Delft University of Technology

Faculty of Civil Engineering and Geosciences Department of Hydraulic Engineering MSc Thesis

THE EFFECT OF VARIABLE GRAIN SIZE DISTRIBUTION ON BEACH’S MORPHOLOGICAL RESPONSE

Graduation committee: Prof.dr.ir. A.J.H.M. Reniers Author:

Dr.ir. Matthieu de Schipper Melike Koktas

Ir. Tjerk Zitman

Dr. Edith L. Gallagher

May 2017

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EXECUTIVE SUMMARY Field studies with in-situ sediment sampling demonstrate the spatial variability in grain size on a sandy beach. However, conventional numerical models that are used to simulate the coastal morphodynamics ignore this variability of sediment grain size and use a uniform grain size distribution of mostly around and assumed fine grain size. This thesis study investigates the importance of variable grain size distribution in a beach’s morphological response.

For this purpose, first a field experiment campaign was conducted at the USACE Field Research Facility (FRF) in Duck, USA, in the spring of 2014. This experiment campaign was called SABER_Duck as an acronym for ‘Stratigraphy And BEach Response’. During SABER_Duck, in-situ swash zone grain size distribution, the prevailing hydrodynamic conditions and the time-series of the cross-shore bathymetry data were collected. The data confirmed a highly variable grain size distribution in the swash zone both vertically and horizontally. Additionally, the two trench survey observations showed the existence of continuous layers of coarse and fine sands comprising the beach stratigraphy.

Secondly, a process based numerical coastal morphology model, XBeach, was chosen to simulate the beach profile response to wave and tidal action. A 1D cross-shore profile model was built and tested with the bathymetry data and accompanying boundary conditions that were collected during SABER_Duck. The default model settings were not an adequate match to the observed beach response; thus, a site-specific calibration was needed. Before proceeding with calibration, sensitivity analysis was performed to determine the dominant parameters. Here, the computation results were found to be sensitive to the model parameters, hmin, form, turb, facua and eps. Then the model was calibrated using the bathymetry, the initial varying grain size distribution in the swash zone and the hydrodynamic boundary conditions that were recorded during a 2- day storm event between 25-27 March 2014 at Duck Beach, USA. After calibration, the model reproduced the measured cross-shore profile evolution sufficiently by using varying grain size distribution in the swash zone.

Modeling study continued with computation of beach responses for four alternative initial bed compositions. Two of these scenarios had uniform grain size distribution along the cross-shore profile, one with fine and one with coarse sand as the mean sediment grain size. The following two scenarios were defined with fine sandy bed composition with coarse sand patches at lower swash and around shoreline, respectively. All scenarios were tested for the same 2-day period with the same hydrodynamic conditions and model results were compared with that of the original scenario. Computed beach response for uniform grain size distribution differed from that for the original varying distribution, corroborating the importance of grain size variability in beach response. The model results for alternative scenarios also demonstrated the importance of the accuracy in spatial distribution of varying grain sizes and the accuracy of the representative grain size in numerical modeling of coastal morphodynamics. Additionally, the grain size distribution in the computed final bed compositions showed layering of different grain sizes similar to those that were observed

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during trench survey and from the core samples, showing that the model was capable of simulating the sediment grain size sorting.

This thesis study clearly showed the importance of variability in grain size distribution in a beach’s morphological response. Furthermore, the numerical model was able to compute the beach response using variable grain size distribution and showed promising results related to the capabilities for the future pursuit of this research topic. Knowledge on the bed sediment composition and its temporal evolution in response to hydrodynamic forcing would advance with continuing experimental and numerical research.

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ABSTRACT Field studies with in-situ sediment sampling demonstrate the spatial variability in grain size on a sandy beach. However, conventional numerical models that are used to simulate the coastal morphodynamics ignore this variability of sediment grain size and use a uniform grain size distribution of mostly around and assumed fine grain size. This thesis study investigates the importance of using variable grain size distribution in numerical modeling of morphological beach response.

For this purpose, in-situ swash zone grain size distribution, beach profile and accompanying wave and tide time series data were obtained at a field campaign at the USACE Field Research Facility (FRF) in Duck, USA, in the spring of 2014. Using this data, a process based numerical coastal morphology model, XBeach, was chosen to simulate the beach profile response to wave and tidal action. 1-D cross-shore model was run for five major scenarios for a 2-day period with available field data in order to compare beach responses in the cases of measured variable and hypothetical uniform distribution of grain sizes in the swash zone respectively.

The data gathered in SABER_Duck, confirmed a highly variable grain size distribution in the swash zone both vertically and horizontally. The numerical model results for alternative grain size distribution scenarios were compared. Computed beach response for uniform grain size distribution differed from that for the original varying distribution, corroborating the importance of grain size variability in beach response. The results for alternative hypothetical bed composition scenarios, demonstrated the importance of the accuracy in spatial distribution of varying grain sizes and the accuracy of the representative grain size. Lastly, the grain size distribution in the computed final bed composition showed layering of different grain sizes similar to those that were observed during field campaign, showing the model’s capability of simulating the sediment grain size sorting.

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PREFACE

With this thesis, I finalize my Master of Science degree in Hydraulic Engineering at the Delft University of Technology. I would like to express my gratitude to those who supported me during my graduation study.

First of all, I would like to thank my committee members, Ad Reniers, Edith Gallagher, Matthieu de Schipper and Tjerk Zitman. Their guidance throughout the research and reporting was highly valuable in getting the insight into details of my research topic, developing my thesis and my skills on scientific research and reporting. I would also like thank Arnold van Rooijen, for his valued guidance and help as my former committee member during the first half of my graduation work. I would also like to thank Heidi Wadman for providing data and insight into data interpretation, and to Shoshan Abrahami for her guidance with my report.

Furthermore, I would like to give special thanks to Aliya van den Brink Sarayeva and Bert Valkenburg for evaluating my research and my report, and for their support. Your support and friendship have been precious to me during this period.

I would like to give another special thanks to John Stals and to my professor Ad Reniers, for their support during my graduation studies, for which I am grateful.

Lastly, I would like to express my gratitude towards my family as well as my devoted friends for their support and believing in me, and for making this possible.

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TABLE OF CONTENTS

EXECUTIVE SUMMARY ...... 3 ABSTRACT ...... 5 PREFACE ...... 7 1 INTRODUCTION ...... 11 1.1 BACKGROUND ...... 11 1.2 RESEARCH OBJECTIVE ...... 12 1.3 APPROACH AND OUTLINE OF THE THESIS REPORT ...... 12 2 SEDIMENT GRAIN SIZE CLASSIFICATIONS AND SEDIMENT CLASSIFICATIONS ...... 14 3 SABER_DUCK FIELD EXPERIMENT ...... 17 3.1 INTRODUCTION ...... 17 3.2 FIELD SURVEY METHODS ...... 18 3.2.1 Walking survey ...... 18 3.2.2 Depth of disturbance measurements ...... 20 3.2.3 Core sampling ...... 22 3.2.4 Trench survey ...... 25 3.3 ANALYSIS OF THE CORE SAMPLES ...... 27 3.3.1 Visual classification of layers ...... 28 3.3.2 Digital Imaging System ...... 33 4 NUMERICAL MODEL DESCRIPTION ...... 36 4.1 COMPUTATION OF HYDRODYNAMICS ...... 36 4.2 COMPUTATION OF SEDIMENT TRANSPORT ...... 36 4.3 SEDIMENT INPUT AND BED COMPOSITION ...... 38 4.4 COMPUTATION OF BOTTOM UPDATING ...... 39 4.5 BOUNDARY CONDITIONS...... 40 ▪ Wave Boundary Conditions ...... 40 ▪ Boundary Conditions for Shallow Water Equations...... 40 ▪ Boundary Conditions for Sediment transport ...... 40 5 NUMERICAL MODELING OF CROSS-SHORE PROFILE ...... 41 5.1 INTRODUCTION ...... 41 5.2 MODEL SET-UP AND BOUNDARY CONDITIONS ...... 41 5.2.1 Model Domain, Grid Set-up and Bathymetry ...... 41 5.2.2 Waves and Tides ...... 42 5.2.3 Initial Bed Composition ...... 43 5.3 MODEL VERIFICATION ...... 44 5.4 SENSITIVITY ANALYSIS ...... 45 ▪ Sensitivity parameter: hmin ...... 46 ▪ Sensitivity parameter: hswitch ...... 47 ▪ Sensitivity parameter: form ...... 48 ▪ Sensitivity parameter: turb ...... 49 ▪ Sensitivity parameter: facua ...... 50 ▪ Sensitivity parameter: eps ...... 51 ▪ Results of Sensitivity Analysis ...... 52 P a g e 9 | 67

5.5 CALIBRATION ...... 53 5.6 MODELING OF ALTERNATIVE SCENARIOS ...... 54 5.6.1 Scenario #1: Original Spatially Varying Distribution ...... 54 5.6.2 Scenario #2: Spatially Uniform Distribution...... 54 5.6.3 Scenario #3: Beach with Overall Fine Sand ...... 56 5.6.4 Scenario #4: Fine Sand Beach with Coarse Patch at Shoreline ...... 57 5.6.5 Scenario #5: Fine Sand Beach with Coarse Patch at Lower Swash ...... 58 5.7 MODEL RESULTS ...... 59 6 CONCLUSION ...... 61 7 DISCUSSION ...... 62 7.1 EXPERIMENT ...... 62 7.1.1 Experiment in general ...... 62 7.1.2 Walking survey ...... 62 7.1.3 Depth of Disturbance measurements ...... 63 7.1.4 Vibracores ...... 63 7.2 NUMERICAL MODELING ...... 63 7.2.1 Site specific calibration need ...... 63 7.2.2 Experiment data requirements ...... 64 7.3 FURTHER RESEARCH AND DEVELOPMENT SUGGESTIONS ...... 64 BIBLIOGRAPHY ...... 65

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1 INTRODUCTION

1.1 BACKGROUND Coasts are the transition zone between bodies of water and land. They have all kinds of different shapes and represent different properties, from wide sandy beaches to gravelly or rocky shores, from very wide dissipative coasts to those with steep slopes, from long-shore uniform structures to very complex 3D structures. Two main parameters, the material of which the coast is made of and the physical forces that have been acting on the coast and reworking it, govern these morphological differences. The physical forces act on and shape the interface between water and land, but the response and the result of the work done depends on the content of the material of the land that is affected.

One of the most active parts in a coastal profile is the swash zone. It lies between the upper and lower limits reached by the waves going up and down the beach. A glimpse of water and land interaction can be observed there even within just one wave cycle as the waves carry sand and gravel particles along with their motion over the beach. Here the effective hydraulic forces and phenomena involve short sea waves, swell, wave breaking, tide, turbulence, bottom friction, shear stress, infragravity waves, wind set-up, cross-shore and long-shore currents with complex three-dimensional structures of these forces in the water column (Bosboom and Stive, 2015). The combination of these forces is what brings the coastal sediment into movement and works the profile that we observe on the beach.

As mentioned above, different materials respond differently to these forces. When the domain is a coast made up of loose material, the primary physical property of the coastal sediments that determines its response is their grain size. Grain size is the governing physical property that determines whether a sediment grain moves under a certain hydraulic loading (Shields, 1936). Loose materials are classified according to their grain sizes, as sand, gravel, silt, pebble and further subclassified as coarse, fine, etc. (Wentworth, 1922). Likewise, the beaches are termed sandy, gravelly etc.

Upon first arrival on a beach the terrain may be identified as a medium sandy beach following its seemingly uniform medium-sized sands. Yet the grain sizes on a beach are variable. A closer look at the beach surface shows this. Fine and medium sands are present together with coarse sand, gravel and pebbles, altogether making up a medium sandy beach upon initial identification. In engineering projects and in conventional numerical models this is done analogously. A mean grain size is obtained and the whole beach is described as a uniform distribution of that particular grain size. Conventional numerical models that are used to simulate the coastal morphodynamics ignore this variability of sediment grain size. However, the effect of the variability in existing grain sizes becomes clear from the observation of different beach slopes on adjacent beaches with slightly different sediment content under otherwise similar conditions with the same physical forcing (Calliari, 1994 and Birkemeier et al., 1985).

Field studies with in-situ sediment sampling demonstrate the spatial variability in grain size. Some examples are cross-shore profile variability (Gallagher et al., 1998), variation in surface P a g e 11 | 67

sediment grain sizes under a rip current system (MacMahan et al., 2005) and the different ripple regimes at adjacent locations (Trembanis et al., 2004). These studies suggest that differential bottom conditions exhibit differential feedback to flow conditions consecutively affecting the local morphodynamics.

Variability in grain size is also observed in the vertical dimension. Schwartz and Birkemeier (2004) collected a large number of sediment core samples along the cross-shore profile over the entire shoreface prism at Duck beach, in the USA. Each core sample represented the in- situ positioning of sediment grains at the coring location. In each sample, there were layers of variable grain sizes and occasionally of materials from different origins. This layering of sediment through the vertical dimension is called stratification. By combining the information gained from each core they created a 2D stratigraphy map of grain sizes and stratification of the whole shoreface prism.

1.2 RESEARCH OBJECTIVE The main objective of the following research is to improve the understanding of how the variable grain size distribution in the swash zone affects the beach response. For this goal, this thesis will study the following research questions (RQs):

• RQ.1: What is the grain size distribution along a cross-shore profile on a real sandy beach? • RQ.2: Can we reproduce the beach response that is observed in-situ by numerical modeling? What do we need for this? ▪ Can we reproduce the profile evolution in the swash zone using variable grain size in numerical modeling? ▪ What is the difference in the response for the case of using uniform grain size distribution in numerical modeling? • RQ.3: What kind of conclusions can be drawn by comparing the results of the two aforementioned modeling approaches? • RQ.4: What are the areas of further research and development related to understanding the role of grain size variability in the swash zone? • RQ.5: What are the capabilities of numerical modeling using variable grain size distribution?

1.3 APPROACH AND OUTLINE OF THE THESIS REPORT The given research questions are addressed by the following approach in consecutive chapters.

Firstly, the scientific classification of different grain sizes is summarized in Chapter 2. Here a brief explanation is given on standardized classification of sediment composition.

Secondly, to study the research question, time series of in-situ swash zone stratigraphy and beach profile data were obtained at a field campaign at the USACE Field Research Facility (FRF) in Duck, USA, in the spring of 2014. This experiment campaign was called SABER_Duck as an acronym for ‘Stratigraphy And BEach Response’. As a part of this thesis project the measurement methodologies and the data are studied and analyzed. The aim of this analysis

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was to understand the nature of the beach response to the wave and tidal action during the period of field campaign. Chapter 3 – SABER_Duck Field Experiment gives a detailed explanation of the methodologies of SABER_Duck field measurements and the gathered data.

Thirdly, a process based numerical coastal morphology model, XBeach, was chosen to simulate the beach profile response to wave and tidal action. With XBeach it is possible to input variable distribution of different grain sizes in the seabed. The model parameters and the theoretical background of numerical computation are described in Chapter 4 – Numerical Model Description.

Fourthly, model studies were carried out to simulate the beach response using in-situ data measured during SABER_Duck experiment campaign. It started with the creation of an initial model set-up for the Duck Beach case. This was followed by the determination of sensitive parameters for SABER_Duck and calibration of the model for the time period of the field measurements. Then, data that was retrieved from the field experiment was used to test the capabilities of the numerical model in simulating the real beach response to wave and tidal action. Later the model was run for five major scenarios that were within the limits of available field data in order to compare beach responses in the cases of variable and uniform distribution of grain sizes in swash zone respectively. This process and the findings of the numerical model work are given in Chapter 5 – Numerical Modeling of Cross-shore Profile.

The reporting proceeds with the conclusions drawn from the thesis study, which are given in Chapter 6 – Conclusion.

Lastly, the discussion of findings and observations made of field measurements and further analysis related to the quality of the data; capabilities of numerical modeling; possibilities for and expected gains from further studies on the topic; and lastly the requirements for further study of stratigraphic evolution of swash zone as a part of beach response. This is given in Chapter 7 – Discussion.

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2 SEDIMENT GRAIN SIZE CLASSIFICATIONS AND SEDIMENT CLASSIFICATIONS Beaches are made up of loose sediment. Loose granular materials are classified and named based on their grain sizes, where grain size refers to the nominal diameter of an individual grain. The most commonly accepted grain size classification scale is Udden-Wentworth Scale (Wentworth, 1922). It also has later been adopted and modified by other engineering and standardization institutions like ISO, USGS and ASTM. In Figure 2.1 the chart for this scale is provided, showing the range limits for each size fraction. In Wentworth Scale sediment grains are classified as clay, silt, sand and gravel, as going from very fine to very coarse grains. Each class is further divided into very fine, fine, medium, coarse and very coarse subclasses. Ranges and names of the size fractions may differ from scale to scale especially for grain sizes that are coarser than 2mm.

Units that are used in this in this scale are mm and phi. Phi (Φ) is a logarithmic modification of metric grain size. It was defined by Krumbein (1937) as:

−Φ Φ = − log2(퐷⁄퐷0) ↔ 퐷 = 퐷0×2

where;

Φ is Krumbein phi scale,

퐷 is nominal diameter of grain,

퐷0 is reference diameter, which is equal to 1 mm.

Any given sample that is collected from field has a combination of grains from different sizes. The schemes of Shepard-Schlee and Folk were designed to classify such sediment sample as found in nature, according to relative proportions of earlier defined size fractions (silt, sand etc.). They are described by the ternary diagrams that are given in Figure 2.2. The two systems differ in the patterns by which the classes were defined in the triangles and the relative emphasis placed on gravel in definitions (Poppe et al., 2005).

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Figure 2.1: Udden-Wentworth Grain Size Scale Chart (Williams et al., 2006)

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Figure 2.2: Sediment Size Classification Schemes of Shepard-Schlee and Folk (Poppe et al., 2005)

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3 SABER_DUCK FIELD EXPERIMENT

3.1 INTRODUCTION Stratigraphy and Beach Response Experiment (SABER_Duck) was conducted during eleven days starting from 25 March 2014 and ending on 04 April 2014 at US Army Corps of Engineers (USACE) Field Research Facility (FRF) at Duck Beach, North Carolina. The experiment was performed by the collaboration of FRF, Heidi Wadman and Jesse McNinch in person, Edith Gallagher, research associate in Franklin and Marshall College and Ad Reniers, associate professor at University of Miami (currently Professor of Free-surface waves in Delft University of Technology).

The goal of the SABER_Duck was to observe the in-situ stratigraphy of swash zone sediments on a steep sandy beach and collect time-series data to evaluate the morphodynamic evolution of the cross-shore profile and the swash zone stratigraphy. Being a novel field experiment on the topic, SABER_Duck possessed the features of a pilot experiment and aimed also to evaluate the potentials and requirements of different methods that were utilized for gathering stratigraphy and morpohology data.

960 m profile line

Figure 3.1: The map of FRF showing the profile lines, along which regular data collections are executed. The profile line in red color coincides with the transect where core samples were collected during SABER_Duck.

This chapter is organized as follows. In Section 2, the field survey methods that were used in the SABER_Duck field campaign are discussed. In Section 3 the core sample analysis is discussed in more detail.

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3.2 FIELD SURVEY METHODS During the SABER_Duck, four in-situ surveying methods were utilized: 1. Walking surveys 2. Depth of disturbance measurements 3. Core sampling 4. Trench survey

The dates on which surveys were performed are given in Table 3.1. By applying multiple methods, data with different characteristics was gathered. The field survey methods are explained in the following subsections.

Table 3.1: survey dates in SABER_Duck for each method Availability of Survey Data on Dates Method of Survey 25/03 26/03 27/03 28/03 29/03 30/03 31/03 01/04 02/04 03/04 04/04 /14 /14 /14 /14 /14 /14 /14 /14 /14 /14 /14

Walking Survey ✗ ✗ ✗ ✗ ✔ ✔ ✔ ✔ ✔ ✗ ✗

Depth of Disturbance ✗ ✗ ✔ ✔ ✔ ✔ ✔ ✔ ✔ ✗ ✗ Measurements ✔ Vibracoring ✔ ✗ ✔ ✔ ✗ ✗ ✗ ✗ ✗ ✗ (2 times)

Trench Survey ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✔ ✔

3.2.1 WALKING SURVEY Walking surveys were performed in order to gather the swash zone bathymetry and its evolution during the SABER_Duck experiment campaign. The surveys were performed in the swash zone covered between 915-1025m North and 60-110m East (with FRF coordinates) (See Figure 3.1 and Figure 3.3). These surveys were performed once per day1 on five adjacent days from March 29th to April 2nd. Walking surveys were carried out with the aid of a Real Time Kinematic (RTK) surveying device which measured and logged its geographic coordinates in a frequent time interval.

The procedure to gather the bathymetry with this instrument was to carry the GPS transmitter at a constant elevation above the ground (Figure 3.2) while walking up and down the swash zone along closely spaced routes as seen in Figure 3.3. In this way, geographic coordinate information is gathered at several locations in the swash zone, where the accuracy of the measurements was in the order of cm (Trimble, 2003). The same procedure was repeated on subsequent days to observe the profile changes in swash zone.

1 Walking survey were performed mainly during high water, on the first day around MSL and on the second day just at the beginning of high water. P a g e 18 | 67

Courtesy http://marine.rutgers.edu

Figure 3.2: Usage of GPS system for walking surveys. In these examples GPS is carried on top of pole.

During the walking survey, geographic coordinates were measured on closely spaced individual points on swash zone. To have the correct geographic coordinates of these points, the elevation of the GPS antenna was subtracted from the measured data. Then the full bathymetry for each measurement day was built by interpolation between the measured points. Figure 3.3 visualizes the walking survey for day 29.03.2014. Here, both the walking track with its individual measurement locations and the full bathymetry of the swash zone

are visible.

Longshore coordinate (m) coordinate Longshore

Cross-shore coordinate (m) Figure 3.3: Walking survey that was performed on 29.03.2014. Longshore and cross-shore coordinates are given with respect to FRF reference point. Colorbar shows the bed level in meters with respect to NAVD, blue dots show the individual locations where the 'walking survey' data was measured. The circles on the 980m profile represent rebar locations (Section 3.2.2). The circles on the 960m profile show the core locations (Section 3.2.3). P a g e 19 | 67

Using the walking survey bathymetry data daily long-shore averaged cross-shore profiles of swash zone were derived. By subtracting the averaged cross-shore profile from the entire bathymetry the shoals and troughs in bottom profile of survey area were obtained. While repeating this procedure every day, a visual representation of long-shore evolution of the bathymetry was acquired (Figure 3.4). This enabled the examination of the trend in long- shore sediment transport. This trend was important to see if cross-shore profile in a specific transect was affected by the long-shore transport. In the case where long-shore transport affects the cross-shore evolution, it should be counted for in the cross-shore morphodynamics analysis. In our study, we didn’t observe a long-shore transport effect on the swash zone bathymetry as the locations of the shoals and troughs didn’t change along the beach.

Figure 3.4: Bathymetric features of swash zone around the daily longshore averaged bottom profile. Figures were obtained by subtracting the daily long-shore averaged cross-shore profile from daily bathymetry data.

3.2.2 DEPTH OF DISTURBANCE MEASUREMENTS Depth of disturbance (DoD) is the thickness of the bottom sand layer in the swash zone affected by the hydrodynamic processes (e.g. waves and currents) along a tidal cycle or longer time period; one or two days (Anfuso, 2005). Rebar and loose-fitting washer combination was utilized during SABER_Duck for DoD measurements. The rebars were positioned vertically into the bottom and the ring-shaped washers were moving freely around the rebars as shown in Figure 3.5.

During the measurements, the rebars stayed rigid and the washers moved freely up and down with the wave and tide action. Measurements began with recording the distance between the top of the rebar and the top of the bottom surface at each rebar location. One day passed between each DoD reading. During this period between the consecutive readings, the hydrodynamic forces reworked the bottom sediment, while gravity caused the change of the elevation of washers around the rebars. After this, each day the depth of the washer below the bottom surface was recorded. Figure 3.5 shows rebar measurements that were carried out during the SABER_Duck.

The washer initially stayed at the ground surface level. This level was noted. Repeated swash cycles caused repeated erosion and deposition. The washers penetrated down along the rebar in case of erosion during a certain swash event. In case of accretion the washers were covered by sand. Over the course of the experiment the vertical location of the washer P a g e 20 | 67

indicates the lowest vertical level a washer penetrated at that specific rebar location. This process provides an easy representation of the active layer in the swash zone.

a' a'

a

b b

Figure 3.5: Rebar - washer measurements. Initially washer stays at bottom surface. The distance from top of the rebar to the top of the bottom surface was recorded, ‘a’. The next day two values were read. The distance from the top of the rebar to the top of the bottom surface was recorded as ‘a’’, which gave information on total erosion-accretion at the location. The distance between the top of the bottom surface and the washer ‘b’ was measured to have information on the erosion max depth that the wave action had reached.

In SABER_Duck depth of disturbance measurements were performed at six locations on a cross-shore transect at 980m profile (Figure 3.3). The measurements were done on seven adjacent days from 27.03.2014 to 02.04.20142. The data is given in Table 3.2.

Table 3.2: Depth of disturbance measurements Local Measured level on Day... (cm)(1) Coordinates Stake (FRF) a a' – b X Y 27/03/14 28/03/14 29/03/14 30/03/14 31/03/14 01/04/14 02/04/14 R1 60 980 51 n/a n/a n/a n/a n/a n/a R2 67 980 43 n/a n/a n/a n/a n/a n/a R3 75 980 46 48,5 – 10 37,5 – 12 32,5 – 6 31,5 – 6 40 – 2 45,5 – 3 R4 84 980 47 24 – 30 0,13 – 52 45,5 – 12,5 49 – 10 54 – 4,5 58 – 5 R5 94 980 59 51,5 – 10 65 – 8 79,5 – 23,5 80 – 22 70,5 – 12(2) 66 – 17,5(2) R6 100 980 47 71 – 5 87 – 5 67 – 20 (3) 69 – ? (4) 62 – ? (4) 54 – 18(2) (1) In the measured values, first number gives the distance between the top of the rebar and the top of the bottom surface and second number gives the depth of the washer below the top of the bottom surface, which are depicted with a, a’, b in Figure 3.5. (2) Color of the measurement value changes when a new washer was added (see Figure 3.6). (3) Visually estimated value. (4) Washer was not found.

2 DoD were not performed exactly on the same dates with core sampling. Therefore, only a general trend was observed for depth of disturbance. Moreover, a storm event took place on day 26.03.2014 but unfortunately the DoD measurements only started after the storm. P a g e 21 | 67

There was no activity observed at rebar locations R1 and R2 (landward end of the rebar transect) during the experiment. The reason for this seems to be the fact that tide and wave run up didn’t reach this elevation. Figure 3.6 visualizes the measurement results for rebar locations R3 to R6. Additionally, visual observations by the researcher on site, E. Gallagher, revealed that washers at rebar locations R5 and R6 penetrated about 1cm within 3-4 swash cycles, which can be interpreted as a measure of mixing depth.

This simple DoD research experiment surprisingly provided with very valuable information to visualize the scale of morphodynamic activity in the swash zone.

Figure 3.6: Rebar measurements for locations R3 to R6 (courtesy E. Gallagher)

3.2.3 CORE SAMPLING The goal of the SABER_Duck was the observation of morphodynamic evolution of swash zone stratigraphy. Thus, the main focus of SABER_Duck was on the core sampling surveys.

Core samples were gathered using 2-meter-long steel pipes. Figure 3.7 shows the core sampling procedure via photographs provided in order. In Figure 3.7, Top row: Empty pipes were driven into the sand vertically. Vibration provided by the CRAB3 was utilized while researchers guided and pushed the pipes into the sand manually. Middle row: When this was completed, a cap was placed at the top end of the core, and sealed with tape. Bottom

3 Coastal Research Amphibious Buggy (CRAB) is a three-wheeled vehicle, which consists of a tripod and an operations platform located 10.7 m above the ground. It is partially visible in Figure 3.7 as the yellow painted metal structure on wheels. The maximum significant wave height for operation is 2 m. P a g e 22 | 67

row: Immediately afterwards, the pipes, filled with in-situ sediment, were taken out vertically by the vibration and power provided by the CRAB. In order to get accurate representation of in-situ stratification, this process was performed slowly and carefully. When the pipe came fully out of the ground, another cap was placed at the bottom end of the core, and sealed with tape. In this way, the stability of the sand core was guaranteed. Later the cores were taken to the laboratory for analysis.

Figure 3.7: Core sampling procedure P a g e 23 | 67

Core Sampling Schedule:

Cores samples were collected in late March/early April 2014 at Duck beach swash zone (NC, USA). The core sampling was carried out for four days during the experiment. The schedule of the sampling survey is summarized in Table 3.3. Figure 3.8 shows the locations where the core samples were taken.

On the first day of the survey (25.03.2014) core samples were taken from 8 locations (cores A to H) in the swash zone along three parallel transects on 980m, 965m and 950m cross- shore profiles. After discussion, 965m cross-shore profile was chosen as the transect for the time series sampling. On the second day (27.03.2014) core samples were taken from six locations (cores I to N) on the 965m cross-shore profile. Within these locations, the cores N,

K and I coincided with the cores A, D and G of 25.03.2014, respectively (Figure 3.8).

rdinate (m) rdinate

Longshore coo Longshore Bed level w.r.t. NAVD (m) level Bed

Cross-shore coordinate (m)

Figure 3.8: Core locations in swash zone4

On 28.03.2014 core samples were taken from eight locations; the six core locations from day two and two new locations at the seaward end of the same transect (cores O and P). During the first three days of core sampling, survey was performed at low tide.

On the fourth and last day (01.04.2014), core sampling was performed twice, both at low tide and high tide. At low tide, samples were taken from five adjacent locations from K to O, and from location B. Later at high tide, sampling was repeated at four adjacent locations from I to L, and at locations C and E.

As having been the main focus of SABER_Duck field campaign, analysis of core samples is explained in a separate section in detail (Section 3.3).

4 The coordinates of Core D was approximated because of faulty registration of data. P a g e 24 | 67

Table 3.3: SABER_Duck core sampling schedule. The cores written in red color are the cores that are chosen for the visualization of core sample analysis in the following section (Section 3.1.3). Availability on experiment instances

Core 25-03-2014 27-03-2014 28-03-2014 01-04-2014 01-04-2014 Latitude Longitude Notes ID Low tide Low tide Low tide Low tide High tide

A 36 11 10.18863 -75 45 6.92550 X

B 36 11 09.70050 -75 45 6.92839 X X

C 36 11 10.35224 -75 45 8.11257 X X

D 36 11 09.51646 -75 45 7.84618 X

E 36 11 09.50909 -75 45 7.72214 X X

F 36 11 10.21958 -75 45 8.75261 X

G 36 11 09.76599 -75 45 8.56470 X

H 36 11 09.35736 -75 45 8.40741 X X X

I 36 11 09.68436 -75 45 8.48551 X X X ~same as Core G

J 36 11 09.83273 -75 45 8.13155 X X X

K 36 11 09.93920 -75 45 7.85015 X X X X ~same as Core D

L 36 11 10.06452 -75 45 7.54517 X X X X

M 36 11 10.16719 -75 45 7.29196 2 cores X X

N 36 11 10.23567 -75 45 7.13223 X X X ~same as Core A

O 36 11 10.33349 -75 45 6.91645 X X ~same as Core A

P 36 11 10.42594 -75 45 6.74293 X

3.2.4 TRENCH SURVEY The last two days of the field campaign (03.04.2014 and 04.04.2014) two big trenches were dug across the beach by an excavator, one in longshore and one in cross-shore direction. Figure 3.9 shows the alignment of these trenches with respect to the shore. The trenches were approximately 1.5 m deep. The cross-shore trench was aligned to pass through the peak of a beach cusp inside the measurement area. For safety reasons the cross-shore trench was limited in seaward direction by the distance that the excavator was able to dig. Figure 3.10 shows some pictures of the trench survey in SABER_Duck.

cross-shore N trench land

long-shore trench

water

Figure 3.9: Schematization of survey trenches on the beach. Note that the beach cusp dimensions are exaggerated.

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The aim of the trench survey was to see the stratigraphy trend in the horizontal dimension. Furthermore, the trench survey was used to provide with an undisturbed view of in-situ grain size stratigraphy.

The in-situ trench analysis is shown in Figure 3.11. The trench survey analysis was done by visual observation. The grain size stratigraphy was registered corresponding to the grain size classification definition (for grain size classification chart see Chapter 2). At the same time, synoptic pictures of trenches were taken at every 1m interval. In these photographs a tape was placed along the vertical axis to provide with the depth information. These were accompanied with the photographs that show layering in a closer view (also shown in Figure 3.11).

Examination of the two trenches showed the existence of continuous layers of coarse and fine sands comprising the beach stratigraphy. Gallagher et al. (2016), attributes the thicker (~2–10 cm) coarse layers (above mean sea level) to storm erosion and storm surge. Thinner (1–2 cm) coarse layers were also visible in the trenches. They are thought to result from similar elevated sea level and swash action processes but on smaller temporal scales.

a) Cross-shore trench

b) Long-shore trench Figure 3.10: Two trenches were dug during SABER_Duck: one cross-shore and one long-shore.

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Figure 3.11: Observations in cross-shore trench

3.3 ANALYSIS OF THE CORE SAMPLES The Core samples inside the steel pipes were brought to the FRF laboratory for analysis. In the laboratory, they were cut into halves as shown in Figure 3.12. From this moment on, two different types of analysis were performed on them: 1) Visual classification of sand layers by experienced geologist (traditional description) 2) Detailed digital imaging system (DIS) analysis on the core samples.

Figure 3.12: Cores were cut into halves in the laboratory

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3.3.1 VISUAL CLASSIFICATION OF LAYERS An expert geologist examined first halves of the core samples visually. The layers found in the cores were registered corresponding to their grain size classification (Chapter 2). Photographs of the registered layers were taken for future reference. Additionally, small samples were taken from the core sand approximately in every 5-10 cm for further analysis of grain sizes patches. These samples were taken where they were descriptive for the layers observed in the cores.

To illustrate the results of this analysis, four core locations, which had samples taken on all four sampling days, were chosen. These were Core A/N, Core A/O, Core D/K and Core G/I. The aforementioned pairs of cores were the ones with proximate locations (see Table 3.3), which allowed the time series comparison. The chosen cores were all located on 965m cross-shore transect (Figure 3.8). Visualization of the logs of this grain size classification analysis is provided within Figures Figure 3.13 to Figure 3.16. In these figures, time series of core sample logs are given separately for each location. Grain size stratigraphy is drawn as was observed in the sample in the laboratory. Core sample logs are drawn vertically to represent the in-situ alignment of the cores and corresponding layering. In the figures, the numbers on the vertical dimension shows the distance in cm from the top of the sediment sample inside the core pipe (not the top edge of pipe itself). Samples were of different length due to the imperfect conditions during the collection of the vibracores, which included but was not limited to the compaction by the vibration and different degrees of fluidity during specific sampling events.

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Figure 3.13: Stratification in Core samples G - I

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Figure 3.14: Stratification in Core samples D - K

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Figure 3.15: Stratification in Core samples A - N

* Sand content is shown with solid hatch when it is the main content of the layer. Sand content is shown with colored dots when it is secondary content of the layer.

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Figure 3.16: Stratification in Core samples A - O

* Sand content is shown with solid hatch when it is the main content of the layer. Sand content is shown with colored dots when it is secondary content of the layer.

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3.3.2 DIGITAL IMAGING SYSTEM On the second halves of the cores the digital imaging system (DIS) method (Bruin et al., 2004 and Gallagher et al., 2011) was applied. This method was previously used in-situ during field experiments in Truc Vert, France in May 2006 and March–April 2008, and in Monterey, CA in May 2007 and in April–May 2009.

The picturing set-up is shown in Figure 3.17. A core half was placed on a conveyor belt and was moveable longitudinally by rolling motion. The camera was placed rigid above the core and kept its perpendicular distance during the picturing of the whole core. At each step the core was shifted 1 cm longitudinally. A picture of 2 by 2 cm size was taken every 1 cm interval. This provided with 50% overlapping, thereby creating a much more accurate analysis as shown in Figure 3.18.

Figure 3.17: Set-up of the DIS picturing. A core half is moved longitudinally on a conveyor belt under a fixed camera that was positioned perpendicularly.

Further analyses of the gathered pictures continued with a computer algorithm. For this step, smaller picture bins were taken from the core photographs (see Figure 3.19). Each bin had dimensions of 2 mm vertically and 18 mm horizontally (these vertical and horizontal dimensions refer to the in-situ position of the cores as in Figure 3.18). The computer algorithm calculated the average grain size for the picture bin. For accuracy and elimination of noise, these bins were taken at every 0.5 mm interval (moving vertically), thereby providing two separate data coming from the same picture for each layer of 0.5 mm thickness. For one layer of 0.5 mm thickness, there were two separate pictures taken by the camera. This provided with two pictures for each point along the core, generating two average grain size values, one from each picture. P a g e 33 | 67

Figure 3.18: Photographs taken for DIS analysis were of 2 by 2 cm size. They were taken at every 1 cm step moving vertically (in reference to the in-situ position of the core).

2 mm 0.5 mm

18 mm

(Courtesy Edith Gallagher)

Figure 3.19: 2 by 18 mm picture bins were taken from the photographs for computer analysis. The bins were taken at 0.5 mm steps.

Figure 3.20 summarizes the calculation process of the representative (average) grain size values along the depth of the core. The picture bins were given as input to the computer algorithm. The algorithm computed the average grain size for each 0.5 mm layer by using the data gained from two adjacent picture bins of the same image. Calculation process was explained in detail in Gallagher et al. (2011). The initial averages of grain sizes were noisy (see the green lines in Figure 3.20). As shown in Figure 3.18, there were two photographs of P a g e 34 | 67

2 by 2 cm that were overlapping at each location. Therefore, there were also two average grain size data for the same layer. By averaging these two values again for the same 1 cm bin, the noise in the data was lowered and more accurate information was gained. The final average grain size information by depth is shown with blue asterisks in Figure 3.20.

Figure 3.20: Digital image analysis by computer algorithm. P a g e 35 | 67

4 NUMERICAL MODEL DESCRIPTION

4.1 COMPUTATION OF HYDRODYNAMICS For the computation of the hydrodynamics at Duck the instationary surfbeat mode of XBeach is used. In this mode, variations of short waves on the wave group scale and the associated long waves are resolved. This mode includes computation of wave-driven currents, long waves as well as run up and run down in the swash zone. Below a summary of the model description is given. Details can be found in the XBeach manual (Roelvink et al., 2015).

Incident wave-group conditions are defined at the offshore boundary. The wave transformation is computed from the wave action balance. Dissipation of short waves due to wave breaking and bottom friction is accounted for in the model. Directionally integrated wave energy dissipation due to breaking is calculated by the extended version of the Roelvink (1993) formula. The wave dissipation is used as input for the roller energy model. Roller energy balance equation accounts for the temporary shoreward momentum in the surface rollers that occurs after wave breaking. The corresponding wave forcing is obtained by calculating the wave and roller related radiation stress gradients.

The model uses the depth-averaged Generalized Lagrangian Mean (GLM) shallow water equations for the computation of long waves and mean flows forced by the radiation stress gradients. GLM formulates the momentum and the continuity equations in terms of a Lagrangian velocity, which is the distance travelled by water particle in one wave period divided by the wave period. This Lagrangian velocity is related to the Eulerian velocity by uL = uE + uS, where uE is Eulerian velocity and uS is the Stokes drift corresponding to the wave and roller-induced mass flux. Bed friction associated with mean currents and long waves is included via bed shear stress. In the current model set-up, the dimensionless bed friction coefficient was calculated using a Chezy value of 65 m1/2/s.

Since the instationary mode of XBeach resolves the hydrodynamics associated with wave group time scale, the short wave shape is not resolved. To account for the nonlinearity of the wave shape and concomitant orbital motion, the extended version (van Thiel de Vries, 2009) of wave shape model of Rienecker and Fenton (1981) is used. In this model, the short wave shape is described by weighted sums of higher harmonics and used to estimate the wave-related sediment transport. In addition, wave breaking induced turbulence energy at the surface is computed and transported towards the seabed for its potential effect on sediment stirring.

4.2 COMPUTATION OF SEDIMENT TRANSPORT In the model ‘van Thiel - van Rijn’ sediment transport formulae were used. In these formulae, critical velocities for currents and waves are calculated separately from Shields (1936) and Komen and Miller (1975) respectively. Then they are combined in a weighted sum to reach the critical velocity. Xbeach includes the effects of bed slope into sediment transport computations.

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In XBeach sediment concentrations in the water column are modeled using a depth averaged advection diffusion scheme with a source-sink term based on equilibrium sediment concentrations from Gallappatti and Vreuglenhil (1985).

퐸 퐸 휕ℎ퐶 휕ℎ퐶푢 휕ℎ퐶푣 휕 휕퐶 휕 휕퐶 ℎ퐶푒푞−ℎ퐶 + + + [퐷ℎℎ ] + [퐷ℎℎ ] = Equation 4.1 휕푡 휕푥 휕푦 휕푥 휕푥 휕푦 휕푦 푇푠

In Equation 4.1 C represents the depth-averaged sediment concentration, which varies on the wave-group time scale, and Dh is the sediment diffusion coefficient. The entrainment of the sediment is represented by an adaptation time Ts, given by a simple approximation based on the local water depth h and sediment fall velocity ws.

The entrainment or deposition of sediment is determined by the mismatch between the actual sediment concentration C and the equilibrium concentration Ceq thus representing the source term in the sediment transport equation.

The transport formulations implemented into XBeach distinguish bed load and suspended load transport. The equilibrium concentrations for the bed load Ceq,b and suspended load

Ceq,s were calculated separately from the following equations, where Asb and Ass are bed load and suspended load coefficients respectively.

1.5 퐴 퐶 = 푠푏 (√푣2 + 0.64 푢2 − 푈 ) 푒푞,푏 ℎ 푚푔 푟푚푠,2 푐푟

2.4 퐴 퐶 = 푠푠 (√푣2 + 0.64 푢2 − 푈 ) Equation 4.2 푒푞,푠 ℎ 푚푔 푟푚푠,2 푐푟

Then the total equilibrium concentration is calculated with:

1 1 퐶 = 푚푎푥 (푚𝑖푛 (퐶 , 퐶 ) + 푚𝑖푛 (퐶 , 퐶 ) , 0) Equation 4.3 푒푞 푒푞,푏 2 푚푎푥 푒푞,푠 2 푚푎푥

The equilibrium sediment concentration Ceq for both the bed load and the suspended load is related to the velocity magnitude (vmg), the orbital velocity (urms) and the fall velocity (ws).

The velocity magnitude, vmg, is the magnitude of the Eulerian velocity, given by:

퐸 2 퐸 2 푣푚푔 = √(푢 ) + (푣 ) Equation 4.4

The root-mean-squared orbital velocity, urms, is obtained from the wave group varying wave energy using linear wave theory and calculated by the following formula, where Trep is the representative wave period, the Hrms is the root-mean-square wave height, h is the water depth and k is wave number.

휋퐻푟푚푠 푢푟푚푠 = Equation 4.5 푇푟푒푝√2 푠𝑖푛ℎ(푘(ℎ+훿퐻푟푚푠))

To account for short wave breaking induced turbulence at the bed, the orbital velocity is adjusted by the following equation (van Thiel de Vries, 2009), where kb is the wave breaking induced turbulence at bed.

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2 2 푢푟푚푠,2 = 푢푟푚푠 + 1.45푘푏 Equation 4.6

Furthermore, the fall velocity, ws, is calculated using the following formulations.

∆푔퐷2 푤 = 훼 √∆푔퐷 + 훼 50 Equation 4.7 푠 1 50 2 푣

where,

0.5 (−120⁄ ) 훼1 = 1.06 tanh (0.016 퐴 푒 퐴 )

−0.59 (−0.0004 퐴) 훼2 = 0.055 tanh(12 퐴 푒 )

Additionally, to account for the wave-related sediment transport Van Thiel de Vries (2009) introduced a parameterization based on the wave skewness and asymmetry, which affects the sediment advection velocity (see Eqn. 2.95). In this equation ua is calculated as function of wave skewness (Sk), wave asymmetry (As), root-mean square velocity urms and two calibration factors fSk and fAs.

푢푎 = (푓푆푘푆푘 − 푓퐴푠퐴푆) 푢푟푚푠 Equation 4.8 ua is combined with the Eulerian velocities to compute the combined wave-and current sediment flux and Equation 4.1 becomes:

퐸 퐸 휕ℎ퐶 휕ℎ퐶(푢 −푢푎 sin 휃) 휕ℎ퐶(푣 −푢푎 cos 휃) 휕 휕퐶 휕 휕퐶 ℎ퐶푒푞−ℎ퐶 + + + [퐷ℎℎ ] + [퐷ℎℎ ] = 휕푡 휕푥 휕푦 휕푥 휕푥 휕푦 휕푦 푇푠

Equation 4.9

A higher ua value means a stronger onshore sediment transport.

4.3 SEDIMENT INPUT AND BED COMPOSITION The sediment input determines the initial composition of the bed and the detail in which processes related to sediment sorting are resolved. Specific sediment distributions are parametrically defined by specifying values for D50, D15 and D90. In XBeach, when the effect of different sediment fractions, sorting and armoring are of importance, a bed composition constituting multiple sediment fractions can be defined. Each sediment fraction is characterized again by a median grain size (D50) and optionally D15 and D90. While using multiple sediment fractions, multiple bed layers are needed to describe the vertical distribution of the sediment fractions in the bed. Using multiple bed layers, XBeach keeps track of the different sediment fractions both in the horizontal and vertical dimension. Coarse sediments may be deposited on top of fine sediment after which erosion of the coarse sediment is needed to expose the fine sediment again, effectively armoring the bed.

Three types of bed layers are distinguished; the top layers, the variable layer and the bottom layers. At least one of each type is needed. Each bed layer has a thickness. The top layer is the only layer that interacts with the water column and can be eroded, but preserves its thickness. The bottom layers are layers are also of constant thickness and move with the top layer. In between these two groups of layers there is a single variable or “breathing” layer defined. It adapts its thickness to the erosion and sedimentation of the bed. For example, if P a g e 38 | 67

a grid cell is eroded, particular fractions of sediment are removed from the top layer, but the top layer preserves its thickness and takes the same volume of sediment, likely of different composition than the eroded sediment, from the layer below. If this layer is a top layer as well, the thickness is preserved and again the same volume of sediment is taken form a lower bed layer. This continues until the variable or “breathing” layer is reached. This layer adapts its thickness to the amount of erosion. If the thickness of the layer becomes too small, the variable layer is merged with an adjacent bottom layer and a new bottom layer is defined underneath the existing ones to ensure a constant number of bed layers. Reversely, if a grid cell is accreting, the thickness of the variable layer will be increased and with sufficient increase, the variable layer will be split in two effectively creating a new bottom layer. The lowest existing bottom layer is then discarded to ensure a constant number of bed layers. The thickness of the different layer classes can be set separately or at once. Bed layer thicknesses are chosen according to the expected erosion and deposition during the simulation.

Each grid cell in XBeach holds its own sediment distribution and the sediment transport formulations that are used differentiate between sediment fractions. Therefore, the distribution of sediment may change over time and processes like armoring and sorting can be simulated.

In the model inputs, initial bed composition is defined by using external files. There is one file for each sediment fraction. These files are formatted comparable to the bathymetry files. Bed composition files hold information on how much sediment of a specific fraction is in each grid cell and bed layer at the start of the simulation. The values are a volumetric fraction that implies that they should add up to unity over all fractions.

4.4 COMPUTATION OF BOTTOM UPDATING Bed level changes based on the gradients in the sediment transport.

휕푧 푓 휕푞 휕푞 푏 + 푚표푟 ( 푥 + 푦) = 0 Equation 4.10 휕푡 (1−푝) 휕푥 휕푦

In this equation zb is bed level, ρ is the porosity, fmor is morphological acceleration factor, qx and qy are sediment transport rates in x and y direction respectively. In the model, no morphological acceleration was applied, thus the morphological time scale is equal to hydrodynamic time scale.

Moreover, to account for the slumping of sandy material from the dune face to the foreshore during storm-induced dune erosion avalanching is included in computation of bed evolution. Avalanching is introduced via the use of a critical bed slope for both the dry and wet area. If the bed exceeds the relevant critical slope it collapses and slides downward (avalanching). To reduce the impact of these landslides the maximum bed level change due to avalanching is limited to 0.05 m/s/m. Which of the two critical slopes is applied to a grid cell is determined by hswitch keyword. hswitch defines the water depth at which is switched from wetslp to dryslp. In the model, critical slopes were defined as 1.0 and 0.2 respectively for dry and wetslope. When this critical slope is exceeded, material is exchanged between the adjacent cells to the amount needed to bring the slope back to the critical slope. P a g e 39 | 67

Furthermore, XBeach allows the user to specify non-erodible structures in the model. This option was utilized to define a non-erodible bottom at the offshore region starting from the offshore bar. This was done to reach and use values of nonlinearity parameters that were optimum for swash zone morphodynamics, without the effect of sediment transport from the bar. The location of non-erodible bottom was specified in an external file that had the same format with bathymetry file. In this file, erodible top layer at the offshore region specified as zero securing a fully non-erodible bathymetry there. The offshore non-erodible bottom was defined sufficiently away from the area of interest so that the clear water scour didn’t affect the results.

4.5 BOUNDARY CONDITIONS ▪ Wave Boundary Conditions In the model, seaward wave boundary conditions were specified as a series of parametric JONSWAP spectra that were defined by significant wave height, peak wave period and mean direction. Then using a random phase model XBeach generated respective random wave time series with a time step of 0.5 s. This process was repeated every hour of computation by using the parametric input for that hour. In the case of 2D computations the lateral boundaries of the wave model were set as Neumann boundaries, which set the longshore gradient to zero.

▪ Boundary Conditions for Shallow Water Equations For the computation of the long waves a weakly reflective boundary condition was applied at the offshore boundary. This type of boundary condition allowed the imposition of wave and flow conditions and specification of time varying water levels at the offshore boundary while letting the waves and currents that were generated within the domain pass through the boundary towards deeper water with minimum reflection. In the model time-varying water level signal was specified at the offshore boundary corresponding to the tide and surge data. At the lateral boundaries, again Neumann conditions were applied, which satisfied a state of local gradient in surface elevation and velocity.

▪ Boundary Conditions for Sediment transport Neumann boundaries were applied on every boundary for sediment transport. This set the cross-boundary gradients in advection-diffusion equation and in bed load transport to zero. Cross-shore profile changes were possible due to cross-shore transport gradients. The offshore boundary was kept far offshore (~600 m offshore from the shoreline), satisfying an undisturbed computation of bed evolution in swash zone.

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5 NUMERICAL MODELING OF CROSS-SHORE PROFILE

5.1 INTRODUCTION In order to answer the research question, different scenarios were explored in a numerical modeling environment and compared with measured in-situ conditions. XBeach was chosen as the numerical modeling tool. It’s most important capability that is related to this research is the option to define spatially varying sediment grain sizes. With this capability, it is possible to represent the variable grain size distribution that was measured on the beach in the model and to create hypothetical grain size distributions to test the difference in beach response under the forcing conditions.

Prior to the scenario testing, the model should be verified and calibrated in order to reach stable and robust parameter settings with which reliable model results could be achieved with good confidence limits. This process starts with the initial set-up of model and verification of default parameter settings. Here a 1D cross-shore profile was build and tested for its response to the observed wave and tide action. Data for the cross-shore profile and accompanying boundary conditions were collected during SABER_Duck Field Campaign (see Chapter 3) are presented in Section 5.2. The subsequent verification is presented in Section 5.3. After the verification study, it was seen that the default settings for the model parameters were not an adequate match to the observed beach response, and that site- specific calibration was necessary in order to get reliable numerical model result.

To facilitate the calibration model parameters were tested for their sensitivity to the model results by exploring the bed-profile response to changes in their assigned values over one tidal cycle. Parameter values were changed one at a time (OAT) keeping all other parameters at their base values. Sensitivity analysis was done using spatially uniform distribution of sediment grain sizes; variable grain size distribution was not introduced yet at this stage. A description of the sensitivity analysis is given in Section 5.4

Next the model was calibrated by comparing the modeled and measured beach response over the time period that had passed between two consecutive bathymetry measurements obtained during the field campaign (see Chapter 3). At the calibration stage, sensitive parameters were modified until reaching an acceptable fit to the measured cross-shore profiles of SABER_Duck as described in Section 5.5. As a final step the measured spatially varying distribution of grain sizes was entered schematically as the initial bed composition.

Subsequently alternative modeling scenarios were defined to test whether the presence of a variable grain size distribution affects the morphodynamic response during storm conditions described in Sections 5.6. This is followed by analysis of model results in Section 5.7.

5.2 MODEL SET-UP AND BOUNDARY CONDITIONS

5.2.1 MODEL DOMAIN, GRID SET-UP AND BATHYMETRY XBeach uses a coordinate system where computational x-axis is oriented perpendicular towards the coast and y-axis is oriented alongshore. The model was set-up as 1D cross-shore

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profile model and Fast 1D was chosen as the grid type. In this grid type, there is a single alongshore grid and the model domain is single gridline.

The initial profile was obtained from an interpolation in a bathymetric survey at Profile line 62 (965m from FRF reference point) and corresponds to pre-storm conditions (Figure 5.1). The initial bathymetry was obtained by combining the LARC5 offshore bathymetry survey data on 14 March 2014 and a CRAB surf zone survey data on 25 March 2014 (Chapter 3). The model domain started from 0 at the offshore boundary and reached to 638m at the onshore boundary reaching the upper swash zone. To discretize the modeled cross-shore profile 320 equidistant grid points were used with a spacing of 2 meters. The erodible sediment layer is pictured beneath the bottom surface with the sediment grain size shown with color coding (Figure 5.1). For the sake of simplicity, the initial sediment layer was defined as a spatially uniform distribution that matched the cross-shore average grain size of 900 µm.

Figure 5.1: Initial Cross-shore bathymetry and erodible sediment layer. 1D profile starts from offshore boundary and extends to upper swash zone. The grain size in the erodible sediment layer beneath the bottom surface is shown in color (color scale in µm). The green color represents the cross-shore average grain size that was equal to 900 µm. The beach slope at the steep swash zone is approximately 1 in 7.5. the vertical coordinates are with respect to NAVD.

5.2.2 WAVES AND TIDES Wave data was taken from FRF data portal (WEB1) from wave gauge AWAC02 at 6M depth and converted to the parametric format that is requested by XBeach with significant wave height, peak wave period, mean direction information for each computational hour. The wave characteristics time series are given in Figure 5.2. Parametric wave spectra input was given in Jonswap#.inp files, where # is the number of consecutive hour after the start of simulation. Then XBeach generated respective random wave time series with a time step of 0,5 s. This process was repeated every hour of computation by using the parametric input

5 Lighter Amphibious Resupply Cargo (LARC) is an Army amphibious vehicle that is used to deploy instruments, support diving activities, collect data, and tow a variety of sensor and survey "sleds". It has the ability to operate on the beach, over shallow shoals, in breaking waves, and offshore. With its Real- Time Kinematic GPS survey system, LARC can collect accurate position data in these environments.

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for that hour. In the model wave angles were defined according to Cartesian convention. The directional grid for short waves and rollers was defined by single directional bin aligned with the shore normal corresponding to the mean wave direction observed during the period of the model computation.

Figure 5.2: Wave characteristics measured by FRF AWAC02 wave gauge during the storm event used in numerical modeling. Time series of significant wave height in Hrms, peak wave period Tp and wave direction θ with respect to shore normal are given for the computation period.

Water level time series data was taken from NOAA website (WEB2) from tide gauge 8651370 Duck, NC and is given in Figure 5.3. Parametric water level input was given in tide.txt file, containing the water level time series with respect to NAVD measured every 6 minutes.

Figure 5.3: Water level time at FRF 8651370 Duck, NC tide gauge between 25 and 27 March 2014.

5.2.3 INITIAL BED COMPOSITION The mechanics of how the initial bed composition is defined was described in Section 4.3. In the current model 10 distinct sediment fractions were defined by using D50 and D90. The D50 and D90 and values used in the description of sediment fractions are given in Table 5.1. Also, the vertical composition of the bed was defined by using 10 layers, thicknesses of which were 2 cm for the top layer and 10 cm each for the variable layer and the bottom layers.

Table 5.1: Sediment grain sizes used in the definition of different sediment fractions Sediment 1 2 3 4 5 6 7 8 9 10 Fraction No: D50 (mm) 1 2 3 4 5 6.5 8 15 20 25 D90 (mm) 2 4 6 8 10 13 16 19 24 30

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5.3 MODEL VERIFICATION Initial modeling effort was done using the default XBeach settings and measured bathymetry and sea state at Duck beach on March 25, 2014 for a 2-day duration in order to verify the suitability of the defaults settings. Model results for the profile response show excessive changes in the bathymetry that were not observed in-situ (Figure 5.4). Especially the erosion of the beach and bar were severely overestimated.

Figure 5.4: Results of the verification run with default XBeach model settings. The grain size in the erodible sediment layer beneath the bottom surface is shown in color (color scale in µm).

One immediate positive result of verification run was the observation of model’s capability in simulating the sediment grain size sorting in the bed bottom. This can be seen in Figure 5.4 in the reorganized sediment deposits at the both sides offshore bar. This capability was later observed in all model runs that followed. However, it should be noted that model’s accuracy in computing sediment sorting is unknown and is outside the scope of this thesis project.

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5.4 SENSITIVITY ANALYSIS After the unsatisfactory results of the verification run, the model settings were altered to represent the physical conditions of Duck beach. To determine which model parameters were of importance for the model calibration a sensitivity analysis was performed. Looking at the results of the verification run and keeping in mind the goal of the project, six model parameters were selected for the sensitivity analysis. These parameters were hmin, hswitch, form, turb, facua and eps respectively. Brief information on these parameters is given in Table 5.2.

At this stage, model runs were made for a relatively short computational time span equal to the duration of one semidiurnal tidal cycle (44700sec=12hr 25min). During the sensitivity analysis, specific parameters were varied once at a time keeping the other parameters at a fixed value. In this way, the differences that occurred were solely caused by the change in the parameter of interest, but potential non-linear interactions between parameters were ignored. The fixed values of the parameters defined the base case for sensitivity analysis and are given in the last column of Table 5.2 in bold characters. Then resulting bed profiles were drawn and compared in order to determine the model’s sensitivity to each parameter. In the following figures of sensitivity analysis (from Figure 5.5 to Figure 5.10) the base case bed profile is shown with a solid blue line. In the same figures the measured initial bathymetry on March 25 was drawn with a dashed black line as reference, and the measured final bathymetry on March 27 was drawn as a solid grey line as an indication of expected erosion/ accretion after 2 days. At the bottom part of the figures, the vertical differences of computed final bathymetries were drawn with respect to the bathymetry of Base Case run. This shows the order of magnitudes of differences between the resultant bathymetries for alternative parameter values. It also shows where on the cross-shore profile the effects of changing values were dominant.

Table 5.2: Parameters that were studied in sensitivity analysis, Base case values are given in bold characters in the last column Assigned values in Name Definition Default value Range sensitivity analysis

Threshold water depth above hmin 0.2 m 0.001 – 1.0 m 1, 0.1, 0.001 which Stokes drift is included

Water depth at which the grid hswitch cell is switched between wetslp 0.1 m 0.01 – 1.0 m 1, 0.1, 0.01 and dryslp

Equilibrium sediment Soulsby_vanRijn and Soulsby_vanRijn, form vanThiel_vanRijn concentration formulation vanThiel_vanRijn vanThiel_vanRijn

Switch to include short wave none, wave_averaged wave_averaged, turb bore_averaged turbulence and bore_averaged bore_averaged

Calibration factor time averaged flows due to both facua 0.1 0 - 1 0.2, 0.5,0.8, 1.0 wave skewness and wave asymmetry

Threshold water depth about eps 0.005 m 0.001 – 0.1 m 0.1, 0.05, 0.005 which cells are considered wet

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▪ Sensitivity parameter: hmin hmin is the threshold water depth above which Stokes drift is included in XBeach. It is used to prevent very strong return flows or high concentrations close to the waterline. The values that were assigned to hmin in the sensitivity analysis were given in Table 5.2. The results of three model runs with hmin equal to 1, 0.1 and 0.001 meters are shown in Figure 5.5. The analysis showed that the model results were sensitive to the value which hmin took. There was a significant increase in the unrealistic erosion within the swash zone with a decreasing value of hmin. As the model matched the observations best with the highest hmin value, hmin=1m was used in the calibration and final stages of modeling.

Figure 5.5: Sensitivity of model to hmin - threshold water depth above which Stokes drift is included. Model simulations were performed with hmin equal to 1, 0.1 and 0.001 meters. The differences between the alternative cases were in order of 1m at their maximum.

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▪ Sensitivity parameter: hswitch hswitch is the water depth at which the grid cell is switched between wetslp and dryslp. Several values were assigned to hswitch during sensitivity analysis from the full value range. The results of three model runs for one tidal cycle with hswitch equal to 1, 0.1 and 0.01 meters are shown in Figure 5.6. Model results were not very sensitivity to hswitch value, model simulations continued with the default value of this parameter, hswitch=0.1m.

Figure 5.6: Sensitivity of model to hswitch - water depth at which the grid cell is switched between wetslp and dryslp. Model simulations were performed with hswitch equal to 1, 0.1 and 0.01 meters respectively. Note that the red line showing the results for hswitch=0.01 is not visible, because results for hswitch=0.01 and hswitch=0.1 were equal. The differences between the alternative cases were in order of 0.5m at their maximum.

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▪ Sensitivity parameter: form form is the formula to calculate the equilibrium sediment concentration (see Section 4.2). There are two options form this formulation, namely Soulsby_vanRijn (form=1) and vanThiel_vanRijn (form=2). The two options were compared in Figure 5.7. Model results showed significant differences in profile evolution especially in the erosion from the crest of offshore bar and the deeper regions on the both sides of the bar. form=2 (the formula of vanThiel_vanRijn) gave more realistic results for the profile evolution, whereas form=1 resulted in unrealistic range of erosion of the offshore bar within a single tidal cycle.

Figure 5.7: Sensitivity of model to form - formula for equilibrium sediment concentration. Model simulations were performed with form equal to 1 (Soulsby_vanRijn formula) and 2 (vanThiel_vanRijn formula) respectively. The differences between the alternative cases were in order of 0.5m at their maximum.

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▪ Sensitivity parameter: turb turb is the switch to include short wave breaking induced turbulence in the sediment transport calculations. The two options available in XBeach for this inclusion are wave- averaged (turb=1) and bore-averaged (turb=2). The comparison of the two is given in Figure 5.8. Model results were found to be sensitive to the value of turb. The default setting, turb=2, i.e. inclusion of short wave turbulence as bore-averaged, resulted in a shoreward shift of the offshore bar crest and a less favorable outcome. However, both values were considered in calibration phase for the possible non-linear interactions between parameters.

Figure 5.8: Sensitivity of model to turb - switch to include short wave turbulence. Model simulations were performed with turb equal to 1 (wave-averaged) and 2 (bore-averaged) respectively. The differences between the alternative cases were in order of 0.5m at their maximum.

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▪ Sensitivity parameter: facua facua is the calibration factor for short-wave averaged sediment transport due to both wave skewness and wave asymmetry. Several values were assigned to facua during sensitivity analysis (see Table 5.2). The results of sensitivity simulations with facua equal to 1, 0.8, 0.5 and 0.1 are shown in Figure 5.9. The cross-shore profile evolution responded strongly to a changing facua value, resulting in a drastic increase in the onshore sediment transport rate for increasing facua, which makes this a key parameter in the model calibration.

Figure 5.9: Sensitivity of model to facua - calibration factor for time averaged flows due to wave skewness and wave asymmetry. Model simulations were performed with facua equal to 1, 0.8, 0.5 and 0.1 respectively. The differences between the alternative cases were in order of 2m at their maximum.

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▪ Sensitivity parameter: eps eps is the threshold water depth at which cells are considered wet or dry. Figure 5.10 is showing the model results for sensitivity simulations with eps equal to 0.1, 0.05 and 0.005 meters. The model results showed sensitivity to the eps value in the erosion-accretion within the swash zone, with an increasing response for decreasing eps values. The investigation of an optimum value for this parameter is treated in more detail in the calibration.

Figure 5.10: Sensitivity of model to eps - threshold water depth about which cells are considered wet. Model simulations were performed with eps equal to 0.1, 0.05 and 0.005 meters respectively. The differences between the alternative cases were in order of 1m at their maximum.

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▪ Results of Sensitivity Analysis Model results were observed to be sensitive to the changes in parameters ‘hmin, form, turb, facua, eps’ while changing the value of ‘hswitch’ didn’t affect the results much. Results of sensitivity analysis are summarized in Table 5.3. Furthermore, an optimum value was directly recognized from the sensitivity analysis study for parameters hmin and form. No further calibration was needed for these parameters and these optimum values were used in the following stages of modeling. Model calibration continued with the remaining sensitive parameters turb, facua and eps.

Table 5.3: Results of sensitivity analysis Name Sensitive? Range Default value Optimum value found? hmin Yes 0.001 – 1.0 m 0.2 m 1 m hswitch No 0.01 – 1.0 m 0.1 m Default was used. Soulsby_vanRijn and form Yes vanThiel_vanRijn vanThiel_vanRijn vanThiel_vanRijn none, wave_averaged turb Yes bore_averaged studied in Calibration and bore_averaged facua Yes 0 - 1 0.1 studied in Calibration eps Yes 0.001 – 0.1 m 0.005 m studied in Calibration

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5.5 CALIBRATION The goal of the calibration study was to find the values for model parameters that would give an optimal computational response in order to use in the final numerical modeling of alternative scenarios. The efforts were focused on the optimization of turb, facua and eps. There were three main differences in the modeling approach of the calibration phase compared to the sensitivity analysis. Firstly, the measured horizontally varying grain size distribution within the swash zone was entered into the model. The nature of this input is explained in Section 5.6.1. Secondly the model was run for a 2-day computational period which was equal to the time between the two in-situ bathymetry measurements. Thirdly, the offshore bar was fixed as a non-erodible layer to eliminate the sediment transport from there affecting the swash zone calibration.

Two cross-shore profiles were used in calibration; the measured bathymetries of Duck beach on March 25th (before storm) and on March 27th (after storm). The March 25 profile provided with the initial bathymetry input. The model was run for 2 days. The resultant cross-shore profile was then compared to that measured in-situ on March 27. Calibration of turb, facua and eps continued until reaching a satisfactory fit to measured cross-shore profile based on visual comparison. The result of the model run with final calibrated settings is shown in Figure 5.11 and the model settings after calibration are given in Table 5.4. These parameter settings were used in the model scenarios discussed next.

Figure 5.11: Model results for 2 day run with calibrated setting. In the calibrated settings, hmin=1m, hswitch=0.1m, form=2, turb=2, eps=0.08 and facua=0.6. The spatial distribution of the mean grain size is plotted in color (units in µm in the color bar). P a g e 53 | 67

Table 5.4: Calibration results Name Optimum value found hmin 1 m hswitch 0.1 m form vanThiel_vanRijn turb bore_averaged facua 0.6 eps 0.08

5.6 MODELING OF ALTERNATIVE SCENARIOS

5.6.1 SCENARIO #1: ORIGINAL SPATIALLY VARYING DISTRIBUTION This is the original scenario where the in-situ measurement data of grain sizes in swash zone was given into the model as input. The original data was collected during SABER_Duck from the core locations on the cross-shore profile located 960 north of FRF reference point. Each sediment core included detailed grain size information of that location. This spatially varying grain size information was first averaged over the horizontal dimension as explained in Section 3.3.2. This gave the variable average grain size data of the core along the vertical dimension. The resultant numerical grain size data used in the model was acquired form Gallagher et al (2014). For the sake of simplicity in input preparation and interpretation of the model results this variability in the vertical was then eliminated by taking the average of the grain sizes in the top 1m sediment core. This final grain size was assigned as the D50 for the whole vertical at that core location in the numerical model. This procedure was repeated for all core locations on the cross-shore, resulting in a D50 value for each location. The D50s for the grid cells in between two consecutive core locations were determined by interpolation. In this way, initial bed composition data consisting every grid cell on the cross- shore profile that was reflecting the measured variability in the horizontal was prepared. This initial bed composition can be seen in the lower depths of bottom layer of Figure 5.11 where the grid cells were not affected by erosion.

This is the scenario for which the model parameters were calibrated to match the measured profile evolution. Therefore, all model parameters are identical to the final calibration run and the result of the model run with spatially varying distribution of grain sizes was shown in Figure 5.11.

5.6.2 SCENARIO #2: SPATIALLY UNIFORM DISTRIBUTION In this scenario, the same grain size data as in the first scenario was used, only this time the fraction of each sediment class was averaged over the swash zone and assigned as the fraction of that sediment class in all grid cells. In this way, a bed composition with spatially uniform distribution was reached while keeping the fractions of the sediment class fractions equal to that of swash zone in the original scenario. The rest of the model parameters were identical to the previous scenario, too. The result of model run with spatially uniform distribution of grain sizes of Scenario #2 is given in Figure 5.12. At the bottom part of the P a g e 54 | 67

figure, the vertical differences of computed final bathymetry were drawn with respect to the bathymetry of the original scenario with measured varying grain size distribution. This shows the order of magnitudes of differences between the resultant bathymetries for uniform and varying grain size distribution in swash zone. It also shows where on the cross-shore profile the effects of changing values were dominant.

Figure 5.12: Model results for initially spatially uniform scenario. Model with calibrated settings was run for 2 days with the spatially uniform distribution of swash zone grains. The spatial distribution of the mean grain size is plotted in color (units in µm in the color bar). The differences between the two scenarios were in order of 0.1m at their maximum.

Foreword for Scenarios number 3, 4, 5:

In traditional coastal (morphodynamics) modeling the bed composition is defined by a spatially uniform distribution of grain sizes around a representative D50. For the fine sandy beaches, common practice is to choose this representative D50 equal to 200 µm or 250 µm. In some practices sediment sample is collected from upper dry beach surface to measure the representative D50, which often results in similar grain size. While this very fine grain sizes fit within the observations of sediment in upper dry beach and at deep offshore sea bottom, observations of bed composition covering full cross-shore point to drastically larger grain sizes in the areas of high hydrodynamic activity, such as swash zone. However, the sampling and the measurement of the sediment grains in the latter requires greater effort and is a practice, nearly exclusive to scientific projects focused on morphodynamics of hydrodynamically active regions. In the following scenarios, the aforementioned common modeling practice of representation of sandy beaches with uniform distribution of very fine grains will be examined. P a g e 55 | 67

5.6.3 SCENARIO #3: BEACH WITH OVERALL FINE SAND The first test scenario of common practice featured a hypothetical bed composition of very fine grains that were uniformly distributed everywhere along the cross-shore. D50 was defined equal to 250 µm. All other model parameters including computation length and hydrodynamic conditions were kept as in original scenario. The model result is shown in Figure 5.13. The bottom part of the figure shows the vertical differences of computed final bathymetry with respect to the bathymetry of the original scenario with measured varying grain size distribution. This shows the order of magnitudes of differences between the resultant bathymetries for the two scenarios. It also shows where on the cross-shore profile the effects of changing values were dominant.

Figure 5.13: Model results for beach with overall fine sand. The spatial distribution of the mean grain size is plotted in color (units in µm in the color bar). The differences between the two scenarios were in order of 0.4m at their maximum.

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5.6.4 SCENARIO #4: FINE SAND BEACH WITH COARSE PATCH AT SHORELINE A hypothetical bed composition was created as in Scenario #3. This time a patch of coarse grains was introduced in a region around shoreline (between x=590m and x=610m) to see the effects of such coarse patch on beach response. D50 was defined equal to 1500 µm in the coarse patch and 250 µm at the rest of the beach. The model result is shown in Figure 5.14. The bottom part of the figure shows the vertical differences of computed final bathymetry with respect to the bathymetry of the original scenario with measured varying grain size distribution. This shows the order of magnitudes of differences between the resultant bathymetries for the two scenarios. It also shows where on the cross-shore profile the effects of changing values were dominant.

Figure 5.14: Model results for fine sand beach with coarse grain patch around shoreline. The spatial distribution of the mean grain size is plotted in color (units in µm in the color bar). The differences between the two scenarios were in order of 0.2m at their maximum.

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5.6.5 SCENARIO #5: FINE SAND BEACH WITH COARSE PATCH AT LOWER SWASH A hypothetical bed composition was created as in Scenario #4. This time the coarse patch was placed at lower swash area (between x=570m and x=590m), incidentally coinciding with the region where the coarsest grain sizes were measured at SABER_Duck. D50 was defined equal to 1500 µm in the coarse patch and 250 µm at the rest of the beach. The model result is shown in Figure 5.15. The bottom part of the figure shows the vertical differences of computed final bathymetry with respect to the bathymetry of the original scenario with measured varying grain size distribution. This shows the order of magnitudes of differences between the resultant bathymetries for the two scenarios. It also shows where on the cross- shore profile the effects of changing values were dominant. Here it is seen that the coarse patch at lower swash completely stabilizes that region.

Figure 5.15: Model results for fine sand beach with coarse grain patch at lower swash area. The spatial distribution of the mean grain size is plotted in color (units in µm in the color bar). The differences between the two scenarios were in order of 0.3m at their maximum.

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5.7 MODEL RESULTS In this section results of modeling effort are given via comparison of alternative scenarios’ final bed profile to that of original scenario and the initial bed profile. The first comparison is made between the results of the first two scenarios, which were using measured swash zone grain sizes. The difference in the model results of these two scenarios can be seen in Figure 5.16 and is solely representing the effect of the uniform distribution of grain sizes instead of spatially varying distribution.

Figure 5.16: Comparison of the computed cross-shore profiles for the first two scenarios that were using measured grain sizes, one with horizontally varying and other with spatially uniform distribution in sediment input. The differences between the two scenarios were in order of 0.1m at their maximum.

The second comparison is made between the original grain size distribution and the three alternative scenarios with the fine sediments, which represent the common numerical modeling practices. The final bathymetries are compared in Figure 5.17. The results show that after only two-day storm event the usage of different representations of bed composition has clear effects on beach response. The scenario with overall fine sands had the largest volume of the sediment displacement in the cross-shore. Whereas, Scenario #4 and Scenario #5 showed the benefit of coarse patch introduction as they locally improved the stability of beach profile and had lower volumes of the sediment displacement compared to overall fine beach scenario.

Having accretive hydrodynamic conditions, the beach response in the original scenario gave the least cross-shore profile change compared to the test case scenarios of the common modeling practice. P a g e 59 | 67

Furthermore, as mention earlier in Section 5.3, model was capable of simulating the sediment grain size sorting. The grain size distributions in the computed final bed compositions showed layering of different grain sizes similar to those that were observed during trench survey and from the core samples. This is a very promising result for further modeling studies including stratigraphy and variable grain size distribution in the bed bottom.

Figure 5.17: Comparison of the computed cross-shore profiles for the alternative scenarios. Original case shows the final bed profile with measured varying grain size distribution. The bottom part of the figure shows the vertical differences of computed final bathymetres with respect to the bathymetry of the original scenario with measured varying grain size distribution. P a g e 60 | 67

6 CONCLUSION The thesis has focused on the determination of the importance of variable grain size distribution in swash zone and the capabilities of numerical modeling in the computation of beach response using variable grain sizes.

This was done firstly by gathering in-situ time series stratigraphy data in the swash zone, the prevailing hydrodynamic conditions and the time-series of the cross-shore bathymetry in a field experiment campaign. The data gathered in SABER_Duck, confirmed a highly variable grain size distribution in the swash zone both vertically and horizontally. Additionally, the two trench survey observations showed the existence of continuous layers of coarse and fine sands comprising the beach stratigraphy.

Secondly, a process-based numerical model, XBeach, was used to simulate the beach response using this experiment data. XBeach was able to represent the beach response using variable grain size in swash zone. During the preliminary modeling activity, validation of the initial model set-up using default parameters failed. After the execution of sensitivity analysis of model parameters and calibration of the sensitive parameters, a good match between computed and measured cross-shore profile evolutions was reached.

Thirdly, the calibrated model settings were used to compute the beach response with hypothetical uniform grain size distribution. Computed beach response for uniform grain size distribution differed from that for the original varying distribution, corroborating the importance of grain size variability in beach response.

Fourthly, three additional hypothetical bed compositions were tested. The model results demonstrated the importance of the accuracy in spatial distribution of varying grain sizes and the accuracy of the representative grain size in numerical modeling of coastal morphodynamics.

Lastly, the grain size distribution in the computed final bed composition showed layering of different grain sizes similar to those that were observed during trench survey and from the core samples, showing that the model was capable of simulating the sediment grain size sorting.

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7 DISCUSSION This chapter discusses observations related to the experiment and modeling. Furthermore, it addresses the areas of improvements which can be used in future endeavors. It follows the same outline as in the preceding chapters of the report.

7.1 EXPERIMENT

7.1.1 EXPERIMENT IN GENERAL SABER_Duck was a pilot experiment campaign in its study area. For future experiment campaigns one major improvement would be to plan ahead and perform different types of measurements parallel to each other. This will provide with a valuable complete time series data. For example, when looking at Table 7.1, one can notice that not all methods are available on every survey date. This generates an incomplete picture which negatively impacts the modeling efforts. In future projects, using complete and accurate data from parallel measurements help to understand and evaluate different aspects of morphological beach evolution.

Table 7.1: survey dates in SABER_Duck for each method

Availability of Survey Data on Dates

Method of Storm event after storm Quality of Data Survey 25/ 26/ 27/ 29/ 30/ 31/ 01/ 02/ 03/ 04/ 28/0 03/ 03/ 03/ 03/ 03/ 03/ 04/ 04/ 04/ 04/ 3/14 14 14 14 14 14 14 14 14 14 14 Swash zone Walking Survey ✗ ✗ ✗ ✗ ✔ ✔ ✔ ✔ ✔ ✗ ✗ bathymetry Depth of Depth of active Disturbance ✗ ✗ ✔ ✔ ✔ ✔ ✔ ✔ ✔ ✗ ✗ layer in swash Measurements zone ✔ Bottom sediment Vibracoring ✔ ✗ ✔ ✔ ✗ ✗ ✗ (2 ✗ ✗ ✗ grain size times) composition Visual observation of undisturbed Trench Survey ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✔ ✔ grain size stratigraphy

The timing of core sampling is another important aspect in acquiring comparable data. It is rewarding to collect the core samples always at the same time of the day. Moreover, if the cores are collected only once per day, preference could be made to perform this at low water, because it will allow the coring equipment to reach deeper parts of lower swash zone and the samples to be taken from this seaward end too. This is also true for walking surveys and depth of disturbance measurements.

7.1.2 WALKING SURVEY The elevation of GPS transmitter should be cared for within the course of measurements. Simply putting it on the backpack could result in wiggles during a measurement by a single person as he walks. When performed by different persons the base elevation would change

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too. Therefore, it is important to place the GPS transmitter at a fixed level on a stick as shown in Figure 3.2 which would provide with more accurate data.

7.1.3 DEPTH OF DISTURBANCE MEASUREMENTS It is beneficial to become informed about the different options of executing this method, it will require different requirements and will therefore generate different data. As each datatype will focus on distinct aspects of swash zone morphodynamics. For example, the measurements in SABER_Duck focused on the depth to which the active layer reached during a full day while some other techniques concentrate on changes during half tidal cycle.

7.1.4 VIBRACORES Compaction in the vibracores was a problem that could not be prevented within the current settings of SABER_Duck. Vibration shakes the sand grains, reorganizing them and causing them to settle in a more organized and compact form. As a result, the sediment layers, while preserved, often become thinner than they naturally are. This compaction is not linear along the core, because the sediment layers have varying compressibility. The amount of time to collect each core varies too, resulting in varying amounts of compaction. Furthermore, compaction might have caused mixing of some layers, expectedly at the top and the bottom and where the two adjacent layers were of distinct grain sizes. For example, in Figure 3.13, day 25.03.2014, top 0-10cm is likely to had been affected by mixing and compaction caused by vibration. Techniques to neutralize this complication were not available. In such circumstances, measures should be taken to keep compaction to a minimum. Especially when numerical modeling efforts with variable grain size distribution go beyond testing the cross-shore profile and aim for accurate modeling of stratigraphy underneath, it is critical to know how to interpret the compaction in a specific core data. In SABER_Duck, trench observations provided with undisturbed stratigraphy to refer to in this consideration. It is also beneficial to discuss the possible scenarios related to compaction with an experienced geologist.

I worked a lot to establish a descriptive illustration of visual core readings. However, for the future, it worth considering more standardized techniques of doing that, which were previously used in scientific papers. This might facilitate comparing information from different publications.

7.2 NUMERICAL MODELING

7.2.1 SITE SPECIFIC CALIBRATION NEED The initial model, which used default parameters, was found to be not adequate, therefore a long effort of sensitivity analysis and calibration was needed. The optimum values of different parameters were observed to be site-specific. This points to the need for better formulation of phenomena relating to these parameters. For instance, ‘facua’ was one of the sensitive parameters that needed calibration. It took the value of 0.6 in this research, while its default value is equal to 0.1. This is a significant and confusing difference, for which the reason is as of yet unclear.

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Various value combinations were tested during calibration of sensitive parameters. During this phase, model results clearly showed non-linear interactions between different parameters. For example, during the sensitivity analysis, the default bore-averaged inclusion of turbulence in calculations gave less favorable results. However, in calibration runs, where values of multiple parameters were altered simultaneously, the default value of ‘turb’ gave the better fit to the measured final profile. Again, neither the reason for the result in sensitivity analysis, nor the one for the calibration was clear. This unclarity in how the different formulations of physical phenomena and their interactions affect the end result, shows that the numerical modeling is a highly empirical, synthetic study area rather than an analytic research domain. This is the inherent feature of numerical modeling, and understanding and formulations improve via dedicated studies and testing of numerical modeling features.

7.2.2 EXPERIMENT DATA REQUIREMENTS At the time of numerical modeling, numerical grain size data for all vibracores was not ready. In order to progress with the modeling, the numerical grain size data, that was presented in Gallagher et al (2014), was used as initial bed composition input for 25 March 2014 in the model. This data was a sample that had earlier been chosen from several cores collected on different dates during SABER_Duck. This fact limited the testing possibilities of numerical modeling.

Numerical stratigraphy data from the same cores on all days of a time series consideration, is a need for accurate numerical modeling analysis. It is also required for assessing whether the model is capable of simulating the changes in the stratigraphy. Without this data, it is not possible to test the accuracy of model computations in detail. For this purpose, we need to be able to compare model results with in-situ time series stratigraphy data. Complete and accurate data from parallel measurements help to understand and evaluate different aspects of morphological beach evolution.

7.3 FURTHER RESEARCH AND DEVELOPMENT SUGGESTIONS To develop a better parameterization, measurements in a controlled environment, as in laboratory experiments, can be considered. Field campaigns provide good and detailed insight into the real situation. However, converting these field observations into numerical models and then drawing meaningful conclusions from these model results, remain extremely difficult because of the many parameters that are involved in the actual situation under consideration.

Field campaigns are definitely useful and are the primary source of information in the understanding of nature. Therefore, a combination of field, laboratory and modeling works would be ideal in the pursuit of improved knowledge on the subject. A good starting point for laboratory tests could be determining a couple of important parameters and carrying out laboratory tests on them in isolated conditions.

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