TobyTucker_Thesis_Final

School of Civil and Environmental Engineering

Faculty of Engineering

The University of New South Wales

Application of 2D models to examine

sand bar recovery at

Narrabeen-Collaroy

by

Tobias Alexander Tucker

Thesis submitted as a requirement for the degree of Bachelor of

Civil Engineering

Submitted: October 2015

Supervisor: Dr. Kristen Splinter

Student ID: z3417449

Application of 2D models to examine sand bar recovery at Narrabeen-Collaroy

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Abstract

During sustained low energy wave conditions sand bars generally propagate

onshore. There has been little research into the onshore propagation of sand

bars in comparison to the quick erosion of sediment offshore. Three models

have been used to predict the movement of sediment in two dimensions as bars

move onshore. The Plant et al. (2006) model applies coupled linear differential

equations to show dependency of sand bar position (x) on its alongshore

linearity (a). The Splinter et al. (2011) model applies more complex sediment

transport equations creating an alternate model linking bar position and

alongshore linearity. The ShoreFor model (Davidson et al., 2013), applied by

Stokes et al. (2015) to bar position, is only dependent upon wave conditions.

Sand bar data for seven recovery periods across a ten year period was

gathered using photometric techniques applied to timex images obtained from

the Argus network. Wave data was obtained from an offshore wave-rider buoy

and converted to the nearshore using the SWAN model. The Plant et al. model

performed the best at predicting bar position with an average correlation

squared (R2) of 0.703 and an average Root-Mean-Square Error (RMSE) of

8.078 m. The ShoreFor model performed the best at predicting bar variability

with an average R2 and an average RMSE of 0.526 and 8.969 m. The ShoreFor

scored similarly to the Plant et al. model for predicting bar position with an

average R2 and an average RMSE of 0.637 and 2.312 m respectively. The

Splinter et al. model did not show significant skill. The success of the ShoreFor

model suggests bar position and variability are not dependent on each other.

This is further supported as the Plant et al. model parameters did not behave as

expected in addition to a lack of skill shown by the Splinter et al. model.


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Acknowledgments

I would like to thank all the people who have helped me put this together. It has

been the biggest project I have ever attempted and I could not have done it

without all the people around me. So thank you to all my friends who have been

with me all through the year and put up with my endless talk of sand bars and

recovery.

To my supervisor Dr. Kristen Splinter I would like to give a massive thank you.

You have always been patient with me and my questions but more importantly

you helped me to understand the problems myself and learn throughout the

whole year.

I would like to thank Matt Phillips and Josh Simmons for all their help. Always

being willing to listen to my questions and let me throw my ideas off them.

Finally I would like to thank my family and my close friends for encouraging me

no matter what, and I would also like to thank God who I could never have done

this without.


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Abbreviations

BBB – Bagnold, Bowen, Bailard energetic model

BSS – Brier Skill Score

FLIP – Filtered Longshore Intensity Profile

GPS – Global Positioning System

LBT – Longshore Bar-Trough

LiDAR – Lighting Detection And Ranging

LTT – Low Tide Terrace

Max – Maximum

MIKE21 – Mike 21 spectral wind-wave model

Min – Minimum

NC – North Carolina

NSW – New South Wales

PDO – Pacific Decadal Oscillation

PHH06 – Plant et al. (2006) model

PIC – Pixel Intensity Clustering

R2 – Correlation Coefficient\

RBB – Rhythmic Bar and Beach

RMS – Root-Mean-Square

RMSE – Root-Mean-Square Error

RTK – Real Time Kinematic


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SBEACH – Storm Induced Beach Change model

SDR15 – Stokes et al. (2015) model

ShoreFor – Shoreline Forecast model

SHP11 – Splinter et al. (2011) model

SOI – Southern Oscillation Index

SWAN – Simulating Waves And Nearshore model

TBR – Transverse Bar and Rip

Timex – Time exposed image

Unibest-TC – Uniform Beach Sediment Transport Time-dependent Cross-shore\

XBeach – eXtreme Beach behavior model


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Notation

�̇� Derivative of the sand bar alongshore variability (m)

𝒂𝒃 Breaker amplitude (degrees)

𝒂𝒐 Reference bar variability (m)

𝒂 Alongshore variable component of the bar position (m)

𝜶𝟏 − 𝜶𝟒 SHP11 free parameters

𝑨 PHH06 model free parameter matrix

𝑩 PHH06 model free parameter matrix

𝜷 Beach/surf zone gradient

𝑪𝑫 Drag coefficient

𝒄𝒇 Friction number

𝑪𝑽 Relative standard deviation

𝒅𝒕𝒓 Maximum daily tide range (m)

∆𝒐 Reference value for sand bar height (m)

𝜹𝒕𝒊𝒅𝒆 Tidal height (m)

𝜺 Efficiency factor

𝝐 Surf-scaling parameter

𝑭 Forcing (N)

Relative influence of wave angle and morphology on 2D currents

𝒈 Acceleration due to gravity (m.s-2)

𝒉𝒙 Water depth (m)

𝑯𝑺 Significant wave height (m)

𝑯𝒃 Breaking wave height (m)

𝑯𝒃 Depth limited wave height (m)

𝑯𝒓𝒎𝒔 Root-mean-square wave height (m)

𝑯𝒙 Breaking wave height (m)

𝒊𝒕⃗⃗ Sediment transport rate (N.s-1)

𝒊𝒃 Immersed weight bed load transport (N.s-1)

𝒊𝒔 Immersed weight suspended transport (N.s-1)


x

𝑰 Pixel intensity rating

𝒂 2D processes influence factor

𝒌𝒚 Alongshore wave number

𝑲𝒔 Dimensionless suspended load coefficient

𝝀𝟏−𝝀𝟐 ShoreFor bar position free parameters

𝝀𝟑 − 𝝀𝟒 ShoreFor bar variability parameters

𝝁 Sediment packing factor

𝒎 Cross-shore bar length coefficient

𝜽𝒙 Shore-normal wave direction (degrees)

𝒇

Friction angle

Memory decay parameter

𝒑𝒅 Input data (m)

𝒑𝒇 Linear best fit model output (m)

𝒑𝒎 Model output (m)

∆𝒑 Estimated error (m)

𝑷 Wave power (W)

𝝆 Density (kg.m-2)

�̂�𝒙𝒙 Cross-shore sediment transport flow (m2d-1)

𝝈 Standard deviation (m)

𝒓 Forcing efficiency factor

𝑺 Spectral density (m2)

𝒔𝒕𝒓 Maximum spring tide range (m)

𝑻𝒐 Mean wave period (s)

𝑻 Wave period (s)

𝒖 Velocity (ms-1)

𝒖𝟎 Wave orbital velocity (ms-1)

𝒖𝒕⃗⃗⃗⃗ Alongshore velocity (ms-1)

𝒖𝒕̅̅ ̅ Mean cross-shore velocity (ms-1)

𝒖�̃� Oscillatory cross-shore velocity (ms-1)

𝑼𝟎 Symmetrical orbital velocity (ms-1)

𝑼𝟏 Perturbation (ms-1)


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�̅̅̅�𝑺 Mean sediment fall velocity (ms-1)

𝝎𝒐 Shoreline elevation coefficient

𝝎𝒕𝒊𝒅𝒆 Tide coefficient

𝝎𝒘𝒂𝒗𝒆 Wave coefficient

𝝎 Radial frequency (s-1)

𝒘 Settling velocity (ms-1)

𝒙 Mean sand bar position offshore (m)

�̇� Derivative of the mean bar position (m)

𝒙𝒃𝒂𝒓 Bar location offshore (m)

𝒙𝒐 Reference bar location offshore (m)

𝜸𝒃 Fractions of waves breaking

𝜸𝒆𝒒 Equilibrium relative wave height

𝒁𝒔𝒉 Shoreline elevation (m)

𝒁𝒕𝒊𝒅𝒆 Tidal elevation (m)

Dimensionless fall velocity


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Contents

Abstract ......................................................................................................................................... ii

Acknowledgments .........................................................................................................................vi

Abbreviations ............................................................................................................................... vii

Notation ........................................................................................................................................ ix

Contents ....................................................................................................................................... xii

Figures ......................................................................................................................................... xiv

Tables .......................................................................................................................................... xvi

Chapter 1 – Introduction ............................................................................................................... 1

1.1 Background.................................................................................................................... 1

1.2 Narrabeen-Collaroy Data Collection ............................................................................. 3

1.3 Problem Statement ....................................................................................................... 3

1.4 Objective ....................................................................................................................... 5

Chapter 2 – Literature Review ...................................................................................................... 6

2.1 Introduction to Morphology Studies ............................................................................. 6

2.2 Morphology Timescales ................................................................................................ 7

2.3 Morphology of Surf Zones ........................................................................................... 10

2.4 Imaging and Measuring Nearshore Morphology ........................................................ 13

2.5 Modelling Sediment Transport ................................................................................... 17

2.5.1 Energetics Models ................................................................................................... 19

2.5.2 PHH06 Model .......................................................................................................... 23

2.5.3 SHP11 Model ........................................................................................................... 24

2.5.4 SDR15 Model ........................................................................................................... 29

2.6 Summary ..................................................................................................................... 31

Chapter 3 – Site Background ....................................................................................................... 33

3.1 Location ....................................................................................................................... 33

3.2 Environmental Setting ................................................................................................. 33

3.3 Wave Conditions ......................................................................................................... 34

3.4 Sediment Properties .................................................................................................... 35

3.5 History ......................................................................................................................... 35

Chapter 4 – Methodology ........................................................................................................... 37


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4.1 Introduction ................................................................................................................ 37

4.2 Defining Recovery Periods .......................................................................................... 37

4.3 Wave Data ................................................................................................................... 39

4.4 Sand Bar Data .............................................................................................................. 40

4.4.1 Image manipulation ................................................................................................ 41

4.4.2 Mean Sand Bar Position .......................................................................................... 46

4.4.3 Sand Bar Variability ................................................................................................. 46

4.5 Model Preparation and Other Data ............................................................................ 47

4.6 Modelling Sand Bar Recovery ..................................................................................... 52

4.6.1 PHH06 Model Calibration ........................................................................................ 52

4.6.2 SHP11 Model Calibration ........................................................................................ 53

4.6.3 ShoreFor Model Calibration .................................................................................... 54

4.7 Model Skill ................................................................................................................... 55

Chapter 5 – Results ..................................................................................................................... 57

5.1 Recovery Period Data .................................................................................................. 57

5.2 Calibration and Data Comparison ............................................................................... 59

5.3 Calibration Skill ............................................................................................................ 64

5.4 Calibration ................................................................................................................... 66

5.5 PHH06 Boundary Conditions ....................................................................................... 67

Chapter 6 – Discussion ................................................................................................................ 69

6.1 Analysis of Results ....................................................................................................... 69

6.2 Alternative Methodologies ......................................................................................... 73

Chapter 7 – Conclusion ............................................................................................................... 79

7.1 Summary ..................................................................................................................... 79

7.2 Future Work ................................................................................................................ 80

Bibliography ................................................................................................................................ 82

Appendix A .................................................................................................................................. 90

Appendix B .................................................................................................................................. 94


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Figures

Figure 1: (Short 1999) Sketches of the six beach states ranging from

dissipative to reflective. .................................................................................... 11

Figure 2: (Figure 3 in Lippmann and Holman 1990) Binary beach state

classification system. A represents reflective beach and cycles through eight

stages to H representing a dissipative beach. .................................................. 15

Figure 3: (Figure 5 in Ranasinghe et al. 2004) Classification of beach state

depending upon surf zone width and filtered longshore profile variance (FLIP).

......................................................................................................................... 17

Figure 4: (Figure 1 in Hoefel & Elgar 2003) The effect of acceleration skewness

on direction of sediment transport. ................................................................... 21

Figure 5: (Figure 2 from Harley et al. 2011) (a) Aerial photo of Collaroy-

Narrabeen Beach. Depth contour lines (at 2.5m intervals), the location of the

Argus cameras and the alongshore coordinate systems used in this study are

also indicated. (b) The beach with respect to the Sydney coastline and the

location of the Sydney wave-rider buoy. (c) Map of Australia. .......................... 33

Figure 6: On the left a timex image taken on 31 March 2005 at 10am. On the

right the same image converted to plan view and greyscale ............................ 41

Figure 7: A straightened timex image. Axes are with respect to Argus co-

ordinates (x is cross-shore and y is longshore) ................................................ 42

Figure 8: The 0.7 meter contour shoreline (red) plotted on the corrected and

cropped timex image ........................................................................................ 44

Figure 9: Left image is before intensity adjustment, right figure is after (with the

shore removed). ............................................................................................... 45

Figure 10: On left is an image with the shore break. On the right is an image

with the shore break removed. Both images have the mean bar position plotted

(red dashed) and the surf zone boundaries (blue). ........................................... 46

Figure 11: The plot of the demeaned de-trended sand bar position (𝒙′) with

respect to the sand bar shape .......................................................................... 47


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Figure 12: Image of incorrect bar position calculated due to anomaly where the

image is cut on bottom left where light is shining off the surface of the water.

The image has the calculated bar position (red dashed) and the surf zone (blue)

overlayed. ......................................................................................................... 48

Figure 13: Missing data from original recovery period 7 (10 August 2014 to 30

November 2014) ............................................................................................... 49

Figure 14: Data has been interpolated (red) to fill in the gaps in the data

obtained from the SWAN corrected wave-rider buoy data (blue) for RMS wave

height ............................................................................................................... 50

Figure 15: On left average bathymetry (red) with linear fit through 0.7m contour.

On right Difference between profile cross section and the linear fit. ................. 51

Figure 16: PHH06 model calibration results .................................................... 61

Figure 17: SHP11 model calibration results .................................................... 62

Figure 18: ShoreFor model calibration results ................................................. 63

Figure 19: PHH06 calibration results with no boundary conditions .................. 68

Figure 20: On the left is a timex image taken on June 9 2005 showing the

effects of the morning sun. On the right is a timex image during the storm on

June 9 2007. ..................................................................................................... 76

Figure 21: Recovery period data for 9 March 2005 to 9 may 2005 .................. 90

Figure 22: Recovery period data for 9 June 2005 to 11 October 2005 ............ 90

Figure 23: Recovery period data for 1 June 2007 to 30 may 2008 .................. 91

Figure 24: Recovery period data for 17 May 2010 to 27 August 2010 ............ 91

Figure 25: Recovery period data for 24 June 2011 to 23 November 2011 ...... 92

Figure 26: Recovery period data for 1 June 2012 to 27 January 2013 ............ 92

Figure 27: Recovery period data for 10 August 2014 to 15 October 2014 ...... 93


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Tables

Table 1: (Table 1 from Harley et al. 2015) History of data acquisition on

Narrabeen-Collaroy beach ............................................................................... 36

Table 2: Recovery period dates and dengths .................................................. 39

Table 3: Key wave data statistics ..................................................................... 58

Table 4: PHH06 skill scores ............................................................................. 64

Table 5: SHP11 skill scores ............................................................................. 65

Table 6: ShoreFor skill scores ......................................................................... 66

Table 7: Relative standard deviations of model parameters ............................ 67

Table 8: Skill of PHH06 with no boundary conditions ...................................... 68

Table 9: PHH06 Parameters ............................................................................ 94

Table 10: PHH06 Parameters no boundary conditions .................................... 94

Table 11: SHP11 Parameters .......................................................................... 95

Table 12: ShoreFor parameters ....................................................................... 95


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Chapter 1 – Introduction

1.1 Background

Beaches are a unique environment that many communities have developed

their lifestyle and culture around. One of the key attributes of beaches is their

irregularity as they undergo constant change. This irregularity is due to the force

from waves breaking along the coastline and the subsequent interaction with

the sand on the beach.

While beach sediment moves as part of a complex system, its movement on

and offshore at beaches has particular patterns. Generally under high wave

energy conditions sand will move offshore. Conversely, under low energy wave

forcing sand will propagate onshore. The offshore and onshore movement of

sediment can be viewed as a cycle of short, high intensity wave conditions that

move sediment offshore (storm events) and longer periods of less energetic

waves corresponding to sand accreting onshore (recovery periods).

Generally the prediction of offshore sediment transport has been well modelled.

There has been a great amount of research that has looked at understanding

the way in which beaches erode during storm events (Johnson et al. 2012;

Harley, Valentini, et al. 2015; Callaghan et al. 2013; Vousdoukas et al. 2012;

Splinter & Palmsten 2012; Ruessink 2005; Plant & Stockdon 2012; Palmsten &

Holman 2012; McCall et al. 2014; McCall et al. 2010). Such models are key to

understanding the impacts of shoreline recession on coastal structures.

Software packages, such as SBEACH and XBeach (Larson & Kraus 1989;

Roelvink et al. 2009) are able to predict the amount of erosion that will affect a

beach front under certain storm conditions. Other models such as Unibest-TC

have been implemented to successfully model the change in sand bar position

due to storms (Walstra 2000; van Rijn et al. 2003).

In comparison to the modelling of offshore sediment transport there are

significantly less models able to accurately predict the onshore transport of


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sediment. Some erosion models have been applied to describe the recovery

process but with limited success (Pender & Karunarathna 2013). The majority of

sediment transport models looking at the recovery of beaches are one

dimensional lacking a longshore component so that they are limited and only

function in the cross shore direction (Plant et al. 1999; Henderson & Allen 2004;

Bailard 1981; Gallagher et al. 1998; Thornton & Humiston 1996). These models

assume an alongshore linear bar position and do not take into account two

dimensional bathymetry. This is contradictory to observations of beaches where

it is noticed that, as a bar moves onshore after a storm, it transitions from a

linear form to an undulating form before reattaching to the beach (Wright &

Short 1984; Lippmann & Holman 1990). Wright and Short (1984) were able to

classify the morphology of numerous beaches as they transformed through

these phases.

In 2006 Plant et al. developed a two dimensional sediment transport model that

was able to predict to the pattern of sand bar recovery in response to storm

events (herein referred to as PHH06). This model linked the distance of the bar

offshore with how alongshore linear the sand bar was. In what was a particularly

simple model the results showed a clear link between the sand bar position and

its linearity.

Splinter et al. (2011) furthered the work of Plant et al. (2006) adding sediment

transport equations to the model to improve the accuracy of the model (herein

referred to as SHP11). After the PHH06 model yielded unsatisfactory results at

Palm Beach in New South Wales, Australia (Splinter 2009) the SHHP11 model

was able to show some level of skill at predicting the two dimensionality of the

beach profile when the model depended upon a large number of physical

parameters. Again this model showed that both the bar position and its

variability were intrinsically linked.

In a recent paper by Stokes et al. (2015) the concept of disequilibrium stress,

following the equilibrium shoreline model of Davidson et al. (2013), was used to

formulate an additional model that was able to predict the two dimensionality of

a beach (herein referred to as SDR15). In this paper the PHH06 model was


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used for comparison on a double bar, macro-tidal system. Analysis performed

indicated that the SDR15 model performed superiorly at this new site. The

success of this model questioned the dependency that the distance a sandbar

is offshore has on the alongshore variability of the bar. This dependency which

is heavily relied upon in both the PHH06 and SHP11 models described

previously.

The PHH06, SHP11 and SDR15 models will be discussed in more detail in

Chapter 2.

1.2 Narrabeen-Collaroy Data Collection

Narrabeen-Collaroy is a 3.6 kilometer long sandy beach embayment located on

Sydney’s Northern Beaches in Australia. Over the past forty years the

embayment has been extensively monitored using different techniques such as

the emery method, real-time kinematic (RTK) GPS profile surveys, surface

mapping using RTK GPS mounted all-terrain-vehicles, light detection and

ranging, the deployment of unmanned aerial vehicles as well as Argus coastal

imaging (Harley et al. 2015).

Despite the large amount of data collected using various techniques over such

a long period of time, the use of a program to take Argus images and detect

sand bar positions and their alongshore variability has never been applied to

Narrabeen-Collaroy. The use of this technique has been shown to be both a

simple and useful method to obtain data, particularly for offshore bar

features(Lippmann & Holman 1989). Using sand bar data obtained from Argus

images at Narrabeen-Collaroy the skill of two dimensional models in predicting

recovery of sand bar systems can be measured.

1.3 Problem Statement

Currently there are multiple models that have been developed to simulate the

onshore migration of sand bars during a recovery period. The PHH06 model

intrinsically links sand bar position and its variability using a set of

parametrisations. Similarly the SHP11 model links the sand bar position and its


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alongshore variability by incorporating a large number of physical parameters

that describe the longshore and cross-shore bar processes. Using an alternate

theory the SDR15 model incorporates the ShoreFor model (Davidson et al.

2013) with adjustments for bar variability to show that sand bars are behavioural

in nature and their distance offshore and their variability are not intrinsically

linked.

While many different models have been developed to describe sediment

transport there has not been one definitive modelling technique that has been

developed. The three models mentioned previously each show significant skill

in predicting both sand bar position and variability during recovery periods at

different beaches. They all have different approaches to this problem however.

It is unclear if parametric models such as PHH06, process based models such

as SHP11 or behavioural models such as the ShoreFor model are most apt to

simulate sand bars during recovery periods. By comparing these models the

underlying assumptions behind them will be tested to determine which

hypotheses are more aligned with the conditions observed in nature at

Narrabeen-Collaroy.

In order to compare the different approaches to modelling sand bar recovery the

models must all be applied to a singular data set. To avoid bias this data set

should be from a beach separate to that which each model was originally

developed at. Using data obtained from Argus images and applying a technique

that uses light intensities to position the sand bar this new data set will be

obtained from Narrabeen-Collaroy. The models developed by Plant et al.

(2006), Splinter et al. (2011) represent the parametric and process based

approaches to modelling sand bar location and variability. Following the

behavioural approach of Stokes et al. (2015) for the first time the ShoreFor

model (Davidson et al. 2013) will be used to model sand bar location. It will also

be used in a similar method to the SPR15 model to simulate sand bar

alongshore variability. By comparing all three models using the same data set

the strengths and weaknesses of each, with respect to each other, will be

exposed.


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1.4 Objective

The aim of this thesis will be to take all three modelling approaches and apply

them to Narrabeen-Collaroy beach located on Sydney’s Northern Beaches. For

the first time the use of Argus imaging techniques, implemented

computationally, will be used to determine sand bar position and variability at

Narrabeen-Collaroy. Using a range of comparison methods the models skill will

be compared and evaluated. This research will assess which modelling

approach most accurately captures the behaviour of sand bars during a

recovery period.

The results of this the research conducted in this thesis will be threefold. First it

will provide new insight into the most accurate methods for modelling two

dimensional sand bar migration. Secondly it will determine if each model

translates well to a beach other than the one it was developed at. Finally it will

implement new techniques in order to determine sand bar location at

Narrabeen-Collaroy.

This thesis will be broken into the following sections. In Chapter 2 the literature

on modelling methods as well as recovery of beaches will be investigated. In

Chapter 3 and Chapter 4 there will be a site description and the methodology

for applying the models to Narrabeen-Collaroy will be outlined. Chapter 5 will

describe the results of the model’s application to Narrabeen-Collaroy. In

Chapter 6 the results will be discussed and finally a conclusion will be

presented in Chapter 7 .


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Chapter 2 – Literature Review

2.1 Introduction to Morphology Studies

Recovery is only one aspect of change in morphology of the shore zone. It is

therefore beneficial to have a basic understanding of the erosion forces that

create the morphology prior to recovery. There has been a large amount of

research into the erosion of beaches. This section will outline briefly the forces

associated with the formation of sand bars as well as the mechanisms and

forcing that leads to a beach being eroded. It is these forces, which act during

erosion events, that generally transport sediment offshore and into sand bars.

The less energetic conditions preceding a storm will then lead to the recovery of

sediment onshore.

There has been a considerable amount of research that has focused on the

quick erosion of beaches due to storm events. McKenzie (1958) acknowledged

how important rip-channels were in understanding the evolution of beaches. He

studied the pattern of rip-channels on Sydney’s beaches acknowledging that

they affected the sediment transport in the surf-zone. He found that the seaward

drainage of water was responsible in the creation of channels in the surf-zone

that affected the breaking of waves. This initial work on understanding beach

morphology led to further studies.

Thornton and Humiston (1996) broke down sand bar generation into two key

schools of thought, breakpoint mechanisms and infragravity waves. The

breakpoint mechanism is described by Dyhr-Nielsen and Sorensen (1970)

where forces transporting sediment offshore grow into an in equilibrium with

forces pulling sediment onshore creating a sand bar at the breakpoint.

Alternatively the infragravity wave theory is the idea that wave energy is

reflected off the beach and propagates out seaward (Herbers et al. 1995).

Thornton and Humiston (1996) summarised how at specific locations where

infragravity waves converge with onshore waves, sand bars can be generated.


7

Short and Wright (1981) concluded that it was the magnitude in the variation of

the wave climate that was the biggest factor effecting the level of erosion on a

beach. In their paper they stated that the level of erosion is dependent upon the

state of the beach before a storm develops. They noted that on steep beaches,

which moderate to long swells cut away at, the beach had a majority of its

sediment accreted on the shore. Alternatively for longer and flatter beaches

Short and Wright found that it was steep but low energy local seas from wind

generated waves that caused the most erosion.

With increased research on erosion studies focused on the recovery after

erosion events began to emerge. Concepts developed for the offshore

transportation of sediment were also able to be applied to the accretion of sand

onshore. High energy erosion events are often short lived. Once an erosion

event has passed, waves decrease and a beach will experience its more typical

lower energy forcing conditions. Under these circumstances the profile of the

beach will begin to recover as sediment accretes onshore. This process can

take weeks to years and during extreme events sand is lost beyond the surf

zone so there will never be significant forcing to bring a beach back to its

original state (Short & Wright 1981). Nevertheless to an extent there will always

be some form of recovery after these large energy conditions.

2.2 Morphology Timescales

Through wave climates originating from the north around to the south there is

considerable daily and monthly variation as well as seasonal and other longer

term variations in wave height and direction at Narrabeen-Collaroy (Short &

Trembanis 2004). Before qualitatively investigating beach morphology it is worth

understanding the role that the climate with daily, monthly, seasonal and inter-

annual patterns play in determining the current state of a beaches. Different

factors varying from weather patterns to the wave climate have the ability to

affect the nearshore morphology of a beach.

There are numerous forces that act upon a shoreline and are involved in

transporting sediment on a daily basis. Waves directly apply forces to the


8

bathymetry while the tides determine what level of bathymetry the waves can

affect. Additionally, there is also set up due to both storm surge and wind that

depend upon the prevailing conditions (Foster et al. 1974).

While the tide cycles diurnally on the New South Wales coast, as the result of

the forces of the moon acting upon the ocean, there is an additional monthly

cycle that the tides follow where during a month larger tides are associated with

a full moon and lower associated with a new moon. Clarke et al. (1984)

observed that the monthly lunar cycle of the tides affected the sediment on

Coledale, New South Wales, shifting sand from the berm crest to the mid tide

zone. They found this cycle occurred over a 28 day period corresponding to the

lunar cycle.

In addition to their findings on erosion, Short and Wright (1981) found that at

Narrabeen-Collaroy during February and March that large swells generated

from tropical cyclones resulted in the development of large and intense rip

channels which help to contribute to moderate erosion in comparison to smaller

waves that are generally associated with sand accreting on the beach. They

linked weather patterns to the erosion that occurred on their study site.

Throughout the year Narrabeen-Collaroy beach follows a general pattern

eroding in late summer and winter due to high waves forming a bar offshore and

in the remainder of the year the beach recovers with sediment returning

onshore(Short & Wright 1981). The beach clearly shows a tendency to erode or

recover depending upon what the season is. Wright (1979) noticed this on

another site on the East Australian coast where southern and south-easterly

waves associated with winter possess a lot more energy than the waves

associated with summer. The effects that seasons play on beach morphology

has additionally been studied at other locations confirming this phenomenon

(Masselink & Pattiaratchi 2001).

When studying Surfers Paradise, a double sandbar system located at the

northern end of the Gold Coast in Queensland, Australia, Ruessink et al. (2009)

found that there was a strong correlation to sand bar movement and the

different seasons of the year. Using time exposed (timex) images captured by


9

four Argus cameras they found sand-bars generally migrated offshore in higher

energy winter periods. Conversely they found it was the lower energy summer

wave conditions that brought the sand-bars closer inshore. In addition to this

they also found that in double sandbar systems there was a tendency for outer

bars to have a long term offshore propensity on the inter-annul timescale and

inner bars to have a more sporadic offshore migration.

Along with these trends there have been a significant number of observations of

inter-annual and inter-decadal patterns spanning across a number of years.

Short and Trembanis (2004) noticed long term changes in the variation of wave

size and direction due to the Southern Oscillation Index (SOI) and Pacific

Decadal Oscillation (PDO). The SOI is the large scale atmospheric pattern

present over the Indian and Pacific oceans and has two extremes, El Niño and

La Niña (Phinn & Hastings 1992). El Niño events are generally associated with

high pressure atmospheric conditions close to Australia and La Niña events are

the converse. Wave data during La Niña events were found to indicate that

during these times there is a relative increase in wave power across the eastern

Australian coast (Phinn & Hastings 1992; Shand et al. 2011). The PDO

describes the inter-decadal pattern of the climate in the Pacific. The key

differences between it and the SOI is that rather than lasting from six to

eighteen months the PDO can last twenty to thirty years. The PDO effects are

most readily seen in the mid-latitudes and secondary effects seen in the tropics,

opposite to the SOI. Finally the causes for the PDO are unknown compared to

the well understood SOI (Mantua & Hare 2002).

Recently another large factor has started to impact on the coastline system, the

constantly changing conditions due climate change (Nielsen & Adamantidis

2007; Mariani et al. 2012). The consequences of the mean sea level rising have

been the focus of a large amount of research in recent years. It has been

determined that coastal development will now need to start considering the

effects of sea level rise (Walsh et al. 2004). In addition to this a significant

amount of research needs to be conducted on the effects that the rising sea

level will have on the overall climate. Hemer et al. (2007) found that anomalies


10

associated with the wind in the southern ocean had a large impact on the

variability of wave climate in that region and stressed the need for further

research on the effects of climate change.

2.3 Morphology of Surf Zones

The nearshore morphology of beaches is very irregular. This is due to the large

number of varying forces, as previously described, that are exerting energy on

the shore at any one time. There have been numerous studies that have tried to

capture the patterns of this variability in an understandable model. In Australia

there are 15 different beach types (Short 2006). These beaches vary in

steepness, sediment size and rip formation in addition to having geological

structures such as rocks or marine reefs that form part of the beach. Various

behavioural models have been developed that explain different

morphodynamics beach states. Wright and Short (1984) developed one of the

classic models comprising of six different beach states used to describe the

nearshore bathymetry. These states are dissipative, longshore bar-trough

(LBT), rhythmic bar and beach (RBB), transverse bar and rip (TBR), low tide

terrace (LTT) and reflective, as can be seen in Figure 1. This model

incorporated a dimensionless fall velocity parameter () as shown in equation

(1) where 𝐻𝑏 is the breaking wave height, �̅�𝑠 is the mean sediment fall velocity

and 𝑇 is the wave period.

=𝐻𝑏

�̅�𝑆𝑇 (1)


11

Figure 1: (Short 1999) Sketches of the six beach states ranging from

dissipative to reflective.

Intuitively the sediment fall velocity will depend on the beach sediment grain

size while the other factors will depend upon wave conditions. In this model

there are two end states, reflective and dissipative. When 1 a beach is

reflective meaning that the wave energy is in essence reflected out to sea and


12

not exerting a force on the beach. This state is synonymous with beaches that

have a large slope with a large grain size and mild wave conditions. When

6 a beach is dissipative. This is where all the energy of the wave is lost due to

interaction with the sea floor as the wave propagates toward the shoreline. This

is the opposite of a reflective beach in that it is generally associated with small

beach slopes, small grain sizes, larger waves, large surf zones and one to

multiple offshore sandbars. Effectively no energy reaches the shoreline. When 1

< < 6 a beach will be in an intermediate condition between these reflective

and dissipative states and will exhibit behaviours as such. As seen in equation

(1) the breaker height will have a large effect on what state the beach is in. If a

beach is naturally reflective an increase in the wave height will shift the beach

toward the dissipative side of the spectrum. The same can be said for a

dissipative beach where the usual swell conditions are decreased. On

dissipative beaches the swash zone will generally be much larger as the waves

take less energy to move up a mild slope on the beach. Again reflective

beaches are the opposite with steep slopes reflecting wave energy. The

extremity of the reflective state can be seen where 𝐻𝑏 = 0 resulting in no swash

zone as the shore will be constant (assuming tidal and other such variations can

be neglected). Due to this it is generally true that dissipative beaches have a

much larger beach width than reflective beaches with the same grain size.

Wright and Short also developed a descriptive surf-scaling parameter that is

shown in equation (2). This equation uses breaker amplitude (𝑎𝑏) and radial

frequency (𝜔), expressed in terms of period (𝑇) shown in equation (3), along

with the acceleration due to gravity (𝑔) and beach/surf zone gradient (tan𝛽) to

determine whether a beach is reflective or dissipative (Wright & Short, 1984).

This then defines what state a beach is in, determined by the beach slope along

with the wave conditions in a quantitative manner showing the difference

between reflective and dissipative beaches with respect to shape in particular.

This equation can be used to readily quantify existing beach states determining

if they are reflective, dissipative or in-between. Reflective beaches are when ϵ <

1 and dissipative beaches are when ϵ > 2.5.


13

𝜖 =𝑎𝑏𝜔

2

(𝑔 tan2 𝛽) (2)

𝜔 =2𝜋

𝑇 (3)

The effect of storms on the beach morphology is quite dramatic. Through

changing wave heights, physical models have been able to recreate the

processes transforming beaches between the reflective and dissipative states

(Michallet et al. 2013). In particular this study showed that storms drive sand

offshore, and also that stationary waves force the morphology of the beach into

equilibrium. This is consistent with equation (1) in that it is the wave conditions

that are changing the morphology of a beach with a constant sediment type.

Extrapolating this theory, it can then be shown that generally storm events will

result in offshore sediment transport or bar migration. The higher wave height

(𝐻𝑏) associated with storm conditions will increase the dimensionless fall

velocity (). This will result in the shifting of the beach state from the more

reflective states to a more dissipative state. Likewise wave conditions with less

energy would result in sand bars migrating onshore. The sand in dissipative

conditions will primarily be stored below mean sea level in offshore sandbars

while the reflective conditions will lead to sand being stored above mean sea

level in the upper beach berms and on the dunes (Wright & Short 1984).

2.4 Imaging and Measuring Nearshore Morphology

Understanding the nearshore morphology and processes involved in sustaining

it is critical for the long term survival of the beach. As the morphology moves

from a TBR or LTT to a dissipative condition due to the large waves associated

with a storm event the majority of sand above the sea will be transported

offshore. Many different methods are available to study the shoreline and the

erosion due to storms as well as the recovery afterwards. One method that can

be employed to study the coast is digital imagery. Using various


14

photogrammetry techniques images of the beach can manipulated in such a

way that they can be objectively used to gather data.

Timex images are created by averaging each pixel of a range of images taken

of the same frame every second over a period of time. Using timex images has

been shown to be the most efficient way to use a camera system to isolate

regions of breaking and wave breaking on a beach (Holman et al. 2003).

Holman et al. observed that a 10 minute timex was the optimum time to

observe the wave groups common in oceanic environments. This is due to the

nature by which waves propagate to the shore in groups over an average time

interval.

Using this technique of averaging images taken every second over a ten minute

interval to create a timex image, investigations were done on Duck, North

Carolina, to determine the effectiveness of this form of data (Lippmann &

Holman 1989). The timex image shows the area of dissipation of breaking

waves. The results of the study found that the position of a sandbar can be

calculated to accuracy of less than 5% of the distance that the sandbar is

offshore with correct camera positioning. The amount of foam created from a

dissipating wave could induce up to 35% error. This study showed the value

that a timex image contribute to the ability of gathering data about beach

morphology. It was also a significant discovery because of the ease by which

timex images can be taken. It removes any need for actual surveying or even to

enter the water to record the bar position.

Lippmann and Holman furthered their research in 1990 developing a subjective

classification system to define the state of a beach using a ten minute long

timex image. In their method they broke up the LBT and RBB states, as

described by Wright & Short (1984), into two (each), creating eight different

possible classification categories. They then used a binary system to classify

which state a timex image depicted. This can be seen in Figure 2 where A is a

reflective beach and then each letter represents alphabetically a new state (the

effect that gradually increasing 𝐻𝑏 in equation (1) would have on a beach with

constant sediment size and wave period) until H is reached, which is a


15

dissipative beach. Lippmann and Holman (1990) found when they tested sixty

images on nine individuals over sixty percent of people always agreed on the

consensus bar type. Conversely less than twenty percent of people agreed on

any bar type other than the consensus thus proving that their classification

system was fairly robust. Using this system enabled them to effectively classify

different beach states enabling the calculations of the probability of each beach

state occurring on their studied beach; Duck, North Carolina. While generally a

useful classification system, this method is a fairly laborious task consuming a

lot of time.

Figure 2: (Figure 3 in Lippmann and Holman 1990) Binary beach state classification system. A represents reflective beach and cycles through eight

stages to H representing a dissipative beach.

With empirical relationships between wave height and beach profile developed

an objective way to study beach morphology was developed using timex

images of waves breaking on the beach shore (Ranasinghe et al. 2004). This

method was able to combine an objective way of studying beach morphology

with numerical modelling. In their methodology they reverted back to the six

states as describe by Wright and Short (1984). The four intermediate states


16

were then classified depending upon different shoreline properties. Using the

fact that RBB and TBR states are generally more longshore variable,

Ranasinghe et al. (2004) determined that if an image possessed a higher

variation in intensity they could split these two categories. In addition to this they

took the theory presented by Wright and Short (1984) that the surf zone width

decreases from LBT to LTT. Ranasinghe et al. (2004) were able to find both the

a cross-shore limit that represented where the waves began to break as well as

a cross-shore contour representing where the shoreline was using the

differences in intensities (in the cross-shore direction). The area between these

two lines was classified as the surf zone. A filtered longshore intensity profile

(FLIP) was then taken of the shore zone and when compared to the shore zone

width and a beach state was able to be classified. Generally TBR states had the

highest intensity and lowest surf zone width transitioning through the RBB state

to a LBT state which had the lowest intensity and highest surf zone width. LTT

generally had a low intensity and low surf zone width. An example of these

classifications applied by Ranasinghe et al. for Palm Beach, Sydney, Australia

is mapped in Figure 3. When this system was compared to a visual

identification system similar to the one proposed by Lippmann and Holman

(1990) the two systems aligned over 90% of the time. This new way of studying

timex images could determine the variability of bar morphology without the

human subjectivity that had previously been involved. This was able to add a

new level of confidence to the theories being observed about beach behaviour,

sediment transport and bar migration as well as allowing for the processing of

large amounts of data quickly and efficiently.


17

Figure 3: (Figure 5 in Ranasinghe et al. 2004) Classification of beach state depending upon surf zone width and filtered longshore profile variance (FLIP).

2.5 Modelling Sediment Transport

There are two different categories of models that have been developed to

determine beach bathymetry. The first type is parametric models, such as that

created by Wright and Short (1984) relating breaker conditions to the sediment

fall velocity, that offer a simplified view of what is normally a complex nearshore

system (Splinter et al. 2011). These parametric models offering a simple

behavioural view of sediment transport are able to clearly explain the

morphology of the bathymetry on beaches.

The second type of model is an energetics model which is a lot more complex

and includes the relationship that sand particles have moving both along the

sea bed or moving through the currents where the sand particles are

suspended (Bailard 1981). In general these models try to understand the key

processes involved in sediment transport in order to better predict its

movement.

In some instances these models can cross over. Splinter et al. (2011) created a

model of the two dimensional sandbar position of a beach that incorporated

aspects of both a parametric and energetics based models. This model has


18

been criticised in that combining the parametric model with terms from an

energetics based model an unnecessary complexity was created in relation to

net gain achieved in modelling ability (Stokes et al. 2015). As such it can be

seen that research still needs to be conducted to verify and improve on existing

models to understand the best methods of modelling the transport of sediments

in the shore zone. There has already been a considerable amount of work

however.

With such a great number of factors affecting the coastline it is unsurprising that

recovery of beaches happens in varying timescales. Plant et al. (1999)

developed a simple heuristic equilibrium based model that was able to

determine, linearly, the inter-annual sand bar response to annual wave forcing.

Using bi-weekly bathymetry data a simple model predicting the interaction of

wave height and bar response could be developed. The model assumed that

the alongshore-averaged sand bar height migrates to an equilibrium point which

was found to coincide with the ‘breakpoint’ of waves. The result of the model

was that 80% of the observed alongshore-averaged bar position was predicted.

This model was applied to inter-annual bar migrations that were forced by

weekly to seasonally varying wave conditions and was able to explain the inter-

annual cross-shore migration of sandbars. It suggested that sandbars migrate

towards equilibrium, confirming their hypotheses. While the model worked well

when compared against 16 years of sandbar data at Duck, North Carolina, for

sandbars driven by annual variability in forcing it was unable to explain more

short term sand bar migration which was observed. Ruessink et al. (2009) found

the Plant et al. (1999) model correctly portrayed a sub-seasonal relationship

between the sandbar migration rate in comparison to wave height that

corresponded to data obtained from the Gold Coast, Australia. Additionally,

Pape et al. (2007) found that linear models (such as Plant et al. (1999)) were

unable to predict long term (over forty days) sand bar migration when compared

to non-linear models.


19

Since these observations there has been significant success in modelling the

timescales of sandbar migration on both short and long term scales in two

dimensions (Splinter et al. 2011; Stokes et al. 2015).

2.5.1 Energetics Models

In 1980 Bowen proposed an energetics model of the on and offshore transport

of sediment that aimed to be consistent with the forces of waves, currents and

gravity. Bowen based his work on the model developed by (Bagnold 1963)

which can be seen in equations (4) and (5). 𝑖𝑠 is the immersed weight

suspended transport and 𝑖𝑏 is the immersed weight bed load transport with 휀

the efficiency, 𝐶𝐷 the drag coefficient, 𝜌 the density of water, 𝑤 the settling

velocity, 𝛽 the slope, tan the friction angle of the sediment and 𝑢 the velocity

of the flow with the positive distance seawards as shown in equation (6) where

𝑈1 is a perturbation and 𝑈0 is the symmetrical orbital velocity. This relationship

between 𝑈1 and 𝑈0 underlines the main assumption that orbital velocity is the

major velocity component.

𝑖𝑠 =휀𝑠𝐶𝐷𝜌𝑢3|𝑢|

𝑤 − 𝑢𝛽 (4)

𝑖𝑏 =휀𝑏𝐶𝐷𝜌𝑢3

tan − 𝑢𝛽/|𝑢| (5)

𝑢 = 𝑈0 + 𝑈1, 𝑤ℎ𝑒𝑟𝑒 𝑈0 ≫ 𝑈1 (6)

Bowen (1980) saw two major problems with this model. First it depended upon

the immediate flow conditions and secondly the theory could not describe the

initiation of flow conditions, only fully developed flow.

With this knowledge Bowen (1980) developed a new model derived from the

Bagnold (1963) equations and was able to provide results that did align with the

hypothesis that under certain wave conditions sediment transport (𝑖𝑠 and 𝑖𝑏)


20

would equal zero when the wave conditions reach an equilibrium. In this model

the suspended load term was expressed to the first order as in equation (7).

Here 𝑢1 is the mean flow, 𝑢𝑜 is the wave orbital velocity and 𝛾 =𝛽

𝑤.

𝑖�̅� =휀𝑏𝐶𝐷𝜌

𝑤[16

3𝜋𝑢1𝑢𝑜

3 + 𝛾𝑢05

16

15𝜋] (7)

To further the research of Bowen (1980), in 1981 Bailard focused on

determining the significance of the two components of sediment transport, bed

load and suspended load. Like Bowen (1980), he found that the equations

should not be dependent upon the instantaneous velocity of the current. In

addition to this Bailard hypothesised that the equations should incorporate a

dependency on the slope. As such a new model for the on and offshore

sediment transport rate ⟨𝑖𝑡⃗⃗ ⟩ was created. This can be seen in equation (8)

where 휀𝑏 is the fraction of the energy dissipation rate spent transporting bed

load and 𝑣 is the velocity alongshore. Note that in this expression Bailard

ignored the net suspended transport as he determined this was negligible in

comparison to the bed load transport.

⟨𝑙𝑡⃗⃗ ⟩ =

𝜌𝐶𝑓휀𝑏

tan [⟨|𝑢𝑡⃗⃗ ⃗|2𝑢𝑡⃗⃗ ⃗⟩ −

tan𝛽

tan ⟨|𝑢𝑡⃗⃗ ⃗|3⟩𝑙]

+ 𝜌𝐶𝑓

휀𝑠

𝑊[⟨|𝑢𝑡⃗⃗ ⃗|3𝑢𝑡⃗⃗ ⃗⟩ −

휀𝑠

𝑊tan𝛽 ⟨|𝑢𝑡⃗⃗ ⃗|5⟩𝑙]

(8)

These sets of equations developed by Bagnold (1963), Bowen (1980) and

Bailard (1981) are generally known as the BBB energetics model. The BBB

energetics model for sediment transport were initially developed for steady flow

over smooth river beds (Bailard 1981). It has been found that this model applies

with significant accuracy to qualitatively predict the offshore sand bar migration

especially when incorporating cross-shore varying fall velocity (Gallagher et al.

1998). In their model Gallagher et al. (1998) assuming that longshore sediment

transport flux was negligible in effect to the cross-shore sediment transport

(such that there is conservation of mass in the cross shore direction) and that

the beach slope was negligible, applied the Bailard (1981) equation to find


21

cross-shore flow of sediment (𝑄𝑥) as in equation (9). Here the mean and

oscillatory components of cross-shore velocity are 𝑢𝑡̅̅̅ and 𝑢�̃� respectively.

𝑄𝑥 =

𝜌𝑤𝐶𝑓휀𝑏

(𝑝𝑠 − 𝑝𝑤)tan [⟨|𝑢𝑡⃗⃗ ⃗|2𝑢�̃�⟩ + ⟨|𝑢𝑡⃗⃗ ⃗|2𝑢𝑡̅̅̅⟩ −

tan𝛽

tan ⟨|𝑢𝑡⃗⃗ ⃗|3⟩]

+𝜌𝑤𝐶𝑓휀𝑠

(𝑝𝑠 − 𝑝𝑤)𝑊[⟨|𝑢𝑡⃗⃗ ⃗|3𝑢�̃�⟩ + ⟨|𝑢𝑡⃗⃗ ⃗|3𝑢𝑡̅̅̅⟩ −

휀𝑠

𝑊tan𝛽 ⟨|𝑢𝑡⃗⃗ ⃗|5⟩𝑙]

(9)

Gallagher et al. (1998) found that while this model was able to accurately

predict the shoreward migration of sediment it was unable to model the

behaviour of sand accreting onshore. They hypothesised onshore sediment

transport system was not predicted as the model did not incorporate fluid

accretion or phase lags between sediment and sea water.

Elgar et al. (2001) furthered this work successfully demonstrating (using field

observations from Duck, North Carolina) that onshore bar migration was a

function of the cross-shore gradients of fluid acceleration and fluid velocities.

With this concept Hoefel and Elgar (2003) developed an energetics based

sediment transport model that incorporated the acceleration skewness of

difference between the magnitude of acceleration at the shoreward and

seaward faces of the wave. They hypothesised that this acceleration skewness

determined if sediment transport was on or offshore as shown in Figure 4. The

results of incorporating acceleration skewness improved both the offshore and

onshore skill of modelling sediment transport. This shows the importance of

having the wave components in calculating sediment transport.

Figure 4: (Figure 1 in Hoefel & Elgar 2003) The effect of acceleration skewness on direction of sediment transport.


22

In 2004 Henderson and Allen developed an alternative energetics model that

was able to predict both on and offshore sediment transport. Based on a similar

theory to Hoefel and Elgar (2003) it was hypothesised and proven true that

sediment transport is both a function of wave velocities and sediment motion in

the boundary layer. This model neglected the effects of bedload sediment

transport suggesting that this and other processes, such as gravity driven

sediment transport and turbulence from waves, may be able to improve model

skill if included.

These studies were able to show that net offshore bar migration was driven by

strong undertow associated with storm conditions, while net onshore bar

migration was associated with more weaker gradients associated with fluid

acceleration (Elgar et al. 2001). Thus, using energetics models the complete

mechanisms for both onshore and offshore bar migration was able to be shown.

It must be taken into account that the complexity involved in these energetics

models seems to be ever increasing, in particular for predicting the mechanisms

for onshore bar migration. Since these models were first proposed, further

discoveries about onshore migration have been made. When studying a double

sand bar system in the Gold Coast Australia using cross-wavelet analysis it was

found that under continued low energy conditions the inner bar would propagate

onshore due to the forces associated with the outer bar variability (Ruessink et

al. 2007). Cross-wavelet analysis is applied by allocating a power term to a

discrete section of a sand bar. This term can then be monitored to determine

the changes in sandbar variability over a time series (Ruessink et al. 2007;

Maraun & Kurths 2004; Torrence & Compo 1998). Ruessink et al. (2007)

concluded that further research in this field of numerical modelling will enable

new discoveries from the forces of coupled sand bar systems on individual sand

bars and their movements. Due to the high complexity involved in energetics

models the biggest challenge in their implementation can often be the

computing power needed.


23

2.5.2 PHH06 Model

Using a parametric equation a simple model incorporating alongshore mean

sand bar position and alongshore sand bar variability was hypothesised (Plant

et al. 2006). This can be seen in equation (10) where �̇� is the derivative of the

mean bar position with respect to time and �̇� is the derivative of the sand bar

alongshore variability with respect to time. In order to calibrate the model first a

data set for the mean bar position and its alongshore variability were found.

Using remote sensing techniques bar position was calculated as the mean

distance away from a datum on the beach. From this the bar variability was

calculated as the root mean variance in a band of the alongshore Fourier

decomposition of the bar position data. The coefficients to the matrices were

then calibrated using linear regression. Once calibrated, the model was

successful in showing a sand bar position that macroscopically orbits a time

varying equilibrium position.

[�̇��̇�] = [

𝐴11 𝐴12

𝐴21 𝐴22] [

𝑥𝑎] + [

𝐵11 𝐵12

𝐵21 𝐵22] [

1𝐻𝑟𝑚𝑠

2 ] (10)

In equation (10) 𝑥 is the alongshore mean bar position at a time step and 𝑎 is

alongshore variable component of the bar position, again at a specific time step.

These two parameters are intrinsically linked by matrix A so that they ultimately

depend on each other. The diagonal terms in the A matrix (A11 and A22)

describe the equilibrium conditions of the model. If these terms are both

negative the other terms in the A matrix will not affect the stability of the system

given that they have an opposite sign. Matrix B takes into account the linear

response of the system to forcing due to the wave height in addition to having a

constant that relates to the zero mean values of 𝑥 and 𝛼. The second columns

in matrix B (B12 and B22) describe how the wave height affects the model. This

model macroscopically shows the relationships between the bar location and its

variability and does not include any terms relating to the bar formation, length of

the bars, fluid dynamics or sediment transport over the system.


24

The formation of this model provided three key conclusions. It showed that the

bar position and variability of sand bars are predictable despite the changing

wave conditions constantly experienced. Secondly it showed that the feedback

between the bar position and its alongshore variability is significantly important.

Finally it showed that the bar position is a function of the wave height which

supports the breakpoint hypothesis that was suggested by Plant et al. (1999).

2.5.3 SHP11 Model

Upon application of the PHH06 parametric model to Palm Beach, NSW,

Australia, Splinter (2009) found that while the model showed clear links

between bar position and variability it lacked accuracy when applied to more

complex systems.

To accommodate this Splinter et al. (2011) introduced the principles of

sediment transport in a set of dynamically coupled equations for the rate of bar

migration (�̇�) with respect to time and rate of change of the bar variability (�̇�)

with respect to time. These equations are shown in equations (11) and (12).

�̇� = 𝛼1𝑎 (�̂�𝑥𝑥

𝑥𝑥𝑜

𝜇∆𝑜𝑒𝑚𝛽𝑥)(𝛾𝑏 − 𝑎𝛾𝑒𝑞) (11)

The rate of bar migration is defined using the conservation of mass with

alongshore and cross shore dependency where 𝜇 is the sediment packing factor

and ∆𝑜 is a reference value for bar height at reference location 𝑥𝑜 . 𝑥

𝑥𝑜 and 𝑒𝑚𝛽𝑥

represent the linear variation of the surf zone width and cross-shore bar length

variation respectively (𝑥 is the distance of the sandbar crest position offshore, 𝛽

is the beach slope and 𝑚 is a cross-shore bar length coefficient taken from

Ruessink et al. (2003)). The remaining terms represent the two dimensional

sediment transport rate, derived from the cross-shore sediment transport rate

�̂�𝑥𝑥 in equation (14) when it is multiplied with the factor 𝑎 as described in

equation (13). (𝛾𝑏 − 𝑎𝛾𝑒𝑞) is derived from the variation in velocity (due to

breaking waves in shallow water contributing to undertow) in comparison to an


25

equilibrium term for the amount of waves breaking (𝛾𝑒𝑞), again factored into two

dimensions with the term 𝑎. Essentially this term describes the condition of

when on and offshore sediment transport is at equilibrium. Depending on the

fraction of waves breaking (𝛾𝑏, see equation (17)) the sand bar will be either

propagating on or offshore.

�̇� = 𝛼3

𝑎

𝑎𝑜(

�̂�𝑥𝑥

𝑥𝑐

𝑥𝑜𝜇∆𝑜𝑒𝑚𝛽𝑥

)[𝑇

𝑇𝑜(1 −

3𝑎

𝑥𝑐) − 𝛼4

𝛾𝑏

] (12)

Similar to the rate of bar migration the rate of bar variability change (equation

(12)) is dependent upon the conservation of mass as well as sediment

transport, the linear variation of the surf zone and the variation in the cross-

shore bar length; as described previously. The bar variability (𝑎) divided by a

reference bar variability (𝑎𝑜) models instability. The period (𝑇) and mean wave

period (𝑇𝑜) describe the timescale of growth in sand bar variability, (1 −3𝑎

𝑥)

describes the limit of the variability due to the shoreline and 𝛾𝑏

describes the

effects of the size and direction of the waves. The term is a function of the

shallow water Reynolds number which relies upon the wave friction number (𝑐𝑓)

and the alongshore wave number (𝑘𝑦). It is taken from Wilson (2009) and used

to describe the effects of wave angle on bar variability. When a beach

experiences waves parallel to the shoreline bars tend to decrease in variability

as they are flattened by the forcing of the waves. Similarly waves coming

perpendicular to the shoreline tend to force an increase in bar variability. This

theory is supported by Contardo and Symonds (2015) who observed that

oblique angled moderate waves generated by local sea breezes resulted in less

variable bars. The sediment fall velocity (, as in equation (1)) describes the

effect of large waves on the variability. In general under large wave conditions it

pushes the bar offshore and creating a flatter bar as discussed previously. 𝛾𝑏

describes the fractions of waves breaking and is shown in equation (17).


26

𝑎 = 1 + 𝛼2

𝑎

𝑥 (𝛽 −∆𝑜

𝑥𝑜)𝑏

𝐻𝑥

𝐻𝑏 (13)

Equation (13) is a factor that describes how two dimensional a sand bar is. The

𝑎 term is used to transform the cross-shore sediment transport processes into

a two-dimensional process (in both the cross and alongshore directions). It is

added to the rate of sandbar migration on two assumptions that both the

sediment transport rate (�̂�𝑥𝑥𝑐, see equation (14)) and the equilibrium wave

height (𝛾𝑒𝑞) are dependent upon the sand bar variability. 𝑎

𝑥 describes how the

surf zone variability is assumed to scale with the surf zone width. (𝛽 −∆𝑜

𝑥𝑜)

describes the variance in the water above a bar depending on its proximity to

the shoreline. The 𝑏 term is used to describe the percentage of waves breaking.

It is a function of the water depth (ℎ𝑥) and tidal height (𝛿𝑡𝑖𝑑𝑒). It works so that if

there is no breaking 𝑏 = 0 meaning there is no transport of sediment. Finally the

ratio of breaking wave height (𝐻𝑥) over the depth limited wave height (𝐻𝑏) is

used to describe how waves breaking offshore of the bar effect the variability

much less than waves breaking at the bar (at the bar 𝐻𝑥

𝐻𝑏~1). In equations (11),

(12) and (13) the alpha terms are dimensionless free parameters for model

calibration.

Splinter et al. (2011) parametrised the BBB cross shore sedimentation rates to

form equation (14) where �̂�𝑥𝑥 represents the cross-shore suspended sediment

transport rate.

�̂�𝑥𝑥=

3

5𝜋𝐾𝑠𝑏

𝐻𝑥

ℎ𝑥

3

ℎ𝑥𝑐√𝑔ℎ𝑥 cos 𝜃𝑥 (14)

This equation is derived from the model presented by Bailard (1981) (see

equation(8)). Bed load is neglected as it is assumed that it is small in

comparison to suspended load. Since at the crest of a sandbar there will be no

slope tan 𝛽 = 0. The velocity component is separated into an averaged cross-


27

shore current and a wave orbital velocity both multiplied by the mean velocity

cubed. It is assumed the wave orbital velocity can be neglected. The mean

velocity is taken from Bowen (1980) (see equation (7)). The average cross-

shore current is defined by Svendsen (1984) as having a Stokes drift and

breaking wave component. Assuming the Stokes drift component is negligible

this can be used with the mean velocity from Bowen (1980) and other factors

from Bailard (1981) to calculate �̂�𝑥𝑥 as in equation (14).

The dimensionless suspended load coefficient describing sediment mass (𝐾𝑠) is

defined in equation (15) where 𝜌𝑤 and 𝜌𝑠 are the densities of the water and

sediment respectively, 𝐶𝐷 is the drag coefficient and 𝜖𝑠 is the suspended load

efficiency factor. It is essentially a function of the sediment particle properties.

𝐾𝑠 =𝜌𝑤

(𝜌𝑠 − 𝜌𝑤)𝐶𝐷𝜖𝑠 (15)

The relative wave height at the bar crest is represented by dividing the wave

height modelled at the bar crest (𝐻𝑥) by the depth at the bar crest (ℎ𝑥, derived in

equation (16)).

ℎ𝑥 = 𝑥 (𝛽 −∆𝑜

𝑥𝑜) (16)

The dimensionless fall velocity () is has been explained previously (se

equation (1)). The wave celerity is a function of acceleration due to gravity (𝑔)

the along with the depth at the bar crest (ℎ𝑥). Finally the wave angle with

respect to shore-normal (𝜃) is incorporated into the cross shore sediment

transport rate.

Equation (17) shows how the breaking relative wave height (𝛾𝑏) is evaluated. It

describes the relationship between the breaker height (𝐻𝑏) and the depth at the

bar crest (ℎ𝑥). This relationship describes the relative force a wave will make on

a bar determining the amount of sediment that will be transported. As the depth

increases the impact of the wave will decrease. Similarly as the wave height

decreases the impact of the wave will decrease.


28

𝛾𝑏 =𝐻𝑏

ℎ𝑥 (17)

The model was tested on Palm Beach in Sydney, Australia. Similar to the

method used by Plant et al. (2006) the mean sand bar position offshore was

found using daily timex images of Palm beach and at different cross sections

finding where the most intense light was. This intense light corresponded with

the sand bar location. Using the breakpoint hypothesis (Plant et al. 1999) the

location of white bubbles from breaking waves was used to find the sand bar

position. The mean bar position was then defined as the distance from a

defined shoreline. The bar variability was calculated using a similar method as

Plant et al. (2006) taking the root mean variance in a particular band from a

Fourier decomposition of sand bar data that has been demeaned with an

intensity profile added to it. Wave data was taken from a wave-rider buoy and

converted to nearshore using hindcasting. The model was then run using a

fourth order Runge-Kutta scheme.

A global set of parameters was calculated for the storms in addition to individual

parameters for each storm. These parameters were found by fitting a weighted

nonlinear regression to the data. The parameters that were calculated for

individual storms only slightly increased the models performance. There was

significant variance in these parameters, which suggested that despite the large

number of physical processes incorporated in this model there are still some

missing that would be required for true global parameters. This highlights the

complex systems that are trying to be captured in the recovery process.

The model was tested using two different scenarios. An uncoupled model

defined where equations (11) and (12) were not dynamically coupled. A coupled

model, with this dependence, was also run where both the bar position and bar

variability were intrinsically linked, following the hypothesis by Plant et al.

(2006). The coupled model performed best in the majority of events with


29

increased skill measured in terms of correlation squared, root mean square

error, brier skill and relative bias.

Using energetics based sediment transport equations this new model explained

both that sediment transport is non-linearly dependent upon waves breaking

over the bar and that two dimensional had morphology influence on bar

migration rates. The results showed that including the two dimensional terms

significantly increased the models accuracy. It also correctly predicted 49% of

the variance in the sandbar position and 41% of the variance in the alongshore

variable morphology.

This provided an alternative model to the PHH06 model that again suggested

the link between bar position and bar variability.

2.5.4 SDR15 Model

Recently, Stokes et al. (2015) proposed the use of an equilibrium formulation

derived for cross-shore shoreline migration, known as the ShoreFor model

(Davidson et al. 2013), to study the intertidal two-dimensionality of beaches.

Stokes et al. argued that process based models such as the SHP11 model were

unable to accurately describe large scale beach changes and that behavioural

models would be better suited to the task.

Stokes et al. (2015) disregarded the dynamic coupling of bar position and bar

variability instead applying a modified version of the ShoreFor model to

determine the two dimensional intertidal variability of bathymetry at a macro-

tidal beach. They hypothesised that alongshore variability is dependent upon

wave power in addition to the sediment fall velocity. This formulation can be

found in the modified ShoreFor model found in equation (18).

�̇� = 𝜆3 + 𝜆4(𝐹+ + 𝑟𝐹−) (18)

Forcing (𝐹) is described in equation (19). The disequilibrium stress (∆) is

defined by Wright et al. (1985) and is the deviation of the instantaneous

sediment fall velocity (, equation (1)) away from an equilibrium sediment fall


30

velocity (𝑒𝑞). Wright et al. hypothesised that the rate beach states changed

was dependent upon the size and direction of this disequilibrium stress. Forcing

is a function of this disequilibrium stress which has been normalised by its

standard deviation (𝜎∆). This will control the direction of the beach state

change. The magnitude of the change will then be controlled by the square root

of the wave power (𝑃) and the 𝜆4 parameter. Due to the model being used at a

macro-tidal beach Stokes et al. (2015) included a tidal term with the maximum

daily tide range (𝑑𝑡𝑟) being divided by the maximum spring tide range (𝑠𝑡𝑟). It

was found that at the location this model was being implemented at the low

spring tide corresponded rip currents formed that produced a maximum amount

of sediment transport. The introduction of the tidal terms meant the function was

weighted so that power is maximised during the spring tide where it is

approximately twice as big as the power during the neap tide.

Since different physical processes cause increasing and decreasing three

dimensionality Stokes et al. (2015) implemented a positive and negative forcing

term where 𝐹−is taken when > 𝑒𝑞 and 𝐹+ when < 𝑒𝑞. The term 𝑟

describes the ratio between the positive and negative forcing terms and is

calculated from wave characteristics. It is essentially the efficiency of the

negative disequilibria to alter the two dimensional nature of the beach and is

defined in equation (20).

𝑟 = |∑ �̂�𝑖

+𝑛𝑖=0

∑ �̂�𝑖−𝑛

𝑖=0

| (20)

The equilibrium sediment fall velocity (𝑒𝑞) is defined in equation (21). It is

highly dependent upon a free memory decay parameter () and is also a

function of the antecedent sediment fall velocity. The memory decay parameter

is varied from 1 to 1000 and the case that yields the maximum correlation

squared of the equilibrium sediment fall velocity term is chosen. This decay

𝐹 = [𝑃0.5𝑑𝑡𝑟

𝑠𝑡𝑟]

∆

𝜎∆ (19)


31

parameter () is equal to the number of days (𝑡) it takes the equilibrium

sediment fall velocity to drop 10%.

𝑒𝑞 = [∑10−

𝑡

2

𝑡=1

]

−1

∑𝑡10−

𝑡

2

𝑡=1

(21)

In order to determine the skill of the SDR15 model at predicting alongshore

variability it was compared the PHH06 model. Both models parameters

(𝜆3, 𝜆4, 𝐴 𝑎𝑛𝑑 𝐵) were calibrated to Perranporth, a beach located in the

Northwest of Cornwall, in the United Kingdom using a least squares regression

method (the decay parameter () was calibrated as outlined previously).

Perranporth is a macro-tidal beach with a double sand bar system. The inner

and outer sand bars were calibrated separately. 5.5 years of bar data was

gathered using an Argus video camera. Other parameters were found using an

RTK GPS system mounted on an all-terrain-vehicle in addition to a wave-rider

buoy.

This model was able to successfully perform to a greater degree of accuracy

than the PHH06 model explaining 42% of variability in the outer bar and 61% of

variability in the inner bar system. This model has only been tested under cross-

shore orientated wave power however and has not been verified for alongshore

wave power. The results were significant however as they suggest that the bar

position and bar variability are not dependent upon each other as hypothesised

by Plant et al. (2006).

2.6 Summary

In summary the use of Argus images has been found to be a reliable way to

remotely survey beaches and determine both bar position and variability. In

addition there have been numerous attempts at modelling the process of sand

bar recovery through different beach states after a storm. Plant et al. (2006)

developed a model that relied heavily upon free parameters that intrinsically

linked bar position and bar variability. Splinter et al. (2011) used the same

concept of linking bar position and bar variability however used a large number


32

of physical parameters to describe their relationship. Stokes et al. (2015)

hypothesised that there was actually no inherent link between the bar position

and bar variability instead applying Wright et al.'s (1985) concept of sediment

fall velocities disequilibrium stress using the ShoreFor model (Davidson et al.

2013), modified for alongshore variability.

In the next chapter a site description of Narrabeen-Collaroy will be presented.

Following this the methodology used to take the PHH06 model, SHP11 model

and the ShoreFor model (following the concepts presented by Stokes et al.

(2015) suggesting that beach bathymetry is behavioural) and calibrate all three

to Narrabeen-Collaroy will be explained.


33

Chapter 3 – Site Background

3.1 Location

Narrabeen-Collaroy beach is located on Sydney’s Northern Beaches in NSW,

Australia. It is a 3.6 kilometer long beach located approximately 20 kilometers

north of Sydney’s harbor (Harley et al. 2011). This location can be seen in

Figure 5.

Figure 5: (Figure 2 from Harley et al. 2011) (a) Aerial photo of Collaroy-Narrabeen Beach. Depth contour lines (at 2.5m intervals), the location of the Argus cameras and the alongshore coordinate systems used in this study are

also indicated. (b) The beach with respect to the Sydney coastline and the location of the Sydney wave-rider buoy. (c) Map of Australia.

3.2 Environmental Setting

The wave dominated beach faces east and is protected on the south end by the

36 meter high Long Reef Headland. It connects with the 20 meter high

Narrabeen Head at the north end. The beach has approximately 17 rip channels

that increase in intensity toward the northern end of the beach (Short 2007). In


34

addition to this the beach is embayed on the southern side (Harley & Turner

2007).

There is a lagoon that flows out to sea on the northern end of Narrabeen-

Collaroy. It has a 2 kilometer squared surface area and flows through a 2

kilometer long 150 meter wide channel to where it reaches the beach. The

entrance has been known to close up (Morris & Turner 2010). A particularly

strong rip channel is known to be associated with the entrance of the lagoon

(Short 2007).

3.3 Wave Conditions

Narrabeen-Collaroy experiences day to day wave conditions averaging from 1

to 1.5 meters in height (Short 2007). Deepwater waves generally come from the

south east and have an average period of approximately 10 seconds. Waves

tend to increase above a 3m significant wave height 5 percent of the time

(Phillips et al. 2015).

While the beach is protected to both the north and south by large headlands it is

notable that due to the length of the beach that any protection which would be

provided by the headlands is negligible unless the right conditions are

presented. Since waves are generally from the south east this generally leaves

the northern end of the beach particularly exposed to erosion.

The beach has a semi diurnal tide that has an average maximum of 1.3 meters

and an average minimum of 0.7 meters. (Short 2007; Wright 1979). These

conditions affect the transport of sediment along the Narrabeen-Collaroy

shoreline on a daily basis.

In 1981 Short and Wright were able to class the major wave climate at

Narrabeen-Collaroy into four seasonal climate events. These included year

round cyclones passing through the Tasman Sea generating south-east swell.

Tropical cyclones off the New South Wales coast producing east and south-east

waves between May and August. Tropical cyclones of south Queensland and

northern New South Wales producing north-easterly and easterly swells from


35

February to March and finally sea breezes from December to March producing

waves from the northeast. These findings show that the wave climate also has a

significant dependence upon seasonal conditions at Narrabeen-Collaroy.

3.4 Sediment Properties

The beach is made up of 0.3 millimeter fine to medium sized quarts particles

with roughly 30% carbonate (Harley et al. 2011). Narrabeen-Collaroy has a

natural state varying from TBR in the north to LTT in the south (Short 2007).

Short observed that since the beach neither sits at the two extreme dissipative

and reflective conditions it is likely to shift under differing wave conditions

The sediment from the lagoon is medium sized quartz/carbonate particles

approximately 0.4mm. There is little interaction between the sediment in the

lagoon and that on the beach however sediment from the lagoon has been

known to be used to nourish the southern end of the beach (Morris & Turner

2010; M. D. Harley et al. 2011)

Studies on alongshore sediment transport have found that the coastline is

comprised of cells containing different sediment characteristics (Sanderson &

Eliot 1999). As a result of this the type of sediment at any particular beach

would be generally unchanging. With a constant sediment type and hence a

constant fall velocity, the morphology of surf zones is solely dependent upon the

breaker height and wave period. Since Narrabeen-Collaroy has a mean sized

sediment comprised of quartz and carbonate (Harley et al. 2011) it is the wave

conditions in association with the other cyclic variations and weather patterns

that will change the morphology of the shoreline.

3.5 History

There have been several significantly large storms that have affected the

coastline on eastern New South Wales. Three significant storms well known for

their damage include the 1974 ‘Sygna Storm’, the 1997 ‘Mothers Day Storm’

and the 2008 ‘Pasha Bulker Storm’ (Shand et al. 2011). Some of the damage

due to the ‘Sygna Storm’ includes destruction of dunes at the lagoons entrance,


36

damage to roads and buildings, severe dune erosion and the need for

emergency rock wall construction to protect residential buildings on the

shoreline (Foster et al. 1974).

Narrabeen-Collaroy has a highly developed shoreline and is subject to a long

history of coastal erosion issues due to development located within the active

coastal zone. Costs of damage to this coastline due to erosion have the

potential to be extremely significant. This includes significant costs could be

associated with sand nourishment due to sand being taken offshore during

storm events (Hennecke et al. 2004). Due to the fact the coastline along this

stretch of beach is highly developed however, there is an even greater risk to

property. Erosion of the dune could threaten the foundation of many buildings.

In the past forty years there has been significant investigated of the beach

profile at Narrabeen-Collaroy. This includes a large variety of methodologies

and data acquisition techniques. A summary of these methods was outlined by

Harley, et al. (2015) and can be seen in Table 1.

Table 1: (Table 1 from Harley et al. 2015) History of data acquisition on Narrabeen-Collaroy beach


37

Chapter 4 – Methodology

4.1 Introduction

In order to accurately determine the effectiveness of the PHH06, SHP11 and

ShoreFor models at modelling the mean sand bar position offshore and its

alongshore variability a reliable data set needed to be gathered to calibrate and

compare each model against. Wave data was taken from the Sydney wave-

rider buoy. Sand bar data was gathered using a method similar to that

employed by Splinter et al. (2011). All other data was taken from either literature

or other techniques detailed later in this chapter. Using a set of MATLAB codes

the three models were able to be calibrated. The resulting outputs were then

compared against each other using various criteria to determine each models

skill at replicating the observed conditions. These steps are outlined in detail in

the following chapter.

4.2 Defining Recovery Periods

In a recent paper, Phillips et al. (2015) mapped out a set of ten recovery periods

spanning from 2004 until 2014 to measure the accretion of sand onshore at

Narrabeen-Collaroy. These periods were based upon key storm erosion events,

measured in terms of beach width decrease, followed by periods of recovery,

measured by beach width increase. Using this data set as a basis seven key

periods were chosen.

The start of the period was defined by a storm event. Many different

characteristics such as wave height, frequency of waves and wave duration can

be used to determine what a storm is defined as. Using a peaks over threshold

analyses Shand et al. (2011) used two different criteria to define a storm. They

defined a storm as either when the significant wave height is greater than 3

meters or when the significant wave height is greater than 2 meters for duration

of 3 days or more.


38

For the purpose of this thesis the definition presented by Shand et al. (2011) will

be used. Using this definition as a minimum will ensure that there is a criteria

that distinguishes between every day sediment transport and what would be

considered a storm event. In many cases the storm events studied exceeded

the criteria here.

Sand bar data was collected for a small period prior to the storm so that the

models could be tested in their ability to reproduce the effects during storm

periods; simulating a bar move offshore and become alongshore linear.

The length of the recovery period was determined by one of two factors. If a

sandbar had moved substantially onshore and a significant storm event

occurred that caused sand bars to move offshore, resetting the recovery

process, the period was defined up until this storm event. If a sand bar migrated

onshore completely resulting in a reflective beach state the recovery period was

terminated while the beach remained in this state. This was done as it was

observed that once a bar had attached forming a reflective beach often a

second bar would form offshore and begin to move onshore starting a second

recovery event. The exception to this condition was if second or subsequent

recovery events also migrated onshore completely it was included in the period.

In each case the recovery period resulted in a net increase in the beach width in

comparison to directly after the storm.

Determining the end of a recovery period was a subjective process. Argus timex

images were individually viewed to determine whether a beach had reached the

end of its recovery period (either when a new storm occurred or a new sand bar

began to form offshore). In cases where a storm event occurred before a sand

bar had substantially moved onshore the data set spanned the storm event.

The seven key periods chosen are outlined in Table 2.


39

Table 2: Recovery period dates and lengths

Period Date Length (days)

1 9 March 2005 – 9 May 2005 92

2 9 June 2005 – 11 October 2005 124

3 1 June 2007 – 30 May 2008 364

4 17 May 2010 – 27 August 2010 102

5 24 June 2011 – 23 November 2011 152

6 1 June 2012 – 27 January 2013 240

7 10 August 2014 – 15 October 2014 66

4.3 Wave Data

Since 1974 the New South Wales government established a network of wave-

rider buoys along the New South Wales coastline. This network includes a

directional wave-rider buoy located approximately 11 kilometres off the coast of

Sydney in 92 meters of water (Shand et al. 2011). This buoy records the

offshore wave height, wave period and wave direction.

Once offshore wave data has been gathered, using the wave-rider buoy, it then

needs to be converted into its nearshore equivalent. As waves come closer to

the shoreline they interact with headlands and the sea floor changing their

properties. For this reason the near shore equivalent needs to be calculated

from the offshore wave records. This is done using a numerical model know as

SWAN (Simulating Waves at Nearshore) (Booij et al. 1999). This model is

driven by boundary conditions and local winds. The models solutions agree with

both field and laboratory testing.

From SWAN, when the model was applied to Narrabeen-Collaroy beach, a four

dimensional lookup table was created to easily convert a total of 1573 discrete

offshore wave parameters (wave height, wave period and wave direction) to

nearshore wave parameters by linear interpolation. Using this table the

nearshore wave characteristics are able to be easily determined for the

conditions at Narrabeen-Collaroy. A MATLAB script was developed (Kearney

2013) and used to transform the offshore wave properties obtained from the


40

wave-rider buoy to nearshore wave properties at the 10 meter depth contour off

of Narrabeen-Collaroy.

The SHP11 model requires the shore-normal wave angle as an input

parameter. The wave bearing provided by the SWAN corrected wave-rider buoy

data needed to be converted so that it could be implemented in the model. The

beach co-ordinates, along the section from which data was taken, were

converted to eastings and northings using the log-spiral method outlined by

Harley and Turner (2007). The average gradient of the eastings and northings

was then found with respect to north. From this value it was found that 79.1933°

needed to be subtracted from the wave bearing to find the shore-normal

direction. Note this correction was performed on the nearshore wave data.

4.4 Sand Bar Data

In order to determine the sand bar characteristics at Narrabeen-Collaroy the

Argus camera system was used to find the mean sand bar position and its

alongshore variability. Due to the necessary computing involved a time series

spanning the entire data set was not practical to obtain. Instead the approach

was taken based off that of Splinter et al. (2011) where a data was found for

individual storm events and their subsequent recovery periods. There are five

cameras located on a building overlooking Narrabeen-Collaroy (this location

can be seen in Figure 5). One camera covering a 600 meter section of the

beach (camera 5 covering from 2600 to 2000 in Argus co-ordinates) was used

to analyse the surf zone morphology. From this camera ten minute timex

images were used to obtain data.

Using images as a data source has the difficulty in that images are only record

at specific moments or time periods. For example the ten minute timex images

at Narrabeen-Collaroy are obtained hourly. If images are taken at different tides

the rise or fall in the sea level can affect the sand bar location.

To solve this issue the images that occurred closest to the mid-tide were used.

These images did not always correspond with the exact mid-tide due to the fact


41

timex images are taken on hourly intervals. The scale of this error was

considered negligible in comparison to other error sources.

Using MATLAB a program was developed that calculated the mean sand bar

position and sand bar variability from these ten minute timex images. The

program cycled through all the available mid-tide images available for the given

recovery period. The program then performed various manipulations to the

timex image in order to find the mean sand bar position offshore and its

variability. This is outlined in the following sections.

4.4.1 Image manipulation

The raw timex images from the Argus cameras at Narrabeen-Collaroy did not

lend to easy interpretation by computer programs. As a result the timex image

taken by the camera needed to be manipulated in order to study further. In

order to better quantify sandbar characteristics it is beneficial to take a bird’s

eye view of the beach. The geometric location of the camera was used along

with its focal length, which had been previously calibrated, to correct of the

timex image into a bird’s eye view (Holland et al. 1997). This enables the scale

of the beach and shoreline to be fitted to an axis and allows for better

interpretation of the bar properties. During this process code is also used to

convert the image into black and white (see Figure 6). This allows for the use of

pixel intensities on a scale from zero to one, where zero is black and one is

white, to be used in locating the bar position later on.

Figure 6: On the left a timex image taken on 31 March 2005 at 10am. On the right the same image converted to plan view and greyscale


42

Once this has been completed there are still difficulties associated with the

beaches curvature. The beach was straightened using a log-spiral technique

(Harley & Turner 2007). This method was found to have particularly better

results on certain beaches such as Narrabeen-Collaroy that have a greater

curvature at one end due to an embayment. In this method a log spiral is fitted

to the beach curvature (Yasso 1965) and then transformed out to Cartesian

coordinates. Using this techniques allowed for the straightening the timex

images of Narrabeen-Collaroy so that data could be collected with greater ease.

This technique solved the issue where features of the beach were curved

making it difficult to measure distances accurately. As can be seen in Figure 7

there is now a cross-shore axis (x) and an alongshore axis (y).

Figure 7: A straightened timex image. Axes are with respect to Argus co-ordinates (x is cross-shore and y is longshore)

As can be seen in Figure 7 the image quality reduces in the alongshore

direction (as y gets smaller). For this reason the image was cut so only a

section from y=2600 meters to y=2000 meters was used. As well as this only

the surf-zone needs to be captured so the cross shore distances were limited

from x=0 meters to x=200 meters. In May 2014 a new Argus camera was

installed which meant these limits for the cross-shore had to be extended to

x=300 meters for the last recovery period.


43

Once the image of the beach has been manipulated so that it is viewed from a

plan view and its curvature had been removes, features of the shoreline and

nearshore morphology could then be found.

The shoreline was found by applying a shoreline elevation model to a shoreline

found using the Pixel Intensity Clustering (PIC) technique applied to Argus

images that had been corrected using a similar method to the one described

previously (Harley et al. 2011). The PIC technique is applied to coloured Argus

images. Aarninkhof (2003) found that dry and wet sand particles have different

hues and saturations. By measuring the amount of hue and saturation in each

image pixel, the pixels in the Argus images can be put into a histogram with two

maximums representing wet and dry sand clusters. The saddle point between

these two points then corresponds to the shoreline. The shoreline elevation

model, a function of both the tide and factors associated with the wave such as

surge and run-up, is then used to find the elevation of this shoreline. The

shoreline elevation model is described in equation (22) which calculates the

shoreline elevation (𝑍𝑠ℎ) from the tidal elevation (𝑍𝑡𝑖𝑑𝑒) and wave run-up

(calculated from the offshore significant wave height (𝐻𝑆) and period (T)) with

three empirically derived coefficients (𝜔𝑜 , 𝜔𝑡𝑖𝑑𝑒 𝑎𝑛𝑑 𝜔𝑤𝑎𝑣𝑒). The tidal information

was gathered form a tide gauge located at the mouth of Sydney Harbour

approximately 12 kilometres south of Narrabeen-Collaroy.

𝑍𝑠ℎ = 𝜔𝑜 + 𝜔𝑡𝑖𝑑𝑒𝑍𝑡𝑖𝑑𝑒 + 𝜔𝑤𝑎𝑣𝑒√𝐻𝑆

𝑔𝑇2

2𝜋 (22)

The 0.7 meter contour of the shoreline was taken from a pre-existing data set

(Harley et al. 2011). Through a set of MATLAB codes a 50 meter Hanning

window was applied to the shoreline, following the method outlined by Splinter

(2009), to remove erroneous features in the data. After this the shoreline was

then overlayed on the corrected timex image (see Figure 8). This contour line

was then used as a datum from which to measure the mean bar position from.

Additionally this also allows for the removal of section of the image above the

shoreline.


44

Figure 8: The 0.7 meter contour shoreline (red) plotted on the corrected and cropped timex image

Once the shoreline had been found the determination of the location of the sand

bar began. The sandbar position was calculated based upon image intensity.

The position that waves break in a timex image appear at a higher intensity due

to the bubbles created as the wave breaks (Lippmann & Holman 1989).

Following the breakpoint hypothesis (Plant et al. 1999) it can be assumed that

the sand bar moves towards the location of the breaking waves; where the

highest intensity in the timex image can be found.

Due to the position of the Argus camera contrast levels across the image vary

depending upon distance from the camera. Light reflects off parts of the water

differently at locations father away from the camera compared to the parts of

the image closest to the camera. In order for intensities to be calculated with

greater ease the MATLAB program removed these lighting trends showing

more clearly where sand bar was located. The MATLAB code took the image

and for each cross-shore profile calculated an intensity trend (𝐼𝑡𝑟𝑒𝑛𝑑) as the

most offshore available pixel intensity (as this was the darkest generally). Using

this intensity each cross-shore profile was then de-trended using the

methodology applied by Splinter (2009). Since pixel intensities range from 0 to a


45

maximum of 1 a new intensity (𝐼𝑛𝑒𝑤) was calculated by implementing equation

(23).

𝐼𝑛𝑒𝑤 =𝐼𝑜𝑙𝑑 − 𝐼𝑡𝑟𝑒𝑛𝑑

1 − 𝐼𝑡𝑟𝑒𝑛𝑑 (23)

The results of this can be seen in Figure 9.

Figure 9: Left image is before intensity adjustment, right figure is after (with the shore removed).

In order to use intensities to find the sand bar position the shore break needed

to be removed from the image. The shore break could also correspond to an

intensity maximum so if left in could give false values for the sand bar offshore

location. At each cross-shore profile of the timex image it was determined if

there was an intensity maximum within 10 meters of the shoreline. In the cases

where this existed it was removed. A longshore profile was created that

represented the seaward limit of the shore break. Once this was removed for

each cross-shore profile a 50 meter Hanning filter was applied to new longshore

profile to remove anomalies. All points landward from the shore break were then

removed from the image essentially leaving the surf zone. This can be seen in

Figure 10.


46

Figure 10: On left is an image with the shore break. On the right is an image with the shore break removed. Both images have the mean bar position plotted

(red dashed) and the surf zone boundaries (blue).

4.4.2 Mean Sand Bar Position

At 5 meter cross shore profiles a the location of the maximum intensity was

found (Splinter et al. 2011). This corresponded to the location of the sand bar.

The distance a sand bar was offshore (𝑥𝑏𝑎𝑟) was taken as the distance from the

shoreline to this location for each cross shore profile. A 25 meter Hanning filter

was used to smooth the bar position profile. The mean bar position (𝑥) was then

calculated by taking an average of these individual 5 meter interval locations.

A surf zone was defined as the location that pixel intensities were greater than

0.75, again for the 5 meter cross-shore profiles which bar location was found

for. The two locations shoreward and landward of the sand bar which

corresponded to this limit were also put through a 25 meter Hanning filter in

order to remove anomalies. The mean sand bar location and surf zone for the

timex image taken at 10am on 31 March 2015 can be seen in Figure 10 and for

the timex image taken at 3pm on 31 August 2014 in Figure 11.

4.4.3 Sand Bar Variability

Sand bar variability (𝑎) was defined, as outlined by Plant et al. (2006), from the

variance of the demeaned, de-trended Fourier transformation of the bar position


47

data. The demeaned and de-trended bar position (𝑥′) can be seen in Figure 11

with respect to a sand bar.

Figure 11: The plot of the demeaned de-trended sand bar position (𝒙′) with respect to the sand bar shape

This line is approximated by Fourier decomposition. From the Fourier

decomposition the power spectral density is calculated in the band from 25 to

400 meters. Finally the square root of the variance of the spectral density is

defined as the sand bar variability as in equation (24) where the spectral density

(𝑆) of the bar position is calculated from the Fourier transformed and de-trended

relative bar positions ( 𝑥 − 𝑥𝑏𝑎𝑟) within a defined interval.

4.5 Model Preparation and Other Data

In order to ensure that the data being put into the models was valuable, once

the average bar position and bar variability had been calculated for each storm

a program was compiled in MATLAB that could be used to check if the correct

data had been obtained. In some instances light would reflect off the water or

other anomalies would occur meaning that the bar position and variability

calculated were in fact incorrect (See example in Figure 12 where the

𝑎 = √1

𝑛∑(𝑆𝑖 − 𝑆̅)

𝑛

𝑖=1

𝑤ℎ𝑒𝑟𝑒 𝑆 = 𝑓(𝑥 − 𝑥𝑏𝑎𝑟) (24)


48

calculated sand bar location does not correspond to the white in the image

representing the actual sand bar location). The program created plots of each

beach with its corresponding bar location offshore (𝑥𝑏𝑎𝑟). Each image was then

either accepted or rejected subjectively. Images that were rejected

corresponded to those where the bar position was incorrect and giving the

location of a lighting anomaly and not the sand bar location.

Figure 12: Image of incorrect bar position calculated due to anomaly where the image is cut on bottom left where light is shining off the surface of the water.

The image has the calculated bar position (red dashed) and the surf zone (blue) overlayed.

Since there are two separate data sets that are being combined (wave data and

sand bar data) it is first necessary to align both data sets so that they correlate

to each other temporally. This was done through a MATLAB program that took

the dates and times for both wave properties and sand bar properties and

aligned them together. Sand bar data was sampled at varying intervals ranging

from twice a day to spanning multiple days. The majority of wave data was

hourly.

Each recovery periods data set was analysed separately. Six different

parameters were separated into separate vectors with wave height, wave

period, wave direction, mean bar position offshore, bar variability and the

corresponding times that each set of data sets were recorded. It was at this


49

point anomalies in the data could be compared. Initially recovery period 7

spanned from 10 August 2014 to 30 November 2014. When each wave

parameter was plotted together for this storm (see Figure 13) it was noticed that

there was a large period of wave data missing. This period was then able to be

shortened to 15 October 2014 so that error resulting from the interpolation of

wave data would not be introduced. The wave data was missing directly after a

storm event so there was no issue in shortening the recovery period.

Figure 13: Missing data from original recovery period 7 (10 August 2014 to 30 November 2014)

It was during this step that the significant wave height (𝐻𝑠) taken from the

SWAN model was converted to the root mean square (RMS) wave height

(𝐻𝑟𝑚𝑠) as in equation (25).

𝐻𝑟𝑚𝑠 =𝐻𝑠

√2 (25)


50

Due to the fact that bar data and wave data were sampled at varying intervals

producing a time series to be implemented in the models proved challenging.

To overcome this problem linear interpolation was used to find bar data values

for hourly time steps. The data set was then given a weighting of one for original

data values and zero for the interpolated points.

To account for anomalies in the wave data initially a linear interpolation was

used to fill in gaps. Afterwards a Hanning filter with a four hour interval was

used to improve on the linear interpolations. Four hours was chosen based off

trial and error as it approximated the data best without limiting the peaks

significantly (see Figure 14 for an example of the interpolated RMS wave height

for recovery period 6).

Figure 14: Data has been interpolated (red) to fill in the gaps in the data obtained from the SWAN corrected wave-rider buoy data (blue) for RMS wave height

After this manipulation a data set for the wave height, wave period, wave

direction, mean sand bar position and sand bar variability were temporally

aligned and able to be used to calibrate the models.

The SHP11 model required a large number of additional parameters in order to

be calibrated. These were both calculated and found from literature. The

reference bar height (∆𝑜) measured at a reference location (𝑥𝑜) was calculated

from offshore survey data. The underwater profile of two beach profiles (Profile

6 and Profile 4) at Narrabeen-Collaroy (See Figure 5) were measured using Jet


51

Ski mounted single and multi-beam bathymetry surveys on July 2014 and April

2015. The average of four surveys was taken and a linear best fit was created

that passed through the shoreline which was taken as the 0.7 meter contour.

The difference between these two profiles was taken and can be seen in Figure

15, note that the red line is the mean profile and this is why the linear fit does

not pass exactly through the 0.7 meter contour in this figure. From this the

reference bar height and location were found as 0.1596 meters high and 133

meters offshore respectively.

Figure 15: On left average bathymetry (red) with linear fit through 0.7m contour. On right Difference between profile cross section and the linear fit.

Other values for the SHP11 model were taken from literature. The nearshore

beach slope (𝛽) and mean sediment size (𝐷50) were taken as 0.02 and 0.3mm

respectively (Harley et al. 2011). The suspended load efficiency factor (𝜖𝑠) was

taken as 0.015 and the drag coefficient (𝐶𝑑) was taken as 0.003 (Gallagher et

al. 1998). The sediment fall velocity (𝑊) was taken as 0.04m.s-1, the tidal range

(𝛿𝑡𝑖𝑑𝑒) was taken as 1m since Narrabeen-Collaroy is micro-tidal, the wave

friction factor (𝑐𝑓) was taken as 0.01 and the alongshore wave variability

number (𝑘𝑦) was taken as 0.04m-1 (Splinter et al. 2011). The reference wave

period (𝑇𝑜) was taken as 10 seconds as this is the average period at Narrabeen-


52

Collaroy (Phillips et al. 2015). The cross-shore bar length coefficient (𝑚) is

taken as 0.27 (Ruessink et al. 2003).

4.6 Modelling Sand Bar Recovery

Once the data had been collected this enabled the models to be calibrated. The

following sections outline how the PHH06, SHP11 and ShoreFor models were

calibrated.

4.6.1 PHH06 Model Calibration

The PHH06 model has eight free parameters for which to calibrate. In addition

to the mean sand bar position and its alongshore variability it also relies upon a

forcing term equivalent to the RMS wave height squared.

The derivative of the mean bar position (�̇�) and the sand bars alongshore

variability (�̇�) with respect to time were calculated numerically at each time step

using a fourth order Runge-Kutta method. The model parameters were then

calibrated using a non-linear least square curve fit. The non-linear least square

curve fit had multiple iterations to estimate the free parameters (matrix 𝐴 and

matrix 𝐵). After the mean bar position and sand bar alongshore variability were

calculated from the fourth order Runge-Kutta scheme (performed each iteration)

the resulting vectors were then multiplied by the weighting vector mentioned in

section 4.5. This removes any reliance upon the interpolated values so in the

next iteration of the non-linear least square fit the free parameters are only

being calibrated to the data obtained.

In order to speed up the numerical process a set of boundary conditions for the

free parameters were applied. Initially values were chosen so that the output

parameters from previous applications of the model (Plant et al. 2006; Stokes et

al. 2015) fitted within the bounds. These initial free parameters reached the

boundary conditions. As a result the model was run with new boundary

conditions so that the calibrated parameters did not reach the bounds. The

upper bounds (𝐴𝑈𝐵 𝑎𝑛𝑑 𝐵𝑈𝐵) and lower bounds (𝐴𝐿𝐵 𝑎𝑛𝑑 𝐵𝐿𝐵) were:


53

𝐴𝑈𝐵 = [100 10010 10

] 𝐵𝑈𝐵 = [1000 100100 100

]

𝐴𝐿𝐵 = [−100 −100−10 −100

] 𝐵𝐿𝐵 = [−100 0−100 −10

]

The model was calibrated for each individual recovery period. Once the

parameters were calibrated the model was then run with the calculated

parameters to determine its ability to explain the behaviour in the data set. From

this run the model skill was calculated as will be outlined in section 4.7.

4.6.2 SHP11 Model Calibration

The SHP11 model comprises of five free parameters. Since the model is

processed based there are a large number of physical parameters used as

inputs into the model. These inputs include mean sand bar position, sand bar

alongshore variability, RMS wave height, wave period, shore-normal wave

direction as well as the numerous other parameters outlined in section 4.5.

Following Splinter et al. (2011), the free parameter representing the equilibrium

amount of breaking (𝛾𝑒𝑞) was taken as 0.65. The reference bar variability (𝛼𝑜)

was taken as the mean sand bar variability in the corresponding recovery period

data set. The remaining free parameters were calibrated using the same

method as for the PHH06 model, outlined in section 4.6.1, applying a non-linear

least square fit to the solution of a fourth order Runge-Kutta scheme with data

weighted so that only observed data is fitted for.

The bounds implemented for the splinter model were as follows:

𝛼1𝐿𝐵= 0 , 𝛼1𝑈𝐵

= 10


= 10


= 100


= 100


54

Like the PHH06 model calibration was done for each individual time-step and

then the model was run using the calibrated parameters. Again the skill of the fit

was then calculated. This method will be explained in section 4.7.

4.6.3 ShoreFor Model Calibration

Furthering the work of Stokes et al. (2015), the behavioural properties of

offshore sand bars was modelled by applying the ShoreFor model to find the

alongshore variability (𝑎). Additionally, for the first the ShoreFor model was

used to predict the mean sand bar position offshore (𝑥). This was done using

two separately calibrated equations for mean sandbar position offshore

(equation (26)) and sandbar alongshore variability (equation (27)).

�̇� = 𝜆1 + 𝜆2(𝐹+ + 𝐹−) (26)

�̇� = 𝜆3 + 𝜆4(𝐹+ + 𝐹−) (27)

This model works essentially the same as the SDR15 model outlined in section

2.5.4 with only two differences. There is no tidal term factored into the

calculation of the forcing (𝐹, in equation (19)).The forcing efficiency term (𝑟) was

also not used.

The ShoreFor model was implemented using a MATLAB program developed for

the ShoreFor model (Davidson et al. 2013). It was run separately to determine

the mean sandbar position offshore and its alongshore variability. In each case

the shoreline position was replaced with either the data for mean sandbar

position offshore or the sandbar alongshore variability.

The model comprises of six free parameters (𝜆1, 𝜆2, 𝜆3, 𝜆4, 𝜙𝑥 𝑎𝑛𝑑 𝜙𝑎 ) where the

memory decay parameter is calibrated separately for the mean bar position (𝜙𝑥)

and bar variability (𝜙𝑎) by iterating from 1 to 1000. Data the ShoreFor model

required as inputs included the wave height, wave period, mean sand bar

location, sand bar variability, the mean sediment size and the corresponding

times that each data point was recorded at. It was optional to include the sand

bars locations standard deviation. The standard deviation of the sand bar


55

position offshore with respect to the mean was calculated as in equation (28).

The standard deviation of the alongshore sandbar variability was not used.

4.7 Model Skill

In order to compare each models ability to be calibrated to the obtained data

sets, three skill functions were used. These functions measure different aspects

of each models ability to calibrate to the data set. Following Splinter et al.

(2011) and Stokes et al. (2015) three functions were chosen; correlation

squared (R2), Brier Skill Score (BSS) and Root-Mean Square Error (RMSE).

The R2 coefficient is calculated simply from taking the square of the variance

between the data and model output. It yields the variance in data that the model

is able to capture as a percentage.

The BSS is found as in equation (29) with respect to the input data, (𝑝𝑑) model

output, (𝑝𝑚) a linear best fit model (𝑝𝑓) and the estimated error (∆𝑝) for a time

series. A score less than zero indicates the model performed worse than the

linear fit while a score of one indicates the model performed perfectly. Stokes et

al. (2015) defined a score of 0 as ‘poor’, 0.3 as ‘fair’, 0.6 as ‘good’ and 0.8 as

‘excellent’. In addition to this a score of ‘none’ will be used for below 0.

Lippmann and Holman (1989) found that there was generally an error of 5-10%

of the distance to the shoreline when calculating the bar position. The maximum

distance a bar was recorded offshore in the data set was just over 100 meters

so for this reason the estimated error was taken as 5 meters for the bar

𝜎𝑥 = √1

𝑛∑(𝑥𝑏𝑎𝑟𝑖

− 𝑥)

𝑛

𝑖=1

(28)

𝐵𝑆𝑆 =1

𝑛∑1 −

(|𝑝𝑑𝑡− 𝑝𝑚𝑡

| − ∆𝑝)2

(𝑝𝑑𝑡− 𝑝𝑓𝑡

)2

𝑛

𝑡=1

(29)


56

position. The error in calculating the bar variability was estimated to be

approximately 2 meters, roughly 10% of its maximum value.

RMSE is calculated as in equation (30) in terms of the difference between the

observed data and the model output for a time-series.

A smaller RMSE indicates that a model is more accurate. The RMSE is limited

in that it should not be used in comparing the skill of models at calibrating

different parameters (for example skill at calibrating 𝑎 in SHP11 versus skill at

calibrating 𝑥 in PHH06), (Hyndman & Koehler 2006). It can be used however to

compare different models skill at calibrating the same parameter.

The results of the implementation of this methodology will be shown in the

following chapter.

𝑅𝑀𝑆𝐸 = √1

𝑛∑(𝑝𝑑𝑡

− 𝑝𝑚𝑡)2

𝑛

𝑡=1

(30)


57

Chapter 5 – Results

Following the method outlined in Chapter 4 the PHH06, SHP11 and ShoreFor

models were calibrated to determine each models ability at being able to

replicate the sand bars mean position offshore and alongshore variability at

Narrabeen-Collaroy. The results of this calibration are displayed in the following

chapter. First the key attributes of each recovery period will be presented. Next

each models output will be compared to the corresponding data set. Afterwards

the skill scores for each model will be revealed. At the end of the chapter the

calibration of parameters will be looked at in addition to the effects of boundary

conditions on the PHH06 model calibration.

5.1 Recovery Period Data

Seven recovery periods spanning a length of ten years were chosen. These

recovery periods ranged from 66 days to 364 days comprising of both single

storm and multiple storm events. For ease the recovery periods have been

numbered from one to seven with respect to the date they occurred as shown in

Table 2. When each recovery period is being referred to this number will be

used.

For each recovery period five key data sets were obtained. These comprised of

wave height, wave period, wave direction, mean sand bar position offshore and

the sand bars alongshore variability. This data can be seen for each recovery

period in Appendix A. Other data that needed to be obtained has been outlined

in section 4.5. Key aspects of the wave and sand bar data sets for each

recovery period are outlined in the following section.

Sand bar data obtained from the Argus images behaved as expected. Generally

the sand bar propagated offshore after storms and accreted onshore during

smaller wave conditions. When the sand bar moved offshore its alongshore

variability reduced. As the sand bar moved onshore the variability first increased

and then decreased as the sand bar became closer to the shoreline. The peak


58

of the alongshore variability occurred only as the sand bar began to move

onshore. One notable anomaly in the data is that in recovery period 6 from

September 11 until October 1, 2012 the MATLAB program was unable to obtain

sand bar data due to the shoreline data being missing.

Significant attributes for each recovery periods wave conditions can be seen in

Table 3.

Table 3: Key wave data statistics

Max Hs

Date Max Hs

Days Hs>3

Mean Hs

Mean T

Min Max

Mean

Period 1 4.53 23/03/2005 17 0.98 8.53 -17.54 43.71 21.92

Period 2 3.64 1/07/2005 12 0.92 8.55 -20.89 54.77 20.93

Period 3 4.41 9/06/2007 60 1.07 8.32 -27.03 54.56 20.14

Period 4 2.95 26/05/2010 0 1.01 8.56 -34.75 54.00 22.91

Period 5 3.90 22/07/2011 23 0.99 8.70 -35.16 54.56 21.31

Period 6 4.37 6/06/2012 36 0.97 8.27 -32.60 54.51 20.87

Period 7 3.51 30/08/2014 3 1.23 8.59 -22.40 48.27 20.79

The first data set, recovery period 1, spanned a three month period. This

recovery period comprised of the both the largest storm waves as well as

longest period with steady wave conditions. The second recovery period was

only a month after the first. It had the smallest average wave height and also

recorded the most southerly waves coming from 54.77° with respect to shore-

normal. The third recovery period was the longest, spanning almost a year. It

comprised of three separate storm events with initial large wave conditions in

June 2007. The fourth recovery period was the only one which did not have a

storm event that included waves over 3 meters. It had waves over two meters

for over three days in May 2010. Despite not having waves over 3 meters it did

not have the lowest average wave height over the length of the period. The fifth

recovery period corresponded to the largest average period of 8.70 seconds as


59

well as the most northerly swell coming from -35.16° with respect to shore-

normal. The sixth recovery period has the lowest average period which was

8.27 seconds. The final recovery period (7) was the shortest recovery period.

Despite this it had the largest mean significant wave height of 1.23 meters.

Once these data sets had been obtained they provided a baseline which could

be used to compare different models. From these seven data sets the

calibration of the PHH06, SHP11 and ShoreFor models was performed.

5.2 Calibration and Data Comparison

In order to test each models ability to capture changes in mean sandbar

position offshore and its alongshore variability first the models parameters were

calibrated for each individual recovery period. This was done using a non-linear

least square fit as outlined in Chapter 4 . Once calibrated the parameters were

then fed back into each model for the respective recovery periods. The

effectiveness of each model to capture the variations in the data set, from which

it was calibrated, was tested.

The results for the PHH06 model calibration and simulation are shown in Figure

16. Overall the PHH06 model was able to calibrate to the data set well. When

simulating the mean sandbar position offshore the model tended to over predict

the distance that sandbars propagated offshore. This is evident in recovery

periods 1, 2, 3 and 5. When this occurred it can be noticed that at the same

time the model tended to simulate the peak of the alongshore variability earlier

than it actually occurred. Overall the model simulation was able to follow the

patterns of the data set.

The simulation results for the calibrated SHP11 model can be found in Figure

17. When simulating recovery periods 1 and 4 the SHP11 model appeared to

mimic the sand bars offshore position behaviour well. At the same time there

appeared to be a lag when predicting the alongshore sand bar variability. When

simulating recovery periods 5, 6 and 7 the model struggled to reproduce the

behaviour of the alongshore variability having a large and frequent variation

between one and two dimensional sand bars where the data set had a single


60

shift between the two states after storm events. The average bar position

offshore during these events appeared to be accurate with the magnitude

somewhat dampened. When simulating the longest recovery period (period

three) the model showed skill in predicting the mean sandbar location however

it failed to simulate the change in the sandbars alongshore variability.

The performance of the ShoreFor model is displayed in Figure 18. Overall the

model predicted the alongshore variability of the sand bars during the recovery

periods quite well. The simulation was dampened however failing to model the

extreme two and one dimensional sand bar cases the data set displayed. The

prediction of the mean sandbar location offshore varied more. In recovery

periods 4 and 7 it was able to explain the peaks in the data. For recovery

periods 1, 2 and 5 it overestimated the peaks and wasn’t able to capture the

movement of the sandbar close to the shore. For the remaining periods it

behaved similar to the alongshore variability missing the extreme offshore and

close to shore positions.


61

Figure 16: PHH06 model calibration results


62

Figure 17: SHP11 model calibration results


63

Figure 18: ShoreFor model calibration results


64

5.3 Calibration Skill

The following section details how each model performed with respect to the skill

functions outlined in section 4.7 (R2, BSS and RMSE).

The PHH06 model skill scores are shown in Table 4. The PHH06 model

performed the best out of all the models. On average it scored the best in all

skill tests except for the R2 and RMSE when predicting alongshore sandbar

variability where it was outperformed by the ShoreFor model. When scored by

R2 and RMSE the PHH06 model was best at predicting the average sand bar

distance offshore having the best score five out of seven times. When scored by

the BSS the PHH06 model was better at predicting the alongshore sandbar

variability having the best score for six out of the seven recovery periods. The

PHH06 model was the only model to score the best in every skill function. It

achieved this for recovery period 4 during which it had its only ‘excellent’ BSS

score. The PHH06 model had the best average R2 correlation and RMSE for

the mean bar position offshore as well as the best average BSS for the

alongshore sandbar variability.

Table 4: PHH06 skill scores

R2x R2

a BSSx BSSa RMSEx

(m) RMSEa

(m)

Period 1 0.9457 0.5741 0.5804 ‘good’ 0.0916 ‘poor’ 3.1503 1.8652

Period 2 0.7014 0.5534 0.4869 ‘fair’ 0.6519 ‘good’ 8.8583 2.1357

Period 3 0.6881 0.3888 0.6843 ‘good’ 0.5704 ‘fair’ 11.0211 2.8615

Period 4 0.7909 0.6714 0.8095 ‘excellent’ 0.7545 ‘good’ 5.7884 1.9127

Period 5 0.6035 0.4136 0.731 ‘good’ 0.5887 ‘fair’ 9.529 4.1358

Period 6 0.5382 0.4838 0.6316 ‘good’ 0.6727 ‘good’ 9.6584 3.019

Period 7 0.6406 0.5661 0.6031 ‘good’ 0.6704 ‘good’ 8.6682 2.9853

Average 0.7028 0.5087 0.6729 ‘good’ 0.5738 ‘good’ 8.0781 2.7293


65

The SHP11 model performed with the least skill. Its scores are shown in Table

5. It had the best score only twice when skill at predicting the mean sandbar

position offshore was measured using the BSS function for recovery periods 1

and 2. Its BSS for recovery period 1 was the overall best BSS score for all

recovery periods for all models. Despite this it scored worse than the linear best

fit twice. This was when the mean sandbar position offshore was scored by the

BSS for recovery periods 5 and 6. This showed a large unreliability. When

compared to the ShoreFor model on average it performed better at predicting

the alongshore sandbar variability when scored by the BSS.

Table 5: SHP11 skill scores

R2x R2

a BSSx BSSa RMSEx

(m) RMSEa

(m)

Period 1 0.8882 0.0906 0.8567 ‘excellent’ 0.3777 ‘fair’ 4.5536 3.1559


Period 3 0.6098 0.0385 0.7033 ‘good’ 0.0984 ‘poor’ 12.8381 4.2851

Period 4 0.6021 0.2233 0.462 ‘fair’ 0.443 ‘fair’ 7.9891 3.5493

Period 5 0.0799 0.2103 -0.0886 ‘none 0.5492 ‘fair’ 15.2504 4.6151

Period 6 0.3127 0.1765 -0.1372 ‘none 0.5193 ‘fair’ 11.8103 4.3726

Period 7 0.3482 0.1893 0.1812 ‘poor’ 0.3892 ‘fair’ 12.0765 3.7243

Average 0.4710 0.1479 0.3969 ‘fair’ 0.3854 ‘fair’ 10.9961 4.2103

The ShoreFor model was the second best model significantly outperforming the

SHP11 model. The skill scores for the ShoreFor model can be found in Table 6.

Overall the ShoreFor performed the best when being scored by the RMSE and

R2 for alongshore sandbar variability. When scored by the RMSE function for

alongshore variability it was the most skilful model five out of seven times.

Additionally, it had the best R2 coefficient five out of seven times for the

alongshore sandbar variability. The ShoreFor model scored best in five out of

the six functions for recovery period 7 and also had the majority of best scores

for recovery period 5 where the PHH06 model outperformed it when evaluated


66

by the BSS function. The overall best scores for the R2 and RMSE functions

when scoring the alongshore variability was from the ShoreFor model.

Table 6: ShoreFor skill scores

R2x R2

a BSSx BSSa RMSEx

(m) RMSEa

(m)

Period 1 0.9150 0.7095 0.5170 ‘fair’ 0.6673 ‘good’ 3.8955 1.5194

Period 2 0.5348 0.3888 0.7098 ‘good’ -0.0821 ‘none 10.9828 2.2176


Period 4 0.7634 0.5657 0.6211 ‘good’ 0.6227 ‘good’ 6.1226 2.0291

Period 5 0.6037 0.4356 0.5387 ‘fair’ -0.4991 ‘none 9.4772 2.8307

Period 6 0.4154 0.5067 0.5792 ‘fair’ 0.2177 ‘poor’ 10.8492 2.9444

Period 7 0.7004 0.6104 0.7006 ‘good’ 0.6475 ‘good’ 7.8430 2.2083

Average 0.6365 0.5262 0.6398 ‘good’ 0.2819 ‘poor’ 8.9692 2.3123

5.4 Calibration

The resulting parameters for each calibration can be seen in Appendix B. The

relative standard deviations (𝐶𝑉) of each models parameters between each

recovery period are shown in Table 7. The relative standard deviation was

calculated by scaling the standard deviation by the mean parameter value over

all recovery periods.


67

Table 7: Relative standard deviations of model parameters

PHH06 Relative Standard Deviation

𝑨 𝐶𝑉𝐴11= 243% 𝐶𝑉𝐴12

= 302% 𝐶𝑉𝐴21= 106% 𝐶𝑉𝐴22

= 111%

𝑩 𝐶𝑉𝐵11= 132% 𝐶𝑉𝐵12

= 42% 𝐶𝑉𝐵21= 99% 𝐶𝑉𝐵22

= 152%

SHP11 Relative Standard Deviation

𝒙 𝐶𝑉𝛼1= 87% 𝐶𝑉𝛼2

= 68%

𝒂 𝐶𝑉𝛼3= 122% 𝐶𝑉𝛼4

= 33%

ShoreFor Relative Standard Deviation

𝒙 𝐶𝑉𝜆1= 117% 𝐶𝑉𝜆2

= 54% 𝐶𝑉𝜙𝑥= 116%

𝒂 𝐶𝑉𝜆3= 208% 𝐶𝑉𝜆4

= 21% 𝐶𝑉𝜙𝑎= 156%

From Table 7 it can be seen that each models parameters varied quite

substantially between each recovery period. The SHP11 model had the least

deviation between model parameters while the PHH06 model had the greatest

deviation between parameters.

5.5 PHH06 Boundary Conditions

When the PHH06 model was being implemented an investigation was done to

determine the effects of the boundary conditions on the solution. It was found

that having boundary conditions improved the performance of the model. The

results found for the case where no boundary conditions were used for recovery

periods 1 and 2 can be seen in Figure 19. In general the model appeared to

over predict the distance the sand bar propagated offshore while simulating the

propagation onshore after this well. Again, like the PHH06 model with boundary

conditions, the simulated alongshore variability peaked earlier than the data set.


68

Figure 19: PHH06 calibration results with no boundary conditions

The skill scores for the PHH06 model without boundary conditions are shown in

Table 8. Overall the model without boundary conditions performed worse. The

exception to this was when scored by the BSS function recovery period 1

scored better in calculating both the mean sand bar position offshore and its

alongshore variability. This included an ‘excellent’ score for the position

offshore. For recovery period 2 the model without boundary conditions better

calibrated to the alongshore variability when measured by the BSS. Despite this

it scored a BSS of ‘none’ calibrating to the sandbar position offshore.

Table 8: Skill of PHH06 with no boundary conditions

R2x R2

a BSSx BSSa RMSEx

(m) RMSEa

(m)

Period 1 0.7490 0.0388 0.8737 ‘excellent’ 0.3753 ‘fair 7.3431 5.5735

Period 2 0.0045 0.0337 -0.0082 ‘none’ 0.3649 ‘fair’ 37.0535 6.8296

When no boundary conditions were specified it was noticed that the model took

significantly longer to calibrate the parameters.


69

Chapter 6 – Discussion

From the results found in Chapter 5 there are some key findings that will be

discussed. The following chapter will outline reasoning for why the three models

(PHH06, SHP11 and ShoreFor) performed the way in which they did.

Additionally an investigation into alternative methodologies to obtain the data

that could have been employed and the implications of the choices made will be

discussed.

6.1 Analysis of Results

In the following section the key underlying assumptions of each model tested

will be discussed. The PHH06 is a parametric model that assumes the mean

sand bar location offshore and its alongshore variability are intrinsically linked.

The SHP11 model follows this same assumption using a process based model.

The ShoreFor model is behavioural in nature and does not link the mean sand

bar position offshore and its alongshore variability together. From the results

found in Chapter 5 the validity of these assumptions can be tested.

The PHH06 model was the most skilful at predicting the average sand bar

position offshore. In addition to this it was also able to predict the alongshore

variability of sand bars with a large amount of skill. Despite its success at

calibrating well to the different recovery periods there are some notable results

that were found.

The 𝐴 matrix in the PHH06 model (see Appendix B) describes the interaction

between the mean sandbar position offshore and the alongshore variability of

the sandbar. If the diagonal terms in this matrix (𝐴11, 𝑎𝑛𝑑 𝐴22) are negative and

the off diagonal terms (𝐴12, 𝑎𝑛𝑑 𝐴21) have opposite signs this suggests that the

model has a stabilising tendency (Plant et al. 2006). For recovery period 1 and

7 these diagonal terms were opposite signs. Additionally for recovery periods 2

through 6 the off diagonal terms all had the same signs. These findings suggest

that the sand bar system and interaction between the sand bars distance


70

offshore and the sand bars alongshore variability at Narrabeen-Collaroy is

unpredictable. It is possible that the parameters are unable to calibrate over

shorter length time series as this has not been tested in previous studies.

The parameters in both the (𝐴) and (𝐵) matrices varied quite substantially for

each calibration (see parameter values in Table 10 in Appendix B). The 𝐴12

term had the largest relative standard deviation of 302%. None of the

parameters in the 𝐴 matrix had a relative standard deviation below 100%. When

scored by the R2 and RMSE skill functions it is also noticeable that the model

rarely scored the best for both the mean sand bar position offshore and its

longshore variability. In addition to the previous findings this suggests that the

mean sandbar position offshore and its variability are not linked as described in

the PHH06 model. The PHH06 model has a significant number of parameters

and it is reasonable to assume that some of its skill is due to this fact. There

may however be an underlying relationship between the mean sand bar position

offshore and its variability hidden in the parameters which is why it was able to

show a large amount of skill.

When the case of no boundary conditions was used to calibrate the PHH06

model the diagonal parameters in the 𝐴 matrix again exhibited behavior

suggesting that both the sand bar position and its variability are not linked (see

Table 10 in Appendix B). This also showed that the boundary conditions

provided some significance as they were able to improve the model. It appears

that the skill of the model has a large reliance upon the parameters. This further

suggests that the reason the model was able to perform well is because of the

large number of parameters it has and not the dependency between the sand

bar position offshore and its variance. It could also be that by limiting the

parameters it forces a process to be captured by the parameters that affects the

sand bars behaviour. Further investigation into these parameters is needed in

order to ensure this is the case.

The small level of skill exhibited by the SHP11 model further suggests that there

is little dependence between the sand bar position and its alongshore variability.

This is highlighted in Figure 17. In recovery periods 3, 5, 6 and 7 the model


71

seemed to force the alongshore variability to have specific values so that it was

able to calibrate to the sand bars position better.

The parameters for the SHP11 had the least overall relative standard deviation

between the different recovery period calibrations. The relative standard

deviation was only above 100% for 𝛼3. As shown in equation (12) this term is

used to scale the variability. For recovery periods 5, 6 and 7 this parameter

increased above one in an attempt to force the modelled variability to fit closer

to the data set (see Table 11in Appendix B). This caused the increase in

relative standard deviation. The reliance of the model on this parameter in

calibration of the variability suggests that the model found it difficult to show the

behaviour exhibited by the interaction of the sand bar position and its variability.

The large number of physical processes modelled in the SHP11 model

introduces lots of possible sources of error. While it appears, when viewed with

the results of the PHH06 model, that its performance is due to the link between

the sand bar position and its alongshore variability, the reason SHP11 model

did not perform well may have other causes. A number of input data values for

this model were assumed to be the same for Narrabeen-Collaroy as for Palm

Beach where the model was initially developed. These values include the

sediment fall velocity (𝑊), tidal range (𝛿𝑡𝑖𝑑𝑒), the wave friction factor (𝑐𝑓) and the

alongshore variability number (𝑘𝑦). The mean particle size at Narrabeen-

Collaroy is the same as at Palm Beach, (approximately 0.3 millimetres) so the

sediment fall velocity should not affect the calculations. The SHP11 model was

originally run using day timex images so there could be error involved by how

the tidal variation term is incorporated. The wave friction factor and alongshore

variability number will affect the reliance the model has on wave directions. In

addition to these the equilibrium amount of breaking free parameter (𝛾𝑒𝑞) was

taken directly from the Palm Beach calibration. This parameter effects the

amount of sediment transport and specifically parameter 𝛼2 so could be causing

issues in calibration (Splinter et al. 2011).

Initially the reference sand bar location (𝑥𝑜) and reference bar height (∆𝑜) were

taken as the same values that were calculated for Palm Beach. It was found


72

that the model had a large difficulty when it came to calibration. This data set

caused fraction of waves breaking (𝛾𝑏) to become large. The 𝛼3 and 𝛼4

parameters tried to compensate for this by decreasing in value towards zero.

This just resulted in a large reduction of model skill. Additionally to this, the

other parameters tended to hit the boundary conditions. When the reference

sand bar location and reference bar height were calculated for Narrabeen-

Collaroy, as in section 4.6.2, the parameters were able to calibrate within the

bounds. The data taken from Splinter et al. (2011) originally for Palm Beach

could be effecting the model in a similar way reducing the skill.

Recently a modified ShoreFor model was used to measure the change in

bathymetry at a double sand bar beach with measurable success (Stokes et al.

2015). It was suggested that behavioural models best simulate beach

bathymetry. The application of the ShoreFor model to separately simulate sand

bar position and sand bar alongshore variation at Narrabeen-Collaroy displayed

noteworthy skill. The ShoreFor model significantly outperformed the SHP11

model and in many cases was on the same skill level as the PHH06 model.

Overall it modelled the sand bar position and alongshore variability quite well.

When scored by the R2 and RMSE functions the ShoreFor model was the most

accurate at predicting the alongshore sandbar variability. This supported the

findings of Stokes et al. (2015) suggesting that sand bar position and its

alongshore variability were not intrinsically linked. The only shortcoming of the

ShoreFor model when modelling the alongshore variability of sand bars was its

inability to capture the most extreme linear and variable sand bar conditions.

The model showed some difficulty in modelling the sand bar position offshore.

Investigation into the ShoreFor models parameters provides some key

conclusions. The calibration of the 𝜆4 parameter produced the least relative

standard deviation with only 21%. This is the key parameter used to describe

the equilibrium of the model and the only one that interacts with the forcing

terms (Davidson et al. 2013). The corresponding parameter for sandbar location

(𝜆2) also had a low relative standard deviation of 54%. This shows that the

processes that these parameters represent are important in finding the sand


73

bars position and variability. The overall calibration of the remaining parameters

was significantly variable however with all other terms over 100%. This

suggests that the model does not fully incorporate the processes effecting the

sand bar movement.

The ShoreFor model offers room for improvements to be made. The effect of

excluding the forcing factor (𝑟) introduced by Stokes et al. (2015) are unknown.

It is possible that with further adjustments, such as this, that the ShoreFor

model could be improved even further. Stokes et al. (2015) suggested that there

are further improvements that could be made to the SDR15 model, such as

accounting for alongshore wave power, which could further increase model skill.

It is possible that similar modifications could be made to improve the ShoreFor

models ability to model sand bar position offshore.

Looking at all models as a whole several broad conclusions. It appears that the

reason the PHH06 model is performing with such accuracy is due to its large

number of parameters. The model parameters failed to exhibit stable behaviour

as it has in previous applications (Plant et al. 2006; Stokes et al. 2015). The

SHP11 model did not perform well. It appear it is due to the interdependency of

the sand bar position and variability terms, however, due to the large number of

processes involved in the model there could be an alternate underlying issue

due to input data. The ShoreFor model performed quite well at modelling both

mean sand bar position offshore and sand bar alongshore variability. This

suggests these two terms are not linked. While the model performed well it was

not the best and it is possible that adjustments could be made to further

increase the models ability to simulate sand bar behaviour.

6.2 Alternative Methodologies

The methodology outlined in Chapter 4 was not the only method that could have

been employed to obtain and process the data sets that were required to

perform the calibration of the model parameters. In many cases there were

multiple approaches that could have been selected. The following section will

discuss these other approaches and the reasoning as to why they were not


74

selected. First the wave data, then the shoreline position and finally the bar data

acquisition techniques will be discussed.

When choosing the method to model nearshore wave data there are generally

two models that can be used, the SWAN model (as in this thesis) or the MIKE21

model. Strauss et al. (2007) compared both models on the Gold Coast in

Queensland, Australia. The results from the research found that there was no

major difference in accuracy between the two models. No benefit would have

been gained from using the MIKE21 model so the SWAN model was chosen

due to its availability.

When modelling the nearshore wave data in the SWAN model a depth contour

for model outputs has to be chosen. There was the option of either a 10 meter

depth contour or a 15 meter depth contour. The 10 meter contour was chosen

following the decision of Splinter et al. (2011). This is the logical choice as the

models are studying the wave’s interaction with sand bars on the sea floor.

Following linear wave theory, for the average period of 10 seconds at

Narrabeen-Collaroy waves will tend to break in a depth of around 3 meters. As

such we want to calculate the depth as close as possible to this distance which

corresponds to the 10 meter contour.

The shoreline position can be calculated using a number of methods. These

methods include coastal maps and charts, aerial photography, beach surveys,

GPS shorelines, remote sensing, multispectral and hyperspectral imaging,

airborne light detection and ranging technology, microwave sensors and finally

video imaging (Boak & Turner 2005). Plant and Holman (1997) successfully

used video imaging to determine the beach bathymetry in the intertidal zone.

Using a series of time exposed images as the water moves up and down the

beach depending upon tides, contours of the bright bands associated with

breaking waves on the shoreline can be used to determine the slope of the

beach within 10% accuracy. This model can be further improved with colour

images. Sand that has been wet fails to absorb blue light wavelengths. As a

result instead of determining the beach contours from breaking wave intensity

the line between wet and dry sand can be seen by determining the amount of


75

red and blue light differing across the profile (Plant et al. 2007; Boak & Turner

2005). Another method involves comparing both the high tide and low-tide

images of the beach (Alexander & Holman 2004). In this method the difference

in intensity on the cross-shore location of the images can be compared. The

shore break of the high tide is shown by darker sand in the low tide image and

from this vertical tide range, using the typical beach slope, the intertidal zone

can be found. The minimum of this zone is then taken as the shoreline. Plant et

al. (2007) compared different shoreline detection methods, including PIC, in

their skill at accurately finding the shoreline location in comparison to surveyed

shorelines. The PIC techniques consistently performed well explaining over

75% of variability in all trials. For this reason and due to an algorithm being

created (Mitchell Harley et al. 2011) to quickly find the PIC shorelines this

method was chosen.

There are different options available to collect data on the bathymetry of the sea

floor and determine the location of sand bars. One method is using the Jet Ski

mounted single and multi-beam bathymetry surveys. This can become a very

expensive operation however, in particular when seeking to obtain quasi-daily

data. Another approach is to use a coastal research amphibious buggy (CRAB)

such as what was employed by Plant et al. (1999) to obtain bathymetry data at

Duck, North Carolina, USA. This method can be particularly accurate with

measurements up to 10 centimetres. Again the disadvantage of this method is

its ability to be constantly recording data. At Duck it was used to measure only

fortnightly data sets. This is not useful when wanting to measure daily change in

bathymetry which was observed at Narrabeen-Collaroy in this study. For this

reason, in addition to the fact the facilities to implement it were not available, it

was chosen to use timex images employing breakpoint theory (Plant et al.

1999) to determine sand bar location.

Argus timex images still have some limitations. The two main shortcomings are

that it cannot capture images during the night and it fails to capture sand bar

data during storm events. Due to the need for light the Argus cameras

effectively shut off during the night. This means any change in the bathymetry


76

that occurs during this period will not be captured. During storm events the large

wave conditions produce a significantly large amount of white wash (see Figure

20). During this period the sand bar cannot be viewed as the whole image

effectively turns white due to the large amount of energy in the nearshore. The

sand bar data (mean bar position and bar variability), seen in Appendix A, can

be seen to cut out during times when there are large wave heights. This means

the timex images are not suitable to determine what is happening to a sand bar

during a storm and can only capture the pre storm and post storm conditions.

Figure 20: On the left is a timex image taken on June 9 2005 showing the effects of the morning sun. On the right is a timex image during the storm on

June 9 2007.

Other difficulties in using timex images include the effect of lighting on the

images. Two cases can occur. Light can reflect off the water. This is especially

prevalent in the mornings (see Figure 20). The sun rises in the east and reflects

off the water making the whole image appear white and meaning sand bar data

cannot be captured. In other instances shadows can affect images. It was

noticed for example that in afternoons the shadows from pine trees on the

coastline could cover the shoreline darkening the image and making it appear

as though there was a rip channel. Other than effects due to lighting if there are

no waves present, or no waves breaking it appears as if there are no sand bars.

It was assumed that under these conditions the sand bars experience no

movement. While this is true for the case where there are no existing waves it

may not necessarily be true for smaller wave conditions. This assumption also


77

neglects the effects of the currents on the sand bars. It was due to trends such

as these that images were subjectively checked in the methodology.

At Narrabeen-Collaroy there are five individual Argus cameras overlooking a

section of the shoreline. These images can be merged together to form a longer

continuous image of the shoreline. Using this image would have given a longer

section of the beach from which data could have been observed. It was chosen

only to take the image from one camera to save computational time that would

be needed to merge multiple images. This also meant if there was one bad

image (due to lighting effects for example) it would not corrupt the data set.

When finding the sand bar position from Argus images Splinter et al. (2011)

used day long timex (day timex) images. This was done by taking the average

of all the ten minute timex images in a day. For Palm Beach, the location the

SHP11 model was originally tested at, this sort of image was automatically

created by the Argus cameras. This enabled for a daily average of sand bar

location to be sampled; one that spans all the different tidal conditions. At

Narrabeen-Collaroy this image was not generated and would need to be

manually created. In order to save on computational time it was decided to use

the mid-tide ten minute timex images. This introduced difficulties as the time-

steps images were sampled on varied. This issue was overcome with the

weighting scheme during calibration as outlined in the methodology (see section

4.5). Additional benefits that this had was there was less uncertainty due to tidal

conditions as it was being sampled at roughly a constant tide height. When

using a day timex image the tide is varied throughout the day meaning that

depending on the water level the percentage of waves breaking varies. Splinter

et al. (2011) addressed this issue by parametrising the effects the tide. This

issue was not encountered using the ten minute timex images with a single tide.

When choosing which timex image to use, the option of taking low-tide images

was also considered. Low-tide images have a significant advantage as breaker

patterns are visually more pronounced (Ruessink et al. 2009). The low-tide level

is not constant however meaning that the sand bars height changes between

tides. The solution to this is to normalise the bar locations (Alexander & Holman


78

2004) so that they are theoretically put at the same height. The choice to use

only mid-tide images meant this correction was not needed reducing the

computational time on an already computer intensive process.

The straightening of the timex image can be done using different techniques.

One method that has been employed in the past involves straightening the

image using a method by which a circle of particular radius is fitted over the

beach. These polar coordinates are then straightened to Cartesian coordinates

(Alexander & Holman 2004). This is limited in a sense it only works for a beach

where its curve is similar that to the arc of a circle. The shape of Narrabeen-

Collaroy can be seen to be more curved on the south side where there is an

embayment. For this reason the log-spiral technique outlined in the

methodology has been used.

The method outlined in Chapter 4 allowed for multiple data sets to be found

both effectively and efficiently. It was with these data sets that the PHH06,

SHP11 and ShoreFor models were calibrated and scored against each other.

Ultimately the data set enabled for the determination of which models and which

underlying assumptions best modelled sand bar recovery at Narrabeen-

Collaroy.


79

Chapter 7 – Conclusion

7.1 Summary

For over ten years the Argus camera system has been taking ten minute timex

images of the surf zone off Narrabeen-Collaroy. For the first time at Narrabeen-

Collaroy imaging techniques were applied to ten minute timex images which

were able to extract two data sets. One data set comprised of the average sand

bar position offshore. The second data set comprised of the alongshore

variability of sand bars.

Currently there is a lot of work being done to understand the recovery

processes of beaches. This work involves the development of three key models.

The PHH06 model assumes that the mean sandbar position offshore and the

sand bars alongshore variability are linked. Using a set of eight parameters this

model attempts to describe the equilibrium nature of sand bar movement

parametrically. The SHP11 model also assumes that the mean sandbar position

offshore and the sand bars alongshore variability are linked. This model is

highly complex and tries to describe sand bar movement in terms of the many

physical processes involved. The SDR15 model is a modified version of the

ShoreFor model that behaviourally describes the change in the two

dimensionality of the bathymetry in the surf zone. It suggested there was no link

between the mean sand bar position offshore and its alongshore variability.

Following this concept, the ShoreFor model was used to simulate the mean

sand bar position and sand bar alongshore variation in separate model runs.

This was the first time it was used to model the mean sand bar position

offshore. This model was compared to both the PHH06 model and the SHP11

model in their ability to calibrate to seven recovery periods at Narrabeen-

Collaroy.

The PHH06 model had the best skill at calibrating to the data sets obtained.

Despite this the models parameters suggested the system was unstable. The

SHP11 model performed with the least skill. The ShoreFor model significantly


80

outperformed the SHP11 model and scored similar to the PHH06 model. These

findings suggest that the mean sand bar position offshore and the sand bar

alongshore variability are not linked. Additionally it suggests that using

behavioural techniques are the most apt to modelling sand bar movement

during recovery periods specifically at Narrabeen-Collaroy.

In conclusion there is significant space for possible future work to investigate,

validate and improve on the findings discovered as a result of this thesis.

7.2 Future Work

Moving on from findings presented in this thesis there are multiple opportunities

for future research in the field of sand bar recovery and modelling the

movement of sand bars during these periods.

It is difficult to determine just from calibration whether the parameters are

representing true processes in the recovery process or are simply overfitting the

data set. This issue is especially important for the PHH06 model. It is unclear of

whether the model performed well due to its large number of parameters or if it

is due to some underlying relationship picked up by the parameters. To

overcome this issue it is suggested that a further look be taken at the data set.

Instead of just calibrating to each individual data set, a global set of parameters

could be taken similar to the method outlined by Splinter et al. (2011). The

global set of parameters could be calibrated with and then validated by splitting

up the recovery periods. Such an analysis would indicate whether the

hypothesis that the parameters of the PHH06 model are overfitting the data set

is correct. There is also a possibility further insight on the other models. The

SHP11and ShoreFor/SDR15 models were all previously calibrated over multiple

data sets and then validated.

A further look could be taken at the significance of the initial conditions. This

was not covered by this thesis. The resulting parameters from the calibration

process may not necessarily be the optimum parameters. By changing the initial

conditions it would better determine the accuracy of the parameters. If multiple


81

initial conditions were tested and resulted in the same parameters being

calibrated to it would suggest that these were the optimum parameters.

Further research could look into the formulation of the SHP11 model. The

model showed some level of skill at determining the mean sand bar position

offshore. The failure of this model to perform better during calibration could be

due to multiple reasons. The model may not correctly simulate the processes

involved in sand bar migration. If either the mean sand bar position or its

variability processes were incorrectly modelled the error would then affect the

linked term. As well as this it should be ensured that the data used as input into

the model correctly portrays the conditions represented at Narrabeen-Collaroy.

Finally further research can be done to look at the application of the ShoreFor

model to simulate both the sand bar position offshore and the sand bar

variability. Stokes et al. (2015) suggested that additions such as a forcing factor

(𝑟) to the ShoreFor model could result in the better simulation of the two

dimensionality of sand bars. It is possible similar additions could improve the

ShoreFor models ability at predicting the mean sand bar position offshore too.


82

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90

Appendix A

Figure 21: Recovery period data for 9 March 2005 to 9 may 2005

Figure 22: Recovery period data for 9 June 2005 to 11 October 2005


91

Figure 23: Recovery period data for 1 June 2007 to 30 may 2008

Figure 24: Recovery period data for 17 May 2010 to 27 August 2010


92

Figure 25: Recovery period data for 24 June 2011 to 23 November 2011

Figure 26: Recovery period data for 1 June 2012 to 27 January 2013


93

Figure 27: Recovery period data for 10 August 2014 to 15 October 2014


94

Appendix B

Table 9: PHH06 Parameters

A11 A12 A21 A22 B11 B12 B21 B22

Period 1 23.73 -29.28 7.66 -9.44 -15.79 11.13 -5.01 2.85

Period 2 -12.08 12.37 4.31 -4.55 24.07 29.38 -6.53 -4.77

Period 3 -13.48 14.27 2.75 -2.95 8.66 25.07 -1.63 -2.84

Period 4 -11.02 11.63 5.13 -5.45 6.60 17.47 -3.61 -5.85

Period 5 -4.46 4.51 1.18 -1.20 14.62 14.18 -3.88 -3.79

Period 6 -4.30 4.50 1.53 -1.63 9.36 11.49 -3.09 -2.94

Period 7 -18.41 19.53 -2.01 2.11 24.03 11.71 2.79 2.00

Max 23.73 19.53 7.66 2.11 24.07 29.38 2.79 2.85

Min -18.41 -29.28 -2.01 -9.44 -15.79 11.13 -6.53 -5.85

mean -5.72 5.36 2.94 -3.30 10.22 17.20 -2.99 -2.19

SD 13.91 16.17 3.12 3.66 13.51 7.29 2.97 3.33

CV 243% 302% 106% 111% 132% 42% 99% 152%

Table 10: PHH06 Parameters no boundary conditions

A B

Period 1 [−2.1807 2.47399.9882 −11.7917

] [−1.4898 4.20912.0007 −24.2550

]

Period 2 [3.2612 −3.49566.5123 −7.4478

] [−14.1120 4.5613−6.8637 −35.5951

]


95

Table 11: SHP11 Parameters

𝜶𝟏 𝜶𝟐 𝜶𝟑 𝜶𝟒

Period 1

0.172321 0.260488 0.430519 0.095577

Period 2

0.51312 0.11608 0.102462 0.043514

Period 3

0.748668 0.678133 0.019396 0.125024

Period 4

0.122241 0.336741 0.189191 0.064986

Period 5

0.137301 0.138621 6.334077 0.070592

Period 6

0.172034 0.152706 4.665791 0.087295

Period 7

0.122554 0.308266 3.165786 0.11264

Max 0.748668 0.678133 6.334077 0.125024

Min 0.122241 0.11608 0.019396 0.043514

mean 0.284034 0.284434 2.129603 0.085661

SD 0.247 0.194 2.595 0.028

CV 87% 68% 122% 33%

Table 12: ShoreFor parameters

𝝀𝟏 𝝀𝟐 𝝓𝒙 𝝀𝟑 𝝀𝟒 𝝓𝒂

Period 1 -133.529 -7.77E-07 10 -5.8652 -8.92E-08 40

Period 2 -54.9482 -2.13E-06 1 -14.7261 -1.02E-07 50

Period 3 -17.8335 -5.89E-07 75 -4.8807 -7.7199e- 180

Period 4 -19.8221 -9.10E-07 20 5.9175 -1.63E-07 60

Period 5 -48.0256 -1.27E-06 3 -22.4278 -1.27E-07 1000

Period 6 -29.3413 -4.38E-07 65 -5.1394 -1.21E-07 180

Period 7 18.8972 -1.29E-06 10 9.8334 -1.24E-07 55

Max 18.8972 -4.4E-07 75 9.8334 -8.9E-08 1000

Min -133.529 -2.1E-06 1 -22.4278 -1.6E-07 40

mean -40.6574 -1.1E-06 26.28571 -5.3269 -1.2E-07 223.5714

SD 47.458 5.71E-07 30.614 11.087 2.53E-08 347.763

CV 117% 54% 116% 208% 21% 156%

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