that the shape of the coastal profile is maintained meaning that shoreline change is obtained only by shifting the entire cross-shore profile; a shift in the onshore direction corresponds to erosion and shift in the offshore direction corresponds to accretion (Kristensen, 2013). The model treats the nourishment as a small perturbation on the regional shoreline orientation and as a result the perturbations to shoreline is smoothened out and adjacent beaches advance seaward. In the one-line models the morphological evolution of a shoreline nourishment is a diffusive redistribution of the displaced shoreline. This is due to the fact that the transport is predicted to be only a function of the coastline orientation and the same transport is therefore predicted for a non-nourished profile and a profile that has been nourished. By adding a shoreline perturbation into the model domains by simply displacing the existing shoreline, the calculations of the added sediment volume assumes that the nourishment and native sands are compatible in terms of their grain size distributions at every element of the nourished profile. If this is not the case, it cannot be assumed directly that the profile will be displaced the same distance seaward over the profile.

By restraining the distortion of the coastal profile, the one-line models do however allow simulations over longer time spans as they allow for long morphological time steps. More detailed 2D morphological models that master a calculation of the cross-shore transport and a better calculation of the longhshore transport are very time consuming.

As seen in the area presentation, the profile form and slopes vary even within the subsections of Tisvildeleje, Raageleje and Udsholt Strand. In the case of Udsholt Strand, one profile form was accretional, whilst the downdrift profiles were eroding. The selection of profiles is not expected to impose significant changes in observed drift; however, the fact that an active height of 3 m was chosen in the model setups, creates a distortion

Chapter 9 / Discussions

of the amount of sediment available in the profiles. However, the sections where the beaches are backed by cliffs, are protected with some sort of slope protection. In the model this was replicated by inserting revetments along the cliff backed sections to account for the limited sediment availability.

Along all modelled coastlines an updrift littoral barrier was present. The effect of these proved challenging to reproduce in the setups, and in all cases some alterations of the actual beach protection were made in order to keep the coastline somewhat in place. As described earlier in this chapter, the observed distribution of the littoral drift along the shoreline sections was not successfully reproduced in this study. A more accurate distribution may have been replicated by inserting a wave field varying along the outer boundary of the domain. In this study, wave data from a single point just off the coast in the center of each coastline section was used. This method excludes the possible effect of differences in wave energy along the coastline.

Initially, the deterministic bed concentration description was used, but the model provided a better fit when applying empirical bed concentration. Another sensitive parameter was the bed resistance, which was changed from the default of 0.004 m to 0.08 m. Even though this provided a more accurate littoral drift, it is discussable weather this is a true representation for the area.

As previous studies have shown that the mean grain size in the nearshore area from Tisvildeleje to Gilleleje varies between 0.25 and 0.35 mm, the effect of changing the grain size within this range was also investigated in preliminary calibrations. This did however, not seem to have significant effect on the overall sediment budgets.

In a coordinated program for coastal protection of the north coast of Zealand compiled in 1989 by the joint committee (mentioned in chapter 1), it is stated that if the sand in a nourishment has a grain diameter double that of the native sands, the rate of sediment transported from the nourishment can be significantly reduced. In other studies, the use of coarser sediment for nourishment projects is also strongly recommended; however, this was not taken into account in the modeling of nourishment evolution in this project. According to Capobianco et al. (2002) it is nevertheless very common practice to ignore this coarsening of the sediment distribution in modeling of nourishment evolution even though it will in most cases represent a cause of mismatch between a simulated and observed nourishment evolution.

Calibration and verification represent two critical activities in setting up an appropriate model for the design of a beach nourishment project. The calibration of the three LITLINE setups did not follow a standardized procedure, which can complicate the assessment of model drawbacks, as these are difficult to estimate due to the large number of free parameters. Capabianco (2002) has found this to be a general problem in the assessment of models, and points out that this means that the modellers’ experience generally plays a dominant role in the calibration process.

Chapter 10 / Conclusions

10 Conclusions One of the benefits of beach nourishments is that they will adapt into the natural system in which they are introduced. However, this in turn means that when nourishment evolution is predicted, the hydrodynamic forcing and geological settings must be taken wisely into account. Coasts are highly dynamic zones with changes happening on a range of timescales, which complicates the task of designing and predicting the lifespan and effectiveness of a beach nourishment. The present investigation has highlighted that appropriate modeling of beach nourishment evolution requires in-depth understanding of the natural system.

In this present study, the historic shoreline change rates provided insights into temporal shoreline changes as well as rates of erosion along the entire coast stretching from Hundested to Gilleleje. The main findings from this analysis are summarized below:

 The coast is subject to chronic erosion caused by the east directed longshore sediment transport, and the -1 average shoreline recession rate for the past 60 years was determined to be ~0.16 m y .  The erosion rate increases gradually from zero at Hundested to ~ 40.000 m3 y-1 at Gilleleje.  Coastal protection measures in the form of hard structures implemented along significant parts of the coastline, halters erosion in some areas but in turn new erosional hotspots are created downdrift.  The coastline generally suffers from sediment starvation.  The storm event in 2013, Bodil, eroded large amounts of sediment from the cliffs and dunes, which led to beach widening.

Modeling the planform evolution of the 15 schematized nourishment scenarios provided the following conclusions:

 All nourishment scenarios over time converge towards a bell-shape.  All nourishment scenarios spread out symmetrically independently of varying the incoming wave angle within a range of 20 degrees.  Rectangular nourishment designs increase the nourishments’ spatial stability when compared to the bell-shaped nourisments.  The lifespan of a beach nourishment increases with initial longshore width.  A strong diffusional phase is identified within the first year of wave action.  The gradient in longshore sediment transport is higher when applying waves with incidence angles of 10 degrees, and this causes the most rapid diffusion of the nourishment.  The decay in nourishment cross-shore width is exponential.

Modeling of beach nourishments at Tisvildeleje, Raageleje and Udsholt Strand, in which naturally varying waves, meandering coastlines and coastal protection structures were incorporated, provided the following insights:

 The applied LITLINE model will smoothen out natural shoreline undulations as the coastline converges towards its equilibrium orientation.  Calibration of the model to the erosion rates from the historic shoreline analysis did not lead to even erosion along the shoreline sections.  Downdrift migration of the nourishment was not detected when applying natural varying waves.  Littoral barriers such as the breakwater at Tisvilde halted the spreading of the beach nourishment.  The disequilibrium in shoreline orientation at Udsholt Strand produced high potential littoral drift rates.  The model was highly sensitive to changes in local shoreline orientation.

Chapter 10 / Conclusions

Downdrift migration of shoreline perturbations is a behavior associated with the presence of waves with high incidence angles. The planform evolutions of the nourishments at Tisvildeleje, Raageleje and Udsholt Strand predicted using LITLINE, showed no signs of migration. This can be explained by the application of nearshore wave data, as it was found that the transformation of offshore waves using the MIKE21 spectral wave model altered the directional distribution of waves significantly, decreasing the proportion of waves approaching from high incidence angles.

Since LITLINE assumes that the potential drift rate is satisfied, the model was not ideal for modeling the transport patterns of a beach nourishment introduced into a littoral system with a general deficit of sediment. In this study it is hypothesized that nourishment behavior on a sediment deprived beach differs from that of a beach which is well supplied with available sediment; the accretion zone along the updrift flank of nourishment will in a sediment deprived case be reversed into a zone of erosion, and sediment deposition will therefore only occur along the downdrift side of the nourishment. Such a scenario will lead to nourishment migration.

Since the coast of North Zealand is suffering from chronic sediment starvation caused by a combination of natural erosion and extensive implementation of coastal protection structures, the potential for downdrift translation of nourishments at any of the selected subsections is present even though the LITLINE model did not show this. This is found to be in accordance with the observed translation of a beach nourishment monitored during a pilot project at the coastline of northern Zealand conducted in 1987.

On the contrary to what was initially expected, the gradient in sediment transport capacity along the initial nourishments in the schematized setups where higher with an incident wave angle of 10 degrees leading to a rapid transformation of the initial planform during the first year of simulation. This finding underline the importance of analyzing the incoming wave field and the equilibrium orientation of the shoreline in question as this provides an indication of the shoreline stability as well as an insight into the magnitude of the gradients in littoral drift which can be expected when locally altering the shoreline orientation.

Models play a fundamental role in any coastal management strategy. Planning nourishments in the context of a multi-years management strategy requires significant prediction skills. Given the complexity of beach processes, efforts to understand and predict the evolution of nourishment should always be firmly grounded in experience and expertise. In turn, interpreting the results of the models and their validity in the real world demands the understanding of the morphological system.

References

References Abrahamsen, Erik, 2014. Kystsikring langs Nordsjællands kyst – Gilbjerg Hoved og Udsholt Strand. Downloaded 24 January 2016 from http://www.danculture.dk/2014/09/kystsikring-langs- nordsjaellands-kyst-gilbjerg-hoved-og-udsholt-strand/

Ashton A., Murray, A.B. and Arnoult, O., 2001. Formation of coastline features by large-scale instabilities induced by high-angle waves. Nature. 414. 296-300

Ashton, A.; Murray, A. B., 2006a. High-Angle wave instability and emergent shoreline shapes: 1. Modeling of sandwaves, flying spits, and capes. Journal of Geophysical Research, 111, F0411

Ashton, A.; Murray, A. B., 2006b. High-Angle wave instability and emergent shoreline shapes: 2. Wave climate analysis and comparisons to nature. Journal of Geophysical Research, 111, F0412

Bayram, A.; Larson, M.; Hanson, H. 2007. A new formula for the total longshore sediment transport rate. Coastal Engineering, 54, 700-710

Benedet, L.; Finkl, C.W.; Hartog, W.M., 2007. Processes Controlling Development of Erosional Hotspots on a beach Nourishment Project. Journal of Coastal Research, 23(1), 33-48

Bird, E.; Lewis, N., 2015. Beach Renourishment. Springer

Capobianco, M.; Hanson, H.; Larson, M.; Steetzel, H.; Stive, M.J.F.; Chatelus, Y.; Aarninkhof, S.; Karambas, T., 2002. Nourishment design and evaluation: applicability of model concepts. Coastal Engineering, 47, 113-135

Cowell, P. J.; Hanslow, D. J; Meleo, J.F, 1999. The Shoreface. In A.D. Short (Ed.), Handbook of Beach and Shoreface Morphodynamics. John Wiley and Sons Ltd. 39-71

Danish Coastal Authority, 2011. Kystbeskyttelsesstrategi; en strategisk indsats for smukkere kyster. Ministry of Transportation

Danish Coastal Authority, 2013. Kystfodring og sandressourcer. KUP Klima. Ministry of Transportation

Danish Coastal Authority, 2014. Waves and waterlevel during the storm Bodil, Heatherhill Denmark. Downloaded 28 January 2016 from https://www.youtube.com/watch?v=uO7tcv-Pfeo

Danish Environmental Ministry, 2009. Kystbeskyttelsesloven

Davidson-Arnott, R, 2010. Introduction to coastal processes and geomorphology. Cambridge University Press

Davison, T. A.; Nicholls, R. J.; Leatherman, S. P., 1992. Beach Nourishment as a Management tool: An Annotated Bibliography on Developments Associated with the Artificial Nourishment of Beaches. Journal of Coastal Research, Vol. 8(4), 984-1022

de Schipper, M.A.; Vries, S.; Stive, M.J.F.; de Zeeuw, R.C.; Rutten, J.; Ruessink, B.G.; Aaninkhof, S.G.J.; van Gelder-Mass, C., 2014. Morphological development of a mega-nourishment; first observations at the Sand Engine. Coastal Engineering. 34, 1-6

Dean, R.G., 2002. Beach nourishment: Theory and Practice. Advanced Series on Ocean Engineering, 18. World Scientific

100

References

DHI, 2012. Littoral Processes FM; All Modules, Scientific Documentation. MIKE by DHI. DHI Water & Environment. Hørsholm, Denmark

DHI, 2013. Erosionsatlas : Metodeudvikling og pilotprojekt for Sjællands nordkyst. DHI Water & Environment. Hørsholm, Denmark

DHI and Hasløv and Kjærsgaard, 2013. Genanvendelse af havnesand fra Gilleleje og Hornbæk havne: Nordkystens Kommuner

DHI, 2014a. Littoral Processes FM. All Modules. Scientific Documentation. MIKE by DHI. DHI Water & Environment. Hørsholm, Denmark

DHI, 2014b. Littoral Processes FM. Littoral Processes Module; User Guide. MIKE by DHI. DHI Water & Environment. Hørsholm, Denmark

Dutch Ministry of Infrastructure and the Environment, 2013. The Sand Motor; Pilot project for natural coastal protection.

Eriksen, L., 2014. Rågeleje strand efter stormen. Downloaded 24 January 2016 from http://www.eriksenonline.dk/skuret/rageleje-strand-efter-stormen

Fællesudvalget for Kystpleje og Kystsikring af Nordkysten, 1987. Sjællands Nordkyst; Strandfodringsforsøg 1984-1986; Slutrapport

Fællesudvalget for Kystpleje og Kystsikring af Nordkysten, 1989. Samordnet program for kystpleje og kystbeskyttelse

Hallemeier, R.J., 1981. A profile zonation for seasonal sand beaches from wave climate. Coastal Engineering, 4, 1980-1981. 253-277

Hasløv & Kjærsgaard, 2014. Nordkystens Fremtid; Skitseprojekt. Hasløv & Kjærsgaard

Kabuth, A., Kroon, A., Pedersen, J.B.T., 2014. Multidecadal Shoreline Changes in Denmark. Journal of Coastal Research. 30 (4). 714-728

Komar, P.D., 1971. The mechanics of sand transport on beaches. Oceans and Atmospheres, 76,713-721

Komar, P.D., 1979. Beach-slope dependence of longshore currents. J. Waterway, Port. Coastal and ocean Div., ASCE(WWW4), 460-464

Kristensen, S., 2013. Marine and Coastal Morphology: medium and long-term area modeling. PhD Thesis. DTU. Department of Mechanical Engineering, Section of fluid mechanics, coastal and marine engineering

Kærgaard, K., 2011. Numerical Modeling of Shoreline Undulations. PhD Thesis. DTU Mechanical Engineering. Department of Mechanical Engineering.

Kærgaard, K., 2015. A New Approach to Modeling Long-Term Shoreline Evolution Using MIKE 21 FM. Module 1 Introduction to MIKE 21 FM Shoreline Model. DHI Water & Environment. Hørsholm, Denmark

Mangor, K., 2004. Shoreline Management Guidelines. DHI Water & Environment. Hørsholm, Denmark

Mangor, K..; Mocke, G.; Giarrusso, C.; Smit,F.; Bloch,, R.; Fuchs, J. Lumborg, U.;Niemann. S., 2008. Shoreline Managment of the Dubai Coast

101

References

Masselink, G.; Highs, M.; Knight, J. 2011. Introduction to Coastal processes and geomorphology, Hodder

Ministry of Environment and Food of Denmark, 2016. Bekendtgørelse af lov om kystbeskyttelse. LBK nr. 15 of January 8, 2016 .

Moksness, E., Dahl, E., Støttrup, Josianne, 2009. Integrated Coastal Zone Management, Blackwell Publishing Ltd, 2009

Petersen, Bo, 2016. Kystsikringen ved Tisvilde. Tisvildenyt. Januar-februar 2016. 5-7

Post, J.; Lundin, C., 1996, Guidelines for integrated coastal zone management. Environmental sustainable and monograph series No.9. The world Bank, Washington DC

Slott, J.M.; Murray, A.B.; Ashton, A.D., 2010. Large-scale responses of complex-shaped coastlines to local shoreline stabilization and climate change. Journal of Geophysical Research. 115, F03033. The American Geophysical Union

Smith, G.L. and Zarillo, A., 1990. Calculating long-term shoreline recession rates using aerial photographic and beach profiling techniques. Journal of Coastal Research, 6(1), 111-120

Stive, M.J.F.; Schipper, M.A.; Luijendijk, A.P.; Ranasinghe, R.W.M.R.J.B.; Van Thiel De Vries, J.S.M.; Aarninkhoff, S.; Van Gelder-Maas, C.; De Vries, S.; Henriquez, M.; Marx, S., 2013a. The sand engine: A solution for vulnerable deltas in the 21st century? Conference: Coastal Dynamics 2013: 7th International Conference on Coastal Dynamics, Arcachon, France, 24-28 June 2013, At Arcachon, France

Stive, M.J.F.; Schipper M.A.; Luijendijk,A.P. Aarninkhoff, S.; Van Gelder-Maas, C.; Van Thiel De Vries, J.S.M.; De Vries, S.; Henriquez, M., Marx, S. Ranasinghe, R., 2013b. A new alterntive to saving our beaches from sea-level rise: The sand engine, Journal of Coastal Research, 29(5), 1001-1008. Coconut Creek Florida

Thieler, E.R.; Danforth, W.W., 1994. Historical shoreline mapping (1): Improving techniques and reducing positioning errors. Journal of Coastal Research, 10(3), 549-563 van den Berg, T.; Falqués, A.; Ribas, F., 2010. Shoreline sand waves and beach nourishments, Coastal Engineering, 32, 1-10

Work, P.A.; Dean, R.G., 1995. Assessment and Prediction of Beach-Nourishment Evolution. Journal of Waterway, Port, Coastal and Ocean Engineering, 121, 3, 182-189

Yoshinda, J.; Udo, K.; Takeda, Y.; Manu, A.; Framework for proper beach nourishment as adaption to beach erosion due to sea level rise, 2014. Journal of coastal research, 70, 467-472

Aagaard, T.; Hughes, M., 2013, 'Sediment Transport' in DJ Sherman (ed.). Reference Module in Earth Systems and Environmental Sciences: Treatise on Geomorphology. Coastal Geomorphology, 10, 74- 105. Elsevier Science, Amsterdam

Aagaard, T.; Nielsen. N.; Nielsen, J., 2008. Kystmorfologi. Institut for Geografi og Geologi, Københavns Universitet

102

- Appendix A -

Appendix A Elevation chart of the Northern coast of Zealand, Denmark, showing land elevation and depth at sea

Sediment characteristics of the Northern coast of Zealand, Denmark.

103

- Appendix B -

Appendix B Aerial photograph showing the closely placed groynes and breakwaters just east of the Tisvilde breakwater.

Aerial photograph showing the change in orientation along the coastline from Raageleje towards Udsholt

¯ 0 0,25 0,5 1 Kilometers

104

0 230 460 m - Appendix C -

Appendix C

Table with descriptions of the initial nourishment shapes, spacing and size for all 15 schemes investigated in this present study

Scenario Description Single peaked, bell shaped, peak cross-shore position 70 m from coastline, 10 km from updrift domain 1A boundary 1B Single peaked, bell shaped, cross-shore position 35 m from coastline, 10 km from updrift domain boundary

S1 Square shaped, cross-shore displacement of shoreline: 10 m along a 3500 m section, deposit center at 10,000 m

S2 Square shaped, cross-shore displacement of shoreline: 20 m along a 1750 m section, deposit center at 10,000 m

S3 Square shaped, cross-shore displacement of shoreline: 40 m, along a 875 m section, deposit center at 10,000 m

2A Two bell shaped deposits, peaks at 35 m cross-shore, center of deposits positioned with spacing of 1,500 m Two bell shaped deposits, peaks at 46 and 23 m cross-shore, center of deposits positioned with spacing of 2B 1,500 m. Two bell shaped deposits, peaks at 23 and 46 m cross-shore, center of deposits positioned with spacing of 2C 1,500 m. Three bell shaped deposits, peaks at 23 m cross-shore, center of deposits positioned with spacing of 1,500 m, 3A located 8,500 and 10,000 m and 11,500 m from upstream boundary

Three bell shaped deposits, peaks at 35 m, 23 m and 11 m cross-shore, center of deposits positioned with 3B spacing of 1,500 m, located at 8,500, 10,000 m and 11,500 m from upstream boundary

Three bell shaped deposits, peaks at 11 m, 23 m and 35 m cross-shore, center of deposits positioned with 3C spacing of 1,500 m, located at 8500, 10,000 m and 11,500 m from upstream boundary

Three bell shaped deposits, peaks at 11 m, 35 m and 23 m cross-shore, center of deposits positioned with 3D spacing of 1,500 m, located at 8,500, 10.000 m and 11,500 m from upstream boundary

Four bell shaped deposits, peaks at 17 m cross-shore, center of deposits positioned with even spacing of 1,500 4A m, located 7,750 m, 9,250 m, 10,750 m and 12,250 m from upstream boundary

Four bell shaped deposits, peaks at 17 m cross-shore, center of deposits positioned with even spacing of 750 4B m, located 8,875 m, 9,525 m, 10,375 m and 11,125 m from upstream boundary

Four bell shaped deposits, peaks at 17 m cross-shore, center of deposits positioned with even spacing of 3000 4C m, located 5,500, 8,500, 11,500 and 14,500 m

105

- Appendix D -

Appendix D Table providing an overview of nourishment peak height, peak position, nourishment width and volume after 1, 5, 10, 15 and 20 years for all scenarios and variations in wave height and direction.

Hs=0,75m, P= 6, Mean wave direction=60

Year Parameter 1A 1B 2A 2B 2C 3A 3B 3C 3D 4A 4B 4C S1 S2 S3

Height of peak (m) 45,79 30,06 22,62 30,23 35,94 15,05 22,62 22,62 30,23 11,28 12,53 11,28 10,00 19,97 145,45

Position of peak (m) 10025,00 10000,00 10750,00 9275,00 10775,00 10000,00 8500,00 11500,00 10025,00 9250,00 10375,00 5500,00 10225,00 10000,00 10325,00 10350,0 Width (m) 1700,00 2400,00 3025,00 3025,00 2800,00 4425,00 4375,00 4375,00 4225,00 5850,00 3600,00 0 4200,00 2650,00 1425,00 175460,0 175460,0 161750,0 175460,0 175460,0 169080,0 169220,0 168980,0 172250,0 106260,0 175220,0 82930,0 173330,0 177500,0 175000,0 1 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 24,70 20,98 12,74 16,65 16,71 8,71 12,55 12,59 16,67 6,53 11,64 6,14 9,96 17,05 292,40

Position of peak (m) 10000,00 10000,00 10675,00 9275,00 10725,00 10000,00 8525,00 11450,00 10000,00 10750,00 10000,00 8500,00 9975,00 10000,00 10325,00 11150,0 Width (m) 2850,00 3275,00 4050,00 4025,00 3975,00 5325,00 5250,00 5200,00 4900,00 6650,00 4425,00 0 5075,00 3750,00 2125,00 175370,0 174960,0 161750,0 172860,0 172990,0 153140,0 153220,0 153090,0 164250,0 115470,0 169730,0 71004,0 161830,0 175780,0 175820,0 5 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 18,09 16,47 11,30 13,08 13,19 7,87 10,18 10,25 12,97 5,91 11,17 4,51 9,59 13,96 395,90

Position of peak (m) 9975,00 10000,00 10000,00 9375,00 10575,00 10000,00 8725,00 11250,00 9975,00 10725,00 10000,00 8500,00 9975,00 10000,00 10325,00 11675,0 Width (m) 3700,00 4000,00 4750,00 4700,00 4675,00 5925,00 5800,00 5750,00 5325,00 7175,00 5025,00 0 5700,00 4600,00 2725,00 173690,0 172150,0 161750,0 165830,0 166140,0 144460,0 144500,0 144440,0 159070,0 115770,0 162330,0 64988,0 152470,0 169530,0 195590,0 10 Volume m^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 14,87 13,93 10,82 11,56 11,67 7,74 9,32 9,38 11,30 5,84 10,50 3,76 9,04 11,98 479,32

Position of peak (m) 9975,00 10000,00 10000,00 9500,00 10450,00 10000,00 8925,00 11050,00 9975,00 10350,00 10000,00 8500,00 9975,00 10000,00 10325,00 12025,0 Width (m) 4350,00 4600,00 5250,00 5225,00 5175,00 6375,00 6200,00 6150,00 5675,00 7575,00 5475,00 0 6200,00 5200,00 3275,00 169490,0 167250,0 161750,0 158710,0 159080,0 138570,0 138600,0 138560,0 154020,0 114130,0 155620,0 61927,0 144870,0 161740,0 250050,0 15 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 12,98 12,34 10,18 10,61 10,69 7,61 8,76 8,82 10,29 5,83 9,86 3,38 8,52 10,68 547,95

Position of peak (m) 9975,00 10000,00 10000,00 9575,00 10400,00 10000,00 9050,00 10925,00 9975,00 10000,00 10000,00 8500,00 9975,00 10000,00 10325,00 12275,0 Width (m) 4850,00 5050,00 5700,00 5625,00 5600,00 6725,00 6525,00 6500,00 5975,00 7850,00 5875,00 0 6625,00 5750,00 3775,00 164220,0 161750,0 161750,0 152610,0 152980,0 133980,0 133990,0 133970,0 149080,0 112220,0 149880,0 60359,0 138640,0 154340,0 326340,0 20 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Hs=0,75m, P= 6, Mean wave direction=70

106

- Appendix D -

Year Parameter 1A 1B 2A 2B 2C 3A 3B 3C 3D 4A 4B 4C S1 S2 S3

Height of peak (m) 39,18 28,04 19,55 26,08 32,27 13,04 19,55 19,55 26,08 9,77 11,99 9,77 10,00 19,92 34,28

Position of peak (m) 10000,00 10000,00 10750,00 9250,00 10750,00 10000,00 8500,00 11500,00 10000,00 10750,00 10375,00 5500,00 9900,00 10000,00 9925,00 10500,0 Width (m) 1925,00 2550,00 3225,00 3225,00 2925,00 4600,00 4550,00 4525,00 4350,00 6000,00 3750,00 0 4250,00 2750,00 2050,00 175460,0 175450,0 149030,0 175410,0 175460,0 165780,0 166170,0 165400,0 170610,0 109060,0 174750,0 80460,0 172590,0 177500,0 175000,0 1 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 20,04 17,93 11,43 14,10 14,14 8,02 10,81 10,83 14,03 6,02 11,41 5,01 9,91 16,28 19,45

Position of peak (m) 10000,00 10000,00 10450,00 9325,00 10650,00 10000,00 8625,00 11350,00 10000,00 10750,00 10000,00 8500,00 9975,00 10000,00 9900,00 11500,0 Width (m) 3400,00 3725,00 4475,00 4450,00 4425,00 5700,00 5575,00 5550,00 5150,00 7000,00 4800,00 0 5225,00 3950,00 3475,00 174680,0 173580,0 149030,0 168940,0 168860,0 147410,0 147790,0 147040,0 161040,0 116070,0 165230,0 66908,0 159680,0 174740,0 174020,0 5 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 14,56 13,69 10,73 11,45 11,49 7,73 9,25 9,28 11,14 5,84 10,41 3,70 9,38 13,08 14,32 11500,0 Position of peak (m) 10000,00 10000,00 10000,00 9525,00 10450,00 10000,00 8950,00 11025,00 10000,00 10175,00 10000,00 0 9975,00 10000,00 9900,00 12075,0 Width (m) 4425,00 4675,00 5325,00 5250,00 5250,00 6425,00 6225,00 6225,00 5700,00 7600,00 5550,00 0 5900,00 4850,00 4475,00 168800,0 166530,0 149030,0 158090,0 157970,0 137920,0 138220,0 137620,0 153360,0 113880,0 154830,0 61669,0 149350,0 166540,0 167820,0 10 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 11,93 11,44 9,72 10,05 10,08 7,49 8,43 8,45 9,71 5,81 9,43 3,21 8,72 11,14 11,79

Position of peak (m) 9975,00 10000,00 10000,00 9625,00 10375,00 10000,00 9125,00 10875,00 10000,00 10000,00 10000,00 8500,00 9975,00 10000,00 9900,00 12450,0 Width (m) 5200,00 5375,00 5975,00 5900,00 5875,00 6950,00 6725,00 6725,00 6225,00 8050,00 6125,00 0 6450,00 5550,00 5250,00 159920,0 157480,0 149030,0 148650,0 148520,0 130900,0 131160,0 130650,0 145400,0 110740,0 145900,0 59672,0 141000,0 157210,0 158890,0 15 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 10,40 10,07 8,90 9,10 9,12 7,19 7,84 7,85 8,79 5,74 8,66 3,03 8,14 9,89 10,30 11500,0 Position of peak (m) 9975,00 10000,00 10000,00 9650,00 10325,00 10000,00 9200,00 10775,00 10000,00 10000,00 10000,00 0 9975,00 9975,00 9900,00 12700,0 Width (m) 5800,00 5975,00 6475,00 6400,00 6400,00 7375,00 7150,00 7150,00 6675,00 8400,00 6625,00 0 6900,00 6100,00 5850,00 151300,0 149030,0 149030,0 140880,0 140760,0 125290,0 125500,0 125070,0 138290,0 107740,0 138500,0 58942,0 134210,0 148810,0 150330,0 20 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Hs=0,75m, P= 6, Mean wave direction=80

Year Parameter 1A 1B 2A 2B 2C 3A 3B 3C 3D 4A 4B 4C S1 S2 S3

Height of peak (m) 35,32 26,44 17,58 23,46 29,76 11,72 17,57 17,57 23,46 8,79 11,79 8,77 10,00 19,76 31,80

Position of peak (m) 10000,00 10000,00 10750,00 9250,00 10750,00 10000,00 8500,00 11500,00 10000,00 10750,00 10375,00 5500,00 10000,00 10000,00 9925,00 10650,0 Width (m) 2125,00 2700,00 3400,00 3375,00 3025,00 4750,00 4675,00 4700,00 4475,00 6150,00 3900,00 0 4400,00 2900,00 2225,00 175460,0 175430,0 138390,0 175280,0 175450,0 163000,0 163540,0 162500,0 169220,0 110990,0 174110,0 78376,0 171120,0 177480,0 175000,0 1 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

107

- Appendix D -

Height of peak (m) 17,44 15,98 11,25 12,82 12,85 7,84 10,03 10,04 12,63 5,89 11,07 4,36 9,76 14,90 17,04

Position of peak (m) 10000,00 10000,00 10000,00 9425,00 10575,00 10000,00 8775,00 11225,00 10000,00 10725,00 10000,00 8500,00 9975,00 10000,00 9900,00 11750,0 Width (m) 3825,00 4100,00 4825,00 4775,00 4775,00 6000,00 5850,00 5825,00 5375,00 7250,00 5100,00 0 5500,00 4325,00 3875,00 173140,0 171440,0 138390,0 164920,0 164670,0 143420,0 143880,0 142960,0 158270,0 115550,0 161200,0 64374,0 155560,0 172050,0 172330,0 5 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 12,60 12,02 10,02 10,44 10,45 7,57 8,66 8,67 10,08 5,83 9,71 3,31 8,92 11,65 12,44

Position of peak (m) 10000,00 10000,00 10000,00 9600,00 10400,00 10000,00 9075,00 10900,00 10000,00 10000,00 10000,00 8500,00 9975,00 10000,00 9900,00 12350,0 Width (m) 4975,00 5175,00 5775,00 5725,00 5700,00 6800,00 6600,00 6575,00 6050,00 7900,00 5950,00 0 6300,00 5325,00 5025,00 162770,0 160290,0 138390,0 151490,0 151190,0 132910,0 133280,0 132560,0 147830,0 111720,0 148510,0 60100,0 143420,0 160070,0 161750,0 10 Volume m^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 10,31 9,98 8,84 9,04 9,06 7,17 7,80 7,81 8,73 5,73 8,61 3,03 8,10 9,82 10,21

Position of peak (m) 10000,00 10000,00 10000,00 9650,00 10325,00 10000,00 9225,00 10775,00 10000,00 10000,00 10000,00 8500,00 9975,00 9975,00 9900,00 12725,0 Width (m) 5825,00 6000,00 6500,00 6425,00 6425,00 7400,00 7200,00 7175,00 6700,00 8425,00 6650,00 0 6950,00 6125,00 5875,00 150690,0 148400,0 138390,0 140400,0 140140,0 124890,0 125180,0 124590,0 137770,0 107510,0 137970,0 58911,0 133730,0 148200,0 149730,0 15 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 8,97 8,75 7,99 8,12 8,12 6,76 7,18 7,19 7,86 5,58 7,81 2,95 7,45 8,67 8,90

Position of peak (m) 10000,00 10000,00 10000,00 9675,00 10300,00 10000,00 9300,00 10700,00 10000,00 10000,00 10000,00 8525,00 9975,00 9975,00 9900,00 12975,0 Width (m) 6525,00 6650,00 7075,00 7000,00 7025,00 7875,00 7675,00 7675,00 7225,00 8825,00 7200,00 0 7450,00 6775,00 6550,00 140340,0 138390,0 138390,0 131550,0 131330,0 118470,0 118720,0 118230,0 129400,0 103710,0 129520,0 58586,0 125990,0 138350,0 139490,0 20 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Hs=1m, P= 6, Mean wave direction=60

Year Parameter 1A 1B 2A 2B 2C 3A 3B 3C 3D 4A 4B 4C S1 S2 S3

Height of peak (m) 37,28 27,45 18,76 24,93 31,01 12,53 18,75 18,76 24,93 9,39 11,90 9,38 10,00 19,63 30,59 14500,0 Position of peak (m) 10000,00 10025,00 10750,00 9250,00 10750,00 10000,00 8500,00 11500,00 10000,00 10750,00 10375,00 0 9975,00 10000,00 9925,00 10575,0 Width (m) 2025,00 2625,00 3300,00 3300,00 2975,00 4675,00 4625,00 4575,00 4400,00 6075,00 3825,00 0 4450,00 2975,00 2325,00 175460,0 175440,0 144960,0 175360,0 175460,0 164780,0 164800,0 164710,0 170090,0 109800,0 174540,0 79703,0 170340,0 177460,0 175000,0 1 Volume m^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 18,95 17,16 11,32 13,52 13,62 7,93 10,45 10,51 13,44 5,95 11,29 4,74 9,65 14,26 16,04

Position of peak (m) 9975,00 10000,00 10250,00 9350,00 10625,00 10000,00 8675,00 11300,00 9975,00 10750,00 10000,00 8500,00 9975,00 10000,00 9900,00 11575,0 Width (m) 3550,00 3875,00 4600,00 4600,00 4550,00 5825,00 5675,00 5650,00 5225,00 7075,00 4925,00 0 5650,00 4500,00 4075,00 174190,0 172880,0 144960,0 167240,0 167560,0 145860,0 145830,0 145890,0 160020,0 115950,0 163740,0 65878,0 153470,0 170380,0 171030,0 5 Volume m^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10 Height of peak (m) 13,74 13,01 10,47 11,01 11,10 7,68 9,00 9,06 10,71 5,84 10,15 3,53 8,67 11,03 11,67

108

- Appendix D -

11500,0 Position of peak (m) 9975,00 10000,00 10000,00 9550,00 10425,00 10000,00 9000,00 10975,00 9975,00 10000,00 10000,00 0 9975,00 10000,00 9900,00 12175,0 Width (m) 4650,00 4850,00 5500,00 5450,00 5425,00 6575,00 6375,00 6350,00 5825,00 7725,00 5725,00 0 6500,00 5600,00 5275,00 166650,0 164310,0 144960,0 155290,0 155700,0 136010,0 135960,0 136050,0 151320,0 113110,0 152450,0 60975,0 140440,0 156540,0 158200,0 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 11,25 10,84 9,38 9,63 9,69 7,37 8,17 8,21 9,31 5,79 9,11 3,12 7,79 9,26 9,56

Position of peak (m) 9975,00 10000,00 10000,00 9625,00 10350,00 10000,00 9150,00 10825,00 9975,00 10000,00 10000,00 8500,00 9975,00 9975,00 9900,00 12575,0 Width (m) 5450,00 5600,00 6150,00 6100,00 6100,00 7125,00 6925,00 6900,00 6400,00 8175,00 6325,00 0 7200,00 6450,00 6175,00 156460,0 154100,0 144960,0 145210,0 145590,0 128600,0 128560,0 128650,0 142520,0 109550,0 142880,0 59305,0 130120,0 143620,0 144950,0 15 Volume m^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 9,80 9,52 8,54 8,69 8,73 7,03 7,57 7,60 8,41 5,69 8,33 2,99 7,12 8,16 8,33

Position of peak (m) 9975,00 10000,00 10000,00 9650,00 10300,00 10000,00 9250,00 10750,00 9975,00 10000,00 10000,00 8500,00 9975,00 9975,00 9900,00 12825,0 Width (m) 6100,00 6200,00 6700,00 6650,00 6625,00 7575,00 7350,00 7325,00 6875,00 8575,00 6825,00 0 7750,00 7100,00 6875,00 147080,0 144960,0 144960,0 137030,0 137360,0 122670,0 122630,0 122710,0 134870,0 106230,0 135040,0 58761,0 121990,0 133260,0 134160,0 20 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Hs=1m, P= 6, Mean wave direction=70

Year Parameter 1A 1B 2A 2B 2C 3A 3B 3C 3D 4A 4B 4C S1 S2 S3

Height of peak (m) 30,84 24,45 15,49 20,59 26,66 10,38 15,45 15,46 20,59 7,79 11,69 7,70 10,00 19,35 28,62 14500,0 Position of peak (m) 10000,00 10000,00 10750,00 9250,00 10750,00 10000,00 8500,00 11500,00 10000,00 10750,00 10275,00 0 9975,00 10000,00 9925,00 10825,0 Width (m) 2375,00 2875,00 3625,00 3600,00 3175,00 4950,00 4875,00 4875,00 4625,00 6325,00 4075,00 0 4550,00 3100,00 2475,00 175460,0 175360,0 125290,0 174850,0 175410,0 159450,0 159840,0 159060,0 167440,0 113000,0 172920,0 75723,0 169040,0 177380,0 174990,0 1 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 14,87 13,94 10,81 11,59 11,64 7,74 9,33 9,36 11,30 5,84 10,49 3,76 9,43 13,29 14,62 11500,0 Position of peak (m) 10000,00 10000,00 10000,00 9525,00 10475,00 10000,00 8925,00 11050,00 10000,00 10375,00 10000,00 0 9975,00 10000,00 9900,00 12025,0 Width (m) 4350,00 4575,00 5275,00 5200,00 5200,00 6375,00 6200,00 6175,00 5675,00 7550,00 5500,00 0 5850,00 4800,00 4400,00 169420,0 167200,0 125290,0 158900,0 158820,0 138570,0 138850,0 138290,0 153990,0 114120,0 155610,0 61948,0 150100,0 167270,0 168440,0 5 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 10,70 10,34 9,07 9,30 9,32 7,26 7,96 7,98 8,98 5,76 8,83 3,06 8,27 10,15 10,60

Position of peak (m) 9975,00 10000,00 10000,00 9650,00 10350,00 10000,00 9200,00 10800,00 10000,00 10000,00 10000,00 8500,00 9975,00 10000,00 9900,00 12650,0 Width (m) 5675,00 5825,00 6375,00 6300,00 6275,00 7275,00 7075,00 7050,00 6575,00 8325,00 6500,00 0 6800,00 5975,00 5700,00 153220,0 150890,0 125290,0 142540,0 142450,0 126500,0 126700,0 126290,0 139850,0 108410,0 140100,0 59060,0 135680,0 150650,0 152230,0 10 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 8,74 8,54 7,83 7,94 7,96 6,67 7,06 7,08 7,70 5,54 7,66 2,94 7,32 8,47 8,68 11450,0 15 Position of peak (m) 9975,00 10000,00 10000,00 9675,00 10300,00 10000,00 9300,00 10700,00 10000,00 10000,00 10000,00 0 9975,00 9975,00 9900,00

109

- Appendix D -

13025,0 Width (m) 6650,00 6775,00 7175,00 7125,00 7125,00 7975,00 7775,00 7775,00 7325,00 8900,00 7300,00 0 7575,00 6900,00 6675,00 138270,0 136400,0 125290,0 129730,0 129660,0 117190,0 117350,0 117030,0 127720,0 102910,0 127840,0 58550,0 124450,0 136390,0 137430,0 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 7,60 7,47 7,00 7,07 7,08 6,17 6,43 6,44 6,89 5,30 6,88 2,92 6,64 7,44 7,56 10975,0 Position of peak (m) 9975,00 10000,00 10000,00 9700,00 10275,00 10000,00 9350,00 10650,00 10000,00 10000,00 10000,00 0 9975,00 9975,00 9900,00 13275,0 Width (m) 7400,00 7475,00 7850,00 7800,00 7800,00 8525,00 8375,00 8350,00 7975,00 9375,00 7950,00 0 8175,00 7600,00 7400,00 126770,0 125290,0 125290,0 119970,0 119910,0 109880,0 110010,0 109760,0 118320,0 118450,0 58376,0 115790,0 125470,0 126060,0 20 Volume m^3 0 0 0 0 0 0 0 0 0 98165,00 0 0 0 0 0 Hs=1m, P= 6, Mean wave direction=80

Year Parameter 1A 1B 2A 2B 2C 3A 3B 3C 3D 4A 4B 4C S1 S2 S3

Height of peak (m) 27,36 22,54 13,84 18,31 24,10 9,35 13,75 13,76 18,32 7,01 11,67 6,79 10,00 18,71 25,82 14500,0 Position of peak (m) 10000,00 10000,00 10725,00 9250,00 10750,00 10000,00 8525,00 11475,00 10000,00 10750,00 10000,00 0 9975,00 10000,00 9925,00 11000,0 Width (m) 2625,00 3100,00 3850,00 3825,00 3350,00 5150,00 5050,00 5075,00 4775,00 6500,00 4250,00 0 4725,00 3325,00 2750,00 175430,0 175190,0 112860,0 174000,0 175290,0 155920,0 156400,0 155490,0 165640,0 114540,0 171290,0 73067,0 166720,0 177120,0 174950,0 1 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 12,85 12,23 10,12 10,56 10,59 7,60 8,74 8,75 10,22 5,83 9,81 3,36 8,99 11,84 12,68 11500,0 Position of peak (m) 10000,00 10000,00 10000,00 9575,00 10400,00 10000,00 9075,00 10925,00 10000,00 10000,00 10000,00 0 9975,00 10000,00 9900,00 12300,0 Width (m) 4925,00 5100,00 5725,00 5675,00 5650,00 6750,00 6525,00 6550,00 6025,00 7875,00 5900,00 0 6250,00 5275,00 4950,00 163670,0 161180,0 112860,0 152360,0 152140,0 133570,0 133890,0 133270,0 148600,0 112020,0 149350,0 60276,0 144210,0 160970,0 162640,0 5 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 9,22 8,98 8,15 8,29 8,30 6,84 7,30 7,31 8,03 5,61 7,97 2,96 7,58 8,88 9,14 11475,0 Position of peak (m) 10000,00 10000,00 10000,00 9675,00 10300,00 10000,00 9275,00 10725,00 10000,00 10000,00 10000,00 0 9975,00 9975,00 9900,00 12925,0 Width (m) 6375,00 6500,00 6950,00 6900,00 6875,00 7775,00 7575,00 7575,00 7125,00 8750,00 7100,00 0 7350,00 6625,00 6400,00 142440,0 140390,0 112860,0 133280,0 133110,0 119750,0 119970,0 119540,0 131070,0 104490,0 131190,0 58631,0 127520,0 140310,0 141550,0 10 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 7,52 7,39 6,93 7,00 7,01 6,13 6,38 6,39 6,82 5,28 6,81 2,92 6,59 7,37 7,47 10875,0 Position of peak (m) 9975,00 10000,00 10000,00 9700,00 10275,00 10000,00 9350,00 10650,00 10000,00 10000,00 10000,00 0 9975,00 9975,00 9900,00 13300,0 Width (m) 7450,00 7550,00 7900,00 7850,00 7850,00 8575,00 8400,00 8400,00 8025,00 9425,00 8000,00 0 8250,00 7675,00 7475,00 125840,0 124360,0 112860,0 119190,0 119060,0 109250,0 109410,0 109100,0 117530,0 117650,0 58359,0 115060,0 124550,0 125140,0 15 Volume m^3 0 0 0 0 0 0 0 0 0 97737,00 0 0 0 0 0

- Appendix D -

113990,0 112860,0 112860,0 108930,0 108840,0 101270,0 101390,0 101150,0 107610,0 107740,0 58031,0 105820,0 113220,0 113410,0 Volume m^3 0 0 0 0 0 0 0 0 0 92142,00 0 0 0 0 0 Hs=1.25m, P= 6, Mean wave direction=60

Year Parameter 1A 1B 2A 2B 2C 3A 3B 3C 3D 4A 4B 4C S1 S2 S3

Height of peak (m) 28,52 23,13 14,33 18,99 24,93 9,64 14,25 14,27 19,01 7,23 11,67 7,06 9,99 18,33 24,48 14500,0 Position of peak (m) 10000,00 10000,00 10725,00 9250,00 10750,00 10000,00 8500,00 11475,00 10000,00 9250,00 10025,00 0 9975,00 10000,00 9925,00 10925,0 Width (m) 2550,00 3025,00 3775,00 3750,00 3275,00 5075,00 5000,00 5000,00 4725,00 6425,00 4200,00 0 4800,00 3450,00 2875,00 175450,0 175260,0 116800,0 174290,0 175350,0 157050,0 157220,0 156920,0 166230,0 114100,0 171870,0 73919,0 165570,0 176890,0 174890,0 1 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 13,47 12,75 10,36 10,87 10,94 7,65 8,91 8,96 10,55 5,84 10,04 3,47 8,76 11,24 11,92

Position of peak (m) 9975,00 10000,00 10000,00 9550,00 10400,00 10000,00 9025,00 10950,00 9975,00 10000,00 10000,00 8500,00 9975,00 10000,00 9900,00 12225,0 Width (m) 4725,00 4925,00 5575,00 5500,00 5500,00 6625,00 6425,00 6400,00 5875,00 7775,00 5775,00 0 6450,00 5500,00 5200,00 165780,0 163320,0 116800,0 154340,0 154610,0 135220,0 135300,0 135160,0 150480,0 112770,0 151460,0 60741,0 141420,0 157700,0 159370,0 5 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 9,67 9,39 8,45 8,59 8,63 6,99 7,51 7,53 8,32 5,67 8,24 2,98 7,27 8,38 8,58

Position of peak (m) 9975,00 10000,00 10000,00 9650,00 10300,00 10000,00 9250,00 10725,00 9975,00 10000,00 10000,00 8500,00 9975,00 9975,00 9900,00 12825,0 Width (m) 6150,00 6275,00 6750,00 6725,00 6675,00 7625,00 7400,00 7400,00 6925,00 8600,00 6900,00 0 7625,00 6950,00 6725,00 146050,0 143880,0 116800,0 136160,0 136370,0 121980,0 122030,0 121940,0 133990,0 105830,0 134130,0 58728,0 123780,0 135540,0 136550,0 10 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 7,89 7,74 7,21 7,29 7,31 6,31 6,59 6,61 7,10 5,37 7,08 2,93 6,28 6,94 7,01 11200,0 Position of peak (m) 9975,00 10000,00 10000,00 9700,00 10275,00 10000,00 9325,00 10650,00 9975,00 10000,00 10000,00 0 9975,00 9975,00 9900,00 13225,0 Width (m) 7200,00 7300,00 7675,00 7625,00 7625,00 8375,00 8175,00 8175,00 7800,00 9250,00 7775,00 0 8550,00 8000,00 7825,00 129860,0 128240,0 116800,0 122470,0 122630,0 111860,0 111890,0 111830,0 120840,0 120960,0 58424,0 110890,0 119400,0 119770,0 15 Volume m^3 0 0 0 0 0 0 0 0 0 99479,00 0 0 0 0 0

Height of peak (m) 6,86 6,76 6,41 6,46 6,47 5,77 5,97 5,98 6,32 5,07 6,32 2,92 5,62 6,07 6,10

Position of peak (m) 9975,00 10000,00 10000,00 9700,00 10275,00 10000,00 9375,00 10600,00 9975,00 10000,00 10000,00 9975,00 9975,00 9975,00 9900,00 13475,0 Width (m) 7975,00 8075,00 8400,00 8325,00 8325,00 8975,00 8825,00 8800,00 8500,00 9775,00 8475,00 0 9275,00 8850,00 8675,00 118050,0 116800,0 116800,0 112360,0 112480,0 104060,0 104090,0 104040,0 111040,0 111170,0 58175,0 101520,0 108060,0 108060,0 20 Volume m^3 0 0 0 0 0 0 0 0 0 94144,00 0 0 0 0 0 Hs=1.25m, P= 6, Mean wave direction=70

Year Parameter 1A 1B 2A 2B 2C 3A 3B 3C 3D 4A 4B 4C S1 S2 S3

Height of peak (m) 30,84 24,45 15,49 20,59 26,66 10,38 15,45 15,46 20,59 7,79 11,69 7,70 10,00 19,35 28,62 14500,0 1 Position of peak (m) 10000,00 10000,00 10750,00 9250,00 10750,00 10000,00 8500,00 11500,00 10000,00 10750,00 10275,00 0 9975,00 10000,00 9925,00

111

- Appendix D -

10825,0 Width (m) 2375,00 2875,00 3625,00 3600,00 3175,00 4950,00 4875,00 4875,00 4625,00 6325,00 4075,00 0 4550,00 3100,00 2475,00 175460,0 175360,0 125290,0 174850,0 175410,0 159450,0 159840,0 159060,0 167440,0 113000,0 172920,0 75723,0 169040,0 177380,0 174990,0 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 10,70 10,34 9,07 9,30 9,32 7,26 7,96 7,98 8,98 5,76 8,83 3,06 8,27 10,15 10,60

Height of peak (m) 8,74 8,54 7,83 7,94 7,96 6,67 7,06 7,08 7,70 5,54 7,66 2,94 7,32 8,47 8,68 11450,0 Position of peak (m) 9975,00 10000,00 10000,00 9675,00 10300,00 10000,00 9300,00 10700,00 10000,00 10000,00 10000,00 0 9975,00 9975,00 9900,00 13025,0 Width (m) 6650,00 6775,00 7175,00 7125,00 7125,00 7975,00 7775,00 7775,00 7325,00 8900,00 7300,00 0 7575,00 6900,00 6675,00 138270,0 136400,0 125290,0 129730,0 129660,0 117190,0 117350,0 117030,0 127720,0 102910,0 127840,0 58550,0 124450,0 136390,0 137430,0 15 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Year Parameter 1A 1B 2A 2B 2C 3A 3B 3C 3D 4A 4B 4C S1 S2 S3

- Appendix D -

163670,0 161180,0 112860,0 152360,0 152140,0 133570,0 133890,0 133270,0 148600,0 112020,0 149350,0 60276,0 144210,0 160970,0 162640,0 Volume m^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Height of peak (m) 6,54 6,45 6,15 6,19 6,20 5,59 5,76 5,76 6,06 4,95 6,06 2,92 5,91 6,45 6,50 10000,0 Position of peak (m) 9975,00 10000,00 10000,00 9725,00 10275,00 10000,00 9400,00 10600,00 10000,00 10000,00 10000,00 0 9975,00 9975,00 9900,00 13550,0 Width (m) 8275,00 8350,00 8650,00 8600,00 8600,00 9225,00 9050,00 9075,00 8750,00 9950,00 8750,00 0 8925,00 8450,00 8300,00 113990,0 112860,0 112860,0 108930,0 108840,0 101270,0 101390,0 101150,0 107610,0 107740,0 58031,0 105820,0 113220,0 113410,0 20 Volume m^3 0 0 0 0 0 0 0 0 0 92142,00 0 0 0 0 0

113

- Appendix E -

Appendix E Diagrams showing the annual sediment transport for each of the three locations. Data is obtained from erosion rates calculated using the ArcGIS tool DSAS.

Tisvildeleje

Raageleje

Udsholt Strand

114

- Appendix F -

Appendix F Incidence angles of DKBS offshore wave directions distributed in directional interval bins of 10 degrees. First interval is 0/360-10 degrees, next is 10-20 degrees and so forth.

Simulated wave directions extracted from SW results at 9, 7 and 5 m depth, distributed in directional interval bins of 10 degrees. First interval is 0/360-10 degrees, next is 10-20 degrees and so forth.

Tisvildeleje

Raageleje

115

- Appendix F -

Udsholt Strand

116

- Appendix G -

Appendix G Additional time steps for beach nourishment evolution along 400 m section of coastline, Tisvildeleje

117

- Appendix G -

Additional time steps for beach nourishment evolution along 800 m section of coastline, Tisvildeleje

118

- Appendix H -

Appendix H Additional time steps for beach nourishment along 400 m section of coastline at Raageleje

119

- Appendix H -

Additional time steps for beach nourishment along 800 m section of coastline at Raageleje

120

- Appendix I -

Appendix I Additional time steps for beach nourishment along 400 m section of coastline at Udsholt Strand

121

- Appendix I -

Additional time steps for beach nourishment along 800 m section of coastline at Udsholt Strand

122