A study on the Physical Characteristics of Currents and Wave …€¦ · shallowest depths in red,...

A study on the Physical Characteristics of

Currents and Wave Climate at Ramla Bay

May 2016

Michael Petroni

A dissertation presented to the Institute of Earth Systems of the

University of Malta for the degree of Bachelor of Science (Hons) in

Earth Systems

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ii

Abstract

This baseline study investigates the nature of sea current circulation and wave

climate of the wider Ramla Bay area, specifically the significant wave height

and the wave direction, using numerical models. This study was undertaken

because no existing studies or data on the physical hydrodynamics of the area

are available. This information is unconditionally important for the input into

management decisions. Through reviewed literature, it was expected that a

cellular circulation arising from the formations of rip currents within the bay

prevail. This was thought to be the case at Ramla because of the circular

pattern of Posidonia oceanica seagrass beds in the centre of the bay. The

results showed that rip currents were not prevalent during the studied period.

The mapped sea currents were found to predominantly flow along the contours

of the coastline around the embayment. It was, however, concluded that the

occurrence of strong rip currents, should not be excluded as a possibility during

the winter period when strong wave conditions occur. Data from the SWAN

model for wave direction was found to approach the coast predominantly from

the North East direction. Signifying possible accumulation of sediments on the

west side of the embayed beach. Wave direction was also observed to have a

positive relationship to the ensuing current direction but were found to be

statistically insignificant. The significant wave height wave was also found to

be significantly larger in the winter months compared to the summer months.

Within the bay the temporal variation of SWH exhibited less fluctuation

compared to deeper waters. The SWH was also found to be strongly

associated with alterations in atmospheric pressure and showed that Ramla

Bay is powerfully protected during storm events, by drastically attenuating the

wave energy. This is an essential role when considering the dynamics of the

beach morphology, as well as the dynamics of the backshore dunes.

iii

Acknowledgements

I would like to express my gratitude for the assistance offered to me by

Professor Anton Micallef and Mr. Anthony Galea and especially Mr. Adam

Gauci for his exceptional guidance as the primary supervisor of this

dissertation.

I would also like to thank my parents for their assistance and support during

the different stages of the study.

iv

Table of Contents

Declaration of Authenticity…………………………………………………………………………………….i

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

Acknowledgements ................................................................................................... iii

Table of Contents ...................................................................................................... iv

List of Figures ............................................................................................................. vi

List of Tables ............................................................................................................ viii

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

1.1 The dynamic nature of physical coastal oceanography ............................. 1

1.2 The Study Area ................................................................................................. 2

1.3 Research Problem and Motivation of the Study .......................................... 6

1.4 Aims and Objectives of the Study ................................................................. 7

1.5 Significance ....................................................................................................... 9

1.6 Review of Dissertation ................................................................................... 10

Chapter 2 Literature Review ................................................................................... 11

2.1 Features of Embayments .............................................................................. 11

2.2 Geological Control ......................................................................................... 13

2.3 Wind ................................................................................................................. 14

2.4 Waves .............................................................................................................. 15

2.4.1 Wave Orbitals .......................................................................................... 16

2.4.2 Wave Shoaling ........................................................................................ 18

2.4.3 Wave Breaking ........................................................................................ 18

2.4.4 Wave Refraction and Diffraction ........................................................... 19

2.5 Currents ........................................................................................................... 22

2.5.1 Turbulence and Radiation Stress ......................................................... 23

2.5.2 Longshore Currents ................................................................................ 24

2.5.3 Undertow .................................................................................................. 25

2.5.4 Rip Currents ............................................................................................. 25

2.5.5 Embayment classification ...................................................................... 27

2.6 Lagrangian Measurements ........................................................................... 28

2.6.1 Drifters....................................................................................................... 29

2.6.2 Rosario-SHYFEM Model ........................................................................ 29

2.6.3 SWAN Model ........................................................................................... 31

v

Chapter 3 Methodology ........................................................................................... 33

3.1 Materials Used ................................................................................................ 33

3.1.1 Bathymetric Depth Equipment .............................................................. 33

3.1.2 Drifters....................................................................................................... 35

3.2 Data Collection ............................................................................................... 36

3.2.1 Bathymetric depth Data .......................................................................... 36

3.2.2 Drifter Data Collection ............................................................................ 37

3.3 Data Processing ............................................................................................. 39

3.3.1 ARCGIS .................................................................................................... 39

3.3.2 Bathymetric map ..................................................................................... 39

3.3.3 Drifter Data ............................................................................................... 40

3.3.3.1 Calculations .......................................................................................... 40

3.3.4 SWAN Data .............................................................................................. 44

3.4 Modelling Data ................................................................................................ 45

3.4.1 SWAN Model ........................................................................................... 45

3.5 Statistical Analysis ......................................................................................... 46

3.6 Limitations ....................................................................................................... 47

Chapter 4 Results and Discussion ........................................................................ 49

4.1 Bathymetric Results ....................................................................................... 49

4.2 Lagrangian Drifter Currents .......................................................................... 52

4.2.1 Drifter Trajectories: Current Velocities ................................................. 53

4.2.2 Drifter Trajectories: Current Direction .................................................. 55

4.3 SWAN Maps ................................................................................................... 62

4.3.1 Significant Wave Height ......................................................................... 62

4.3.2 Wave Direction ........................................................................................ 63

4.4 Time Series Analysis: Significant Wave Height ........................................ 64

Chapter 5 Conclusion .............................................................................................. 69

References ................................................................................................................ 72

Appendices ................................................................................................................ 88

vi

List of Figures Figure 1.1: Study Site boundary for which drifter tracks were recorded at

Ramla l-Hamra Bay, Gozo, Maltese Islands ................................................... 3 1

Figure 1.2: Satellite Image of Ramla Bay with the easily noticeable circular

pattern of Posidonia Oceanica seagrass beds and the presence of a

crescentic alongshore sand bar, as well as the remnants of the seawall,

marked within the red border .......................................................................... 4 1

Figure 1.3: Plan of culturally historical features present at Ramla Bay. .......... 4 1

Figure 1.4: Wind rose diagram for Malta during the period from 1997-2006.

The diagram illustrates how the Maestral winds are predominantly the most

common and relatively strongest. ................................................................... 5 1

Figure 1.5: Bar char representing values of maximum wind speed (Green)

and minimum wind speeds (Yellow) for the year of 2015 over an area within

14.375oN, 36.125oE to 14.375oN, 36.125oE. The (Red) area on the graph

shows the average wind speeds. .................................................................... 6 1

Figure 1.6: Network of Natura2000 sites in Malta, where the MT0000105

marine site encompasses Ramla Bay and much of the north-east coastal

waters of the Maltese Islands........................................................................ 10 1

Figure 2.1 : The physical zonation of the coast………………………………..11 1

Figure 2.2: Profile of zones describing waves processes over a sandy

seabed. ......................................................................................................... 12 1

Figure 2.3: Transposed forward motion of water particles under the forces of

propagating energy. Arrows show orbital motion is off put slightly in the

direction of wave energy. .............................................................................. 17 1

Figure 2.4: Wave refraction occurrence as waves move into shallower water.

Notice how refraction is not complete and waves still break with some angle,

on the beach. ................................................................................................ 20 1

Figure 2.5: The process of wave refraction where incoming waves alter

direction to align their propagation parallel to the beach ............................... 20 1

Figure 2.6: Wave diffraction and refraction as wave orthogonals approach an

embayment at an oblique angle, whereby the headland has significant control

creating a shadow zone behind the headland.. ............................................. 21 1

Figure 2.7: The anatomy of a rip current. ...................................................... 26 1

Figure 2.8: Rosario SHYFEM gridded mesh consisting of triangular elements

and node, which become more refined closer to the coastline for a higher

resolution ...................................................................................................... 30 1

vii

Figure 3.1: Equipment used to measure bathymetric depths. (A) Line with

weight attached at one end, (B) Diver’s analogue pressure depth gauge, (C)

measuring tape with weighted end. ............................................................... 34 1

Figure 3.2: Diagram illustrating the components of the customised drifter and

a photo of the drifter in the field whilst recording during a calm day .............. 35 1

Figure 3.3: Histogram of the number of tracks taken on the days of fieldwork.

...................................................................................................................... 38 1

Figure 3.4: Diagram of the recorded points of a track. The distance and

bearing between each point was calculated using the haversine formulae. .. 41 1

Figure 3.5: Diagram illustrating the quadrants with 0o representing North with

the corresponding ranges of angles and the trigonometric element which

determines how the V and U components would be calculated. ................... 43 1

Figure 3.6: Point grid used in the SWAN model computations. The yellow

border highlights the Transect taken and within in it are the highlighted points

for the Time Series analysis. ......................................................................... 45 1

Figure 4.1: Bathymetric Map produced from in-situ measurements, with the

shallowest depths in red, graduating down to deeper depths in blue. ........... 51 1

Figure 4.2: Bathymetric Map produced data obtained through numerical

modelling performed by the PORG, with the shallowest depths in red,

graduating down to deeper depths in blue. ................................................... 51 1

Figure 4.3: The complete set of drifter tracks recorded throughout the data

collection period superimposed on a map with bathymetric contours

extrapolated from the bathymetric map interpolation. ................................... 52 1

Figure 4.4: First scatter plot of the measured current direction (y-axis)

against the modelled wave direction (x-axis) with outliers included. ............. 56 1

Figure 4.5: Second scatter plot of measured current direction against

modelled wave direction without outliers included. ....................................... 58 1

Figure 4.6: Scatter plot of U (top) and V (bottom) components of current

velocity and wind speed on 04/09/2015 with the U and V components of the

two points from the tracks at 19:01 (green) and 19:06 (yellow) to test the

relationship of these possible outliers. .......................................................... 59 1

Figure 4.7: Scatter plot of U (top) and V (bottom) components of current

velocity and wind speed on 04/09/2015 with the U and V components of the

two points from the tracks at 19:01 (green) and 19:06 (yellow) to test the

relationship of these possible outliers. .......................................................... 60 1

Figure 4.8: Spatial variation graph of the Significant Wave Height across the

transect. ........................................................................................................ 62 1

viii

Figure 4.9: Time series of the SWH from August 2015 to January 2016 over

point 2, with the atmospheric pressure superimposed in dashed black line. . 65

List of Tables

Table 3.1: Model of the table of the procedures used to process drifter track data. .............................................................................................................. 40 1

Table 4. 1: Table of Pearson correlation and level of significance of the relationship between wave direction and current direction with outliers. Produced in SPSS. ....................................................................................... 57 1

Table 4. 2: Table of Pearson correlation and level of significance of the relationship between wave direction and current direction without outliers. Produced in SPSS. ....................................................................................... 58

List of Appendices

Appendix A - Drifter Tracks

List of Figures

Figure A- 1: Drifter tracks on the 5th of July 2015 with wind direction from the

NNW. ............................................................................................................ 89 1


NW. ............................................................................................................... 89 1


ENE. ............................................................................................................. 89 1


NNE. ............................................................................................................. 89 1


NNW. ............................................................................................................ 89 1

Figure A- 6: Drifter tracks on the 28th of August 2015 with wind direction from

the ENE. ....................................................................................................... 89 1


the ENE. ....................................................................................................... 89 1


the NNE. ....................................................................................................... 89 1

Figure A- 9: Drifter tracks on the 4th of September 2015 with wind direction

from the W. ................................................................................................... 89 1

ix

Figure A- 10: Drifter tracks on the 5th of September with wind direction from

the SW. ......................................................................................................... 89 1

Figure A- 11: Drifter tracks on the 26th of September with wind direction from

the NNW. ...................................................................................................... 89 1

Figure A- 12: Drifter tracks on the 27th of September 2015 with wind direction

from the NNW. .............................................................................................. 89 1

Figure A- 13: Drifter tracks on the 4th of October 2015 with wind direction from

the E. ............................................................................................................ 89 1

Figure A- 14: Velocity time-series of the U (top) and V (bottom) components

of four drifters on the 5th of July 2015. ........................................................... 89 1


of four drifters on the 11th of July 2015. ......................................................... 89 1


of four drifters on the 29th of August 2015. .................................................... 89 1


of four drifters on the 26th of September 2015............................................... 89

List of Tables

Table A- 1: Table of information of drifter tracks. .......................................... 88 1

Table A- 2: Table of the selected drifter track points and SWAN model grid

points that have been selected based on closeness of between the two sets

of points, spatially and temporally. ................................................................ 89

Appendix B – SWAN Significant Wave Height Maps

List of Figures

Figure B- 1: Average Significant Wave Height for August. ................................ 89 1

Figure B- 2: Average Significant Wave Height for September. ......................... 89 1

Figure B- 3: Average Significant Wave Height for October. .............................. 89 1

Figure B- 4: Average Significant Wave Height for November. .......................... 89 1

Figure B- 5: Average Significant Wave Height for December. .......................... 89 1

Figure B- 6: Average Significant Wave Height for January. .............................. 89 1

Figure B- 7: Average Significant Wave Height for the total period of study. ... 89

x

Appendix C – SWAN Mean Wave Direction Maps

List of Figures

Figure C- 1: Average Mean Wave Direction for August. ............................... 89 1

Figure C- 2: Average Mean Wave Direction for September. ......................... 89 1

Figure C- 3: Average Mean Wave Direction for October. .............................. 89 1

Figure C- 4: Average Mean Wave Direction for November. .......................... 89 1

Figure C- 5: Average Mean Wave Direction for December. .......................... 89 1

Figure C- 6: Average Mean Wave Direction for January. .............................. 89

Appendix D – Significant Wave Height Time Series

List of Figures

Figure D- 1: Time-Series for the Significant Wave Height during August

across the five points from the transect. ....................................................... 89 1

Figure D- 2: Time-Series for the Significant Wave Height during September


Figure D- 3: Time-Series for the Significant Wave Height during October


Figure D- 4: Time-Series for the Significant Wave Height during November


Figure D- 5: Time-Series for the Significant Wave Height during December


Figure D- 6: Time-Series for the Significant Wave Height during January

across the five points from the transect. ....................................................... 89

1

Chapter 1 Introduction

1.1 The dynamic nature of physical coastal oceanography

Wave climate and the hydrodynamics of sub-surface currents vary across time

and space, particularly when migrating from deeper water to shallower waters.

Such changes can be attributed to physical and biological factors, such as

bathymetry, topography, geology and vegetation cover. The properties of wave

fields and the generated longshore currents can cause the sand-bar in an

embayed beach to migrate in the cross-shore and longshore direction over

varying time-scales, ultimately altering the beach shape and sediment balance

(Ojeda, Guillén, & Ribas, 2011). The direction of surface waves is governed

by the wind direction. To an extent, the wave direction controls the direction of

the current. However, this is subject to change due to a temporal response lag

at different depths and the physical influence of the coastal topography and

bathymetry (Röhrs et al., 2012). Currents are also generated within the

nearshore zone due to wave breaking and the loss and transfer of wave energy

(Tang, Lyu, & Shen, 2014). The formation of rip currents may be attributed to

the complex changes in wave properties that occur to the wave field

propagating within an embayment (Xie, 2012).

This dissertation examines and analyses the nature of sub-surface currents

within a small embayment. The study focuses on Ramla Bay, which is situated

on the North coast of Gozo. Observations made using satellite images of

Ramla Bay reveal a circular pattern of Posidonia oceanica in the centre of the

bay that extends some 400m from the beach (Figure 1.2). Posidonia oceanica

rely on currents for dispersing fragments for colonization and supplying

sediments suspended in shallow water to form a consolidated sandy substrata,

usually in embayments where sediments tend to collect (Di Carlo,

Badalamenti, Jensen, Koch, & Riggio, 2005). Understanding the sub-surface

current circulation and wave climate of embayments, such as at Ramla Bay,

may be useful to a set foundation towards future studies pertaining various

fields, such as bather safety, sediment transport, biological interactions and

pollutant diffusivity.

2

In operational oceanography, numerical models are used to simulate scenarios

governed by mathematics and physics to produce outcomes that best

represent what is happening in nature. Numerical models bring together data

from other models to produce these outputs, which in turn aid in better

understanding the seas and ocean from day-to-day situations to extreme

events to long term changes. With this information, predictions can be made

(Stewart, 2008). Numerical modelling was used to obtain data simulating the

wave characteristics within the bay and the surrounding area, which would not

be possible using in-situ techniques. In the analysis of results section, the

acquired in-situ data in the field by drifters is compared to the SWAN coastal

model. In particular, the Significant Wave Height (SWH) and Mean Wave

Direction (MWD), are analysed. Understanding how wave climate changes

spatially at the site and inter-annually has direct application to understanding

the forces shaping beach morphodynamics. This is essential for coastal

engineering and management.

1.2 The Study Area

The area of interest is confined to an open embayment, Ramla l-Hamra Bay,

on the North coast of Gozo (Figure 1.1), located approximately at latitude

36.062671oN and longitude 14.283805oE. Ramla Bay is characterised by an

embayed beach facing northwards. Embayed beaches develop along coasts

of discordant orientations outlined by an alternating hill and valley topography

(Castelle & Coco, 2012; McCarroll, Brander, Turner, Power, & Mortlock, 2014),

where predominant wave climate is directed against the coast. The geological

setting of the headland-bay is the product of the bands of faults that run

perpendicular to the coast as part of the horst and graben system that is typical

of the Maltese archipelago (Devoto et al., 2012; Micallef et al., 2013). Bays are

located within the graben sector (the downthrown block, wedged between two

ridges) where beaches may be formed where the mouth of the valley meets

the sea. Protruding headlands correspond to the horst ridges that have been

uplifted through tectonic faulting (Magri, 2006).

3

Figure 1.1: Study Site boundary for which drifter tracks were recorded at Ramla l-Hamra Bay, Gozo, Maltese Islands (Produced in ArcGIS).

The study area boundary for current measurements is clearly defined to

encompass Ramla Bay (Figure 1.1). However, the area covered by modelled

data may exceed this boundary area, with more extensive coverage,

encompassing the surrounding area. The surface bathymetry at Ramla is

capricious with sandy sediments covering most of the central area of the bay,

rock and boulder fields covering both sides of the bottom of the headlands and

extensive, dense Posidonia oceanica beds dominating the areas beyond the

mouth of the embayment (Figure 1.2). In conjunction with the knowledge of

alongshore variation in bar morphology and bathymetry in general; conditions

specific to Ramla Bay may result in complex hydrodynamics of the circulation

within the nearshore due the presence of the submerged ruins of a historic

defence sea wall (Figure 1.3). The wall runs the entire length of the bay but

has undergone severe degradation from interfering beach users and boating

activity (Figure 1.2).

Esri, HERE, DeLorme, MapmyIndia, © OpenStreetMap contributors, and the GIS user community

Esri, HERE, DeLorme,MapmyIndia, © OpenStreetMapcontributors, and the GIS usercommunity

.

0 250 500 750 1,000125Meters

Ramla l-Hamra Area, Gozo

0 2010Kilometers

4

Figure 1.2: Satellite Image of Ramla Bay with the easily noticeable circular pattern of Posidonia Oceanica seagrass beds and the presence of a crescentic alongshore sand bar, as well as the

remnants of the seawall, marked within the red border (Source: Google Earth).

Figure 1.3: Plan of culturally historical features present at Ramla Bay (Source: Azzopardi, 2015).

5

A study by Farrugia, Fsadni, Yousif and Mallia (2005) reveals that annually,

the Maltese Islands experience winds coming from the general North-West

direction (Figure 1.4). As indicated in Figure 1.5, there exists a pattern in the

season variation in wind speed around the Maltese Islands, whereby the

summer months are characterised by relatively weaker winds than those

during the winter months. Studies have observed rip currents to be more likely

to occur and stronger under high energy wave conditions, particularly with high

swells (Haller, 2002). Acknowledging this fact, drifters were deployed in as

many different sea state conditions possible during the data collection time

frame. Unfortunately, strong waves limited the access to Ramla Bay by boat,

during the winter months.

Figure 1.4: Wind rose diagram for Malta during the period from 1997-2006. The diagram illustrates how the North-westerly winds are predominantly the most common and relatively strongest (Source: Galdies, 2011).

6

Figure 1.5: Bar char representing values of maximum wind speed (Green) and minimum wind speeds (Yellow) for the year of 2015 over an area within 14.375oN, 36.125oE to 14.375oN, 36.125oE. The (Red) area on the graph shows the average wind speeds. (Data adapted from WERMED Interface, 2015).

1.3 Research Problem and Motivation of the Study

Understanding the dynamics of currents in shallow embayments, such as

Ramla, is essential in forecasting sediment budgets and biological processes

(Jones & Monismith, 2008). Most of the previous studies that consider the

same area have been concentrated towards beach morphology, sediment

dynamics, coastal management, tourism, etc. and have excluded a direct focus

on the physical hydrodynamic processes. Presently, there is no existing data

for the dynamics of sea currents and wave climate specific to Ramla Bay. The

research carried out in this project will serve as an addendum to the growing

compilation of such data for the Maltese Islands. Its application could be

effective in the role of management, particularly important to Ramla due to its

status as a Natura2000 site (Figure 1.6).

0

2

4

6

8

10

12

14

16

18

20

Jan Feb March April MAY JUN JUL AUG SEP OCT NOV DEC

Win

d S

peed (

m/s

)

Month

Wind Speeds over the Maltese Islands

Average Wind Speed [m/s] Max Wind Speed [m/s] Min Wind Speed [m/s]

7

1.4 Aims and Objectives of the Study

This study will attempt to answer several questions that can be categorised

into the following fields:

1. Biophysical Field

a. Do coastal currents, particularly with rip currents as the main

mechanism, play a role in shaping the circular pattern of Posidonia

oceanica beds observed in the centre of the bay during the summer

period?

2. Hydrodynamic Field

b. How do sub-surface currents behave throughout the Ramla Bay

embayment?

c. What is the nature of the wave climate of the embayment and how

does it vary over the inter-annual period?

d. What is the nature of the relationship between the incoming wave

direction and current direction within the embayment?

e. What is the relationship between the Significant Wave Height and

the atmospheric pressure?

From the biophysical aspect the hypothesis would suggest that the circulation

of currents adhere to a circular gyre pattern due to the nature of the geography

of the bay and to the meteorological and hydrodynamic characteristics,

whereby rip currents are likely to be the predominant driving force of this

circulation system. If rip currents are present, they are expected to occur as

headland rip currents i.e. on the sides of the headlands rather than in the centre

of the bay.

For the field of hydrodynamics, it is hypothesized that the general pattern of

current flow in absence of rip currents would exhibit an alongshore flow parallel

to the coastline and contours. The shallow water processes which alter wave

characteristics, whereby the wave heights increase and the velocity of the

wave orbitals decreases. Therefore, it is hypothesized that weaker currents

measured will be produced within nearshore zone of the bay, where there is

lower energy due to increased dissipation of wave energy due to breaking,

compared to currents in deeper portions of the bay.

8

The wave climate is expected to vary between the calmer summer period and

the high energy winter period. The average direction of the incoming wave field

is suspected to approach predominantly from the north-west direction and

ultimately re-orientate within the bay to be parallel to the beach, due to the

physical control of the embayment geography. The relationship between wave

direction and sub-surface currents should be proportional for poorly stratified

waters. However, because of complex dynamic processes, especially in the

surf-zone, there may be some contradictions to this hypothesis.

It is also hypothesised that the significant wave height (SWH) would be greater

during the winter months and have a larger range of variation between deeper

and shallower water, than would be exhibited in the summer months.

Furthermore, it is suspected that climate has a strong influence on the

behaviour and nature of the SWH. Periods of low atmospheric pressure storm

events would result in accentuating conditions of SWH relative to normal

conditions.

The aim of this study is to develop an understanding of the hydrodynamic

nature concerning the current circulation system and characteristic of the wave

climate present within Ramla Bay, Gozo. The study on wave climate will cover

a six month period between August 2015 and January 2016 (due to the

availability of data) and between July 2015 and October 2015 for current flow

measurements, due to time restraints. Tangentially, it is of additional interest

to conduct a simple bathymetric survey of the bay as a baseline to review the

extent of bathymetric control of mean flows.

The objective is to collect in-situ data on current flow within the defined

boundaries of the study area at Ramla Bay using GPS tracked drifters to

measure sub-surface currents 1m below sea level. The in-situ data is to be

then compared with the modelled output from Rosario-SHYFEM coastal model

for validation. Concurrently, modelled data for wave characteristic produced in

the SWAN model will be statistically analysed to observe the time variance

spatial evolution across the bay. Also, the wave direction will be statistically

correlated to the direction of current flow obtained from drifter measurements

to analyse the relationship between the two parameters. The scope is not to

study the direct biological processes related to the Posidonia oceanica but the

9

physical means by which the biological components may be influenced by local

currents. Furthermore, because of certain limitations and restrictions, the study

could only be focused on a few selected physical parameters, namely, current

direction and speed, wave direction, significant wave height and to a lesser

extent depth and wind. All the raw data collected throughout the study will be

compiled and be made available for future use in other studies.

1.5 Significance

Similar studies on currents, for validating numerical models using empirical

data have been carried out elsewhere in the past, with particular interest on

near-shore circulation and rip currents. However, in Malta, information on the

nature of currents and the influence they exert on the changing environment,

is lacking. Coastal currents, especially those circulating within embayments are

coherent to studies pertaining to sediment transport, the dispersion of

pollutants discharged into the marine environment (Spydell & Feddersen,

2012) and public safety.

Coastal surveyors interested in understanding the evolution the morphological

alterations of the coast, require surveys on hydrodynamic nature and wave

climate of an area and how these also change in time, due to natural or

anthropogenic causes (Inukai, Kuroiwa, Matusbara, & Noda, 2001). More

importantly, at the EU level of management of the marine environment comes

the Marine Strategy Framework Directive (MFSD), accompanied by an

extrinsic link to the NATURA 2000 network (Figure 1.6) and Habitats Directive.

The remnant sand dune systems in the backshore of the embayed beach at

Ramla has recently been observed by the Gaia Foundation, who is responsible

for the management of the area, to migrate towards the sea (A. Micallef,

personal communication, April 20, 2016). This suggests the interplay between

aeolian and wave dynamics altering the beach state, whereby it is possible that

more sediment is accreting to allow for dune migration. This is entirely

speculative as no studies have been undertaken for the area. Nevertheless,

this underlies the importance and relevance of this dissertation as a holistic

source for other studies.

10

Figure 1.6: Network of Natura2000 sites in Malta, where the MT0000105 marine site encompasses Ramla Bay and much of the north-east coastal waters of the Maltese Islands (Source: European Environmental Agency, n.d.). (European Environmental Agency, n.d.).

1.6 Review of Dissertation

In the second Chapter of the dissertation, the compilation of scientific literature

studied on the subject, pertaining to the physical processes of current

formation, wave characteristics and fluid dynamics, will be discussed. The

methods and equipment in oceanographic studies are also discussed. Chapter

three explains the materials used, as well as the methodology undertaken, from

field work to data processing to analysis and the limitations encountered during

the length of the study. The penultimate chapter discusses the results acquired

and the discussion interpreting results. The interpretation makes the link to the

hypotheses and literature reviewed and answers the research questions. The

conclusion outlines the outcome of the project and the significance of the

dissertation to answering the question.

11

Chapter 2 Literature Review

The Literature Review discusses the research conducted in previous studies.

The literature analysed relates to the physical mechanism of the formation and

relationship of waves and currents, particularly within the nearshore zone,

where more complex hydrodynamic processes take place. Also discussed, are

the operations of physical oceanographic research, directly conferring to the

numerical models used in this dissertation.

2.1 Features of Embayments

Embayments are ubiquitous along banded regions of valleys and hills at the

coast; innately identifiable by the curvature of embayed beaches and

accompanying headlands (Castelle & Coco, 2013; Daly, 2013). The general

and simplified profile of any beach will include the swash zone, the surf zone,

the nearshore zone and offshore zone (Figure 2.1).

Figure 2.1 : The physical zonation of the coast (Source: Davidson Arnott, 2009).

The nature of currents and waves changes as they propagate towards and the

coast, whereby the influencing topography and the geology of the coast, are

12

major contributors in deciphering how waves and currents change. Therefore,

it is required to understand not only the wind and wave climate of a study area

but also, the geography of the coast where interactions take place (Conley et

al., 2008).

Figure 2.2: Profile of zones describing waves processes over a sandy seabed (Source: Davidson Arnott, 2009).

Within the surf zone of sandy/shingle beaches, longshore sandbars form

parallel to the shoreline (Figure 2.2). In some cases, crescentic sand bars form.

Sand bars are usually rhythmic and vary seasonally in shape (van Enckevort,

2004). The hydrodynamic influence of the wave climate and subsequent

currents, constantly alter the sand bar and ultimately the features of the sandy,

unconsolidated bathymetric substratum (Price, Ruessink, & Castelle, 2014).

The persistence and changes in hydrodynamic processes are far more variable

within a shorter timeframe compared to morphological processes, which span

longer time scales (Blondeaux, 2001). Storms have a greater capacity to

drastically change a shingle bedform than the usual nearshore hydrodynamic

processes. The morphological profile configuration is reset after major storms

along the coast (Schwartz, 2012). The sand bars are essential for initiating the

wave breaking process, by which the dynamics within the surf zone are

characterized (Van de Lageweg, Bryan, Coco, & Ruessink, 2013). At Ramla

Bay, the sandbar was found to disappear between fluctuating summer and

winter conditions (Azzopardi, 2015). Masselink and Hughes (2003) clarify that

13

the migration of the sand bar infers that the depth of closure and the wave base

also vary accordingly (see Section 2.4.1).

The swash zone refers to the ranging levels of the wave run-up and run-down

along the sloping beach face (foreshore); this is partially where sediment is

uplifted and where wave induced currents are formed (Bakhtyar, Barry, Li,

Jeng, & Yeganeh-Bakhtiary, 2009). Consequently, the hydrodynamic

characteristics of the narrow swash zone alter the morphological shape and

profile of the foreshore seasonally (Larson, Kubota, & Erikson, 2004). These

alterations are largely dependent on the frequency and magnitude of

nearshore waves, the sedimentology of the beach and the general beach

morphology (Vousdoukas, Velegrakis, Dimou, Zervakis, & Conley, 2009).

Subsequent cross-shore currents deliver the suspended material seaward,

where it may be circulated within the bay by alternative currents within the

semi-closed cell of the embayment. This results in erosion of the beach

(Baquerizo, Lozada, Mendoza, & Silva, 2010).

2.2 Geological Control

Geological features are capable of controlling the distribution of wave energy

and therefore the characteristics of the wave spectrum and currents. In the

case of embayments featuring headlands and decreasing depth of the

seafloor, attenuation of the energy of waves propagating towards the coast

occurs (McCarroll et al., 2014). Other than the configuration and shape of the

coast, the surface roughness of the sea bottom will play a major role in the

behaviour and velocity of bottom currents that explicably alter subsequent

current flows above it (Signell, Beardsley, Graber, & Capotondi, 1990). Drag

and surface roughness have greater effects on waves and current dynamics

within the surf zone (i.e. within the wave base zone) rather than outside it.

Bottom roughness is inheritably temporally variable due to modifications in

14

bedform morphology and succession of vegetation growth (Feddersen,

Gallagher, Guza, & Elgar, 2003).

The generalised beach classification parameterisation techniques do not

embody the circumstances undergone with embayed beaches due to the

inherent control and influence that headlands have on nearshore current

circulation (Loureiro, Ferreira, & Cooper, 2013). The topography of headland-

bays coerces the flow of coastal longshore currents, as well as giving rise to

small scale currents localised to an embayment that in some cases give rise to

cellular circulation (Loureiro, Ferreira, & Cooper, 2012).

The Posidonia oceanica seagrass meadows, which are densely abundant

beyond the mouth of the bay, influence wave climate and hydrodynamic

characteristics within the bay by attenuating wave energy. The physiology of

the seagrass meadows, with their flexible and sometimes short aboveground

biomass reduces their capacity to attenuate wave energy, compared to other,

more rigid biomass. However, seagrass meadows compensate by altering the

erodibility of the seabed, making it more consolidated by sediment accretion

(Christianen et al., 2013). Therefore, the morphology of the seabed is more

susceptible to alteration by hydrodynamic processes where it is bare and

unconsolidated. Borg, Rowden, Attrill, Schembri and Jones (2009) studied the

Posidonia oceanica cover at Ramla Bay. They found that the seagrass

coverage is progressively increasing, when contrasted to fragmentation,

despite the high exposure. Evidently, the consolidation of the sandy substrata

is likely to increase, thus the hydrodynamics of the area may be altered due to

this, in the future. Also, they assert the need to understand the localised

hydrodynamic characteristics and wave climate, so as to study the coverage

and fragmentation of Posidonia meadows, as well as other benthic habitats.

2.3 Wind

Numerous forces are responsible for the movement of a body of water. The

oceans are mainly set in motion by surface winds, predominantly by storms in

open waters (Davidson-Arnott, 2009; Klemas, 2012). Wind applies a surface

pressure, which in turn alters the surface elevation of the water, forming waves.

15

For sub-surface currents to be generated, there must be a downward

transmission of momentum from the surface by means of Reynolds Stresses.

Reynolds stress occurs, when the horizontal movement of water at the surface

is out of phase with the surface elevation. Without this process the only method

for momentum transfer down the water column is by turbulent diffusion

(Nielsen, Callaghan, & Baldock, 2011). The veering of surface currents can be

observed with changes in wind direction. However, there tends to be a lag in

veering of sub-surface and deeper currents that are considered to be wind

driven (Drago, 1980).

The wind stress above the sea surface, eventually results in the transfer of

momentum in the form of surface current flow, which can be expressed to be

linear, in essence of a uniform eddy viscosity (Chang, Chen, Tseng, Centurioni,

& Chu, 2012). The height and energy transferred to surface sea waves is

dependent on the wind velocity and duration for which the wind blows in the

same direction (Camilleri, 2012). Concurrently, wind shears have the capability

of dissipating wave energy and therefore current flow (Ardhuin & Jenkins,

2006). Although strong high energy waves in the Mediterranean may occur,

lacks the vast expanses of ocean for a significantly large fetch to develop and

so, is generally lower energy waves compared to coasts surrounding open

ocean systems (Mottershead, Bray, Soar, & Farres, 2014).

2.4 Waves

Waves have considerable effects on the mean flow of water; affecting the

pressure and shear drag (Sullivan, McWilliams, & Moeng, 2000). The

interaction between the atmosphere and sea surface, induces a flux by the

transfer of most of the wind energy and momentum to waves. Wave breaking

results in dissipation of energy, thereby inducing further fluxes in momentum

and turbulent kinetic energy from the wave to surface and sub-surface

boundary layers (Hong & Eng, 2003; Paskyabi & Fer, 2014). Turbulent mixing

is enhanced by the energy flux from wave breaking (Gemmrich & Farmer,

2004), whilst accelerated mean flow is the outcome of stress adhered by the

momentum flux. In saturated sea states, energy and momentum flux that are

16

transferred to wave fields, are balanced by the dissipation of energy from white

capping/wave breaking (Weber, Broström, & Saetra, 2006). If energy is not

dissipated, than momentum and energy is advected by waves and stored

across the wave field (Röhrs et al., 2012).

Haslett (2009) describes the relationship between the surface wind speeds and

the resulting growth in wave height. Wave height is directly proportional to the

square of wind velocity. Sometimes, it is best to obtain a single calculated

measurement for wave height that is representative of the state of the sea at a

point in time. To do this, oceanographers use the Significant Wave Height

(SWH), H1/3, which is the mean of the highest one third of all waves at that point

in time (Brown et al., 1999; Camilleri, 2012). Altunkaynak, ASCE and Özger

(2005) assessed the spatial variation of SWH and found that the climatic

conditions have a powerful influence on the nature of the SWH. They also

explain the importance of SWH in representing and determining the wave

energy. A study on the physical characteristics of the wave climate was

conducted in 2003 for the Maltese Islands. The SWH was the main parameter

measured. However, the scale of the study, using numerical models,

encompassed the entire Maltese Islands and so, the resolution was quite low.

The closest point of model SWH to Ramla was 10km north east of the islands.

The study found that the general 10% of the exceedances of SWH of the year

was below 1.5m (Scott Wilson Kirkpatrick and Co. Ltd, 2003).

The wave height increases with the intensification and duration of onshore

winds. Ultimately waves tend to break further outside the surf zone (Aagaard

& Hughes, 2010). Determining the inter-annual variations in wave climate can

be done by analysing a group of parameters, namely the significant wave

height and the mean wave direction. This understanding can be used to

describe the spatial distribution of wave energy (i.e. wave spectrum) at varying

frequencies and subsequently, describe the wave systems of different sea

states of a given area (Sanil Kumar & Anjali Nair, 2015).

2.4.1 Wave Orbitals

17

Particles at the surface, where waves are present, exhibit a circular orbital

movement; with the highest velocities and forward movement along the crest

and the lowest velocity and backwards movement at the trough (Figure 2.3).

Waves of increasing amplitude, experience an accentuation of this effect. A

net flow is produced , whereby the particles flow in the direction of the travelling

wave (Lentz & Fewings, 2012; Monismith, Cowen, Nepf, Magnaudet, & Thais,

2007; Simpson & Sharples, 2012). This was coined the Lagrangian current,

which is also referred to as the Stokes Drift. Surface drifters are designed to

measure this drift. This orbital effect is transposed down the water column, with

gradually shrinking orbitals succeeding further down. The bottom boundary

layer, present above the seabed, transforms circular orbitals into elliptical orbits

(Simpson & Sharples, 2012). Wave orbitals attenuate down the water column

to a depth equal to half the wavelength – referred to as the wave base. When

the wave base delineation is approached, waves begin to interact with the

seabed. The wave base can be used to define the depth of closure, which

marks the “boundary between the upper and lower shoreface…and can be

used to infer a seaward limit to significant cross-shore sediment transport”

(Masselink & Hughes, 2003, p. 196; Nicholls, Larson, Capobianco, &

Birkemeier, 1998).

Figure 2.3: Transposed forward motion of water particles under the forces of propagating energy. Arrows show orbital motion is off put slightly in the direction of wave energy (Source: “Ocean in Motion: Waves and Tides,” n.d.).

18

2.4.2 Wave Shoaling

Waves propagating towards the coast, i.e. travelling from deep waters to

increasingly shallow water, undergo shoaling (Benetazzo, Carniel, Sclavo, &

Bergamasco, 2013; MacMahan et al., 2011; Newell, Mullarkey, & Clyne, 2005).

Shoaling accounts for the changes of wave properties that eventually lead to

breaking. These changes are characterised by decreasing wavelength, speed

and wave period, which result in increasing wave height and therefore

increased wave steepness (Davidson-Arnott, 2009). The development of

shoals creates alterations in the wave breaking process (Idier, Falqués,

Ruessink, & Garnier, 2011). The interaction of, incoming and outbound, long

waves with shoaling short waves, results in a flux of energy depending on the

phase (Van Dongeren, Svendsen, & Sancho, 1996). Near bottom velocities of

wave orbitals vary greatly and rapidly when waves begin the shoaling process

(Lentz & Fewings, 2012).

2.4.3 Wave Breaking

Wave breaking in the nearshore is the main mechanism for generating physical

processes leading to the set-up and wave-induced currents, including

longshore, rip and undertow currents (Smit, Zijlema, & Stelling, 2013).The

scale of the many different types of motions resulting from breaking waves can

range from large vertical motions to minor turbulence, as a means of releasing

the waves energy (Lubin, Glockner, Kimmoun, & Branger, 2011).

Wave-current interactions have a mutual effect on one another, as waves

contribute to the formation of currents, whilst concurrently currents have an

effect on waves (Benetazzo et al., 2013). This relationship shows that currents

exert the greatest influence when the direction of the current flow opposes that

of the propagating waves. Along shore currents flowing within a shallow

embayments will behave differently depending on the wind stress (Jordi,

Basterretxea, & Wang, 2011), which may give rise to waves or no waves. The

presence of surface waves propagating to shallower water, omitting the area

19

within the surf zone, will drastically reduce the magnitude of the underlying

wind driven sub-surface currents due to frictional drag between the wave-

current interaction (Signell et al., 1990).

2.4.4 Wave Refraction and Diffraction

When the incident wave front travelling from deep water to increasingly

shallower water at an angle to headland-bay coasts, wave refraction occurs

(Kusky, 2008). A physical property of water waves, dictates that wave speed

and wavelength decreases as water depths decrease, whilst the wave height

increases (Pickard & Pond, 1983). Conveyed by Snell’s Law, as one end of

the wave interacts with a shallower depth first, forcing it to decrease in speed,

the other end of the wave continues to travel at the initial speed. As a result,

the wave diverts towards the normal of the beach marked between the deeper

and shallower depths (Figure 2.4). When wave refraction occurs, wave fronts

can be observed to approach shallower water at nearly parallel directions to

the beach (Garrison, 2013; Godin, 2009).

20

Figure 2.5: The process of wave refraction where incoming waves alter direction to align their propagation parallel to the beach (Source: Waugh, 2009). (Waugh, 2009).

Figure 2.4: Wave refraction occurrence as waves move into shallower water. Notice how refraction is not complete and waves still break with some angle, on the beach. (Reproduced from Unit 5: Tsunami Propagation, n.d.).

21

The occurrence of wave orthogonals approaching the headland-bay

perpendicularly, is not a good representation of the general wave climate. For

most of the year, waves approach at an angle. When incident waves approach

an embayment obliquely, the headland controls the direction of the incoming

wave field. By the process of diffraction, coupled with refraction (Yasso, 1965),

wave orthogonals bend around the headland (Davis Jr & Fitzgerald, 2004;

Lutgens & Tarbuck, 2012) and because depth is continuously changing, wave

crests closer to the headland are diverted around it, whilst the further wave

continue moving in their initial direction (Figure 2.5), are subject to refraction.

Diffraction results in variation of wave heights along the incident wave front

(Svendsen, 2006). The outcome gives rise to a shadow zone (Figure 2.6); a

sheltered area where waves are greatly attenuated (Holthuijsen, 2007;

Woodroofe, 2002). It can also occur throughout the water column by means

energy dissipation of bottom waters that interact frictionally when variations in

seabed covers appear, such as seagrass beds on sandy bottom (Dalrymple,

Hwang, & Kirby, 1984).

Figure 2.6: Wave diffraction and refraction as wave orthogonals approach an embayment at an oblique angle, whereby the headland has significant control creating a shadow zone behind the headland. (Source: Woodroofe, 2001).

22

This effectively creates spatial variability in the wave breaking process in the

alongshore direction, such that the shadow experiences low energy waves, as

opposed to the unaffected portion of the shore that receives higher energy

waves. This in turn creates alongshore gradients in radiation stresses

(Aagaard & Vinther, 2008), thus driving longshore currents within the surf zone.

Breaking waves are characterised by two portions, the bore and the roller

region. The bore is the state of the wave after breaking, followed by the roller.

The roller is the surging remnant after the wave has broken whilst approaching

the shore. The vertical turbulence velocities, as well the kinetic energy,

decreases with depth from the trough of the breaking waves. The horizontal

velocities, however, are relatively uniform with depth (Lin & Liu, 1998).

Approaching waves breaking, most commonly at an angle to the shore,

exemplify wave energy dissipation, ensuing a highly turbid region. In this final

stage of the incident waves transformation, momentum is transformed into

currents (Peregrine, 1998).

2.5 Currents

As elaborated in previous sections, currents at and near the surface, are driven

by the wind stress and by Stokes Drift resulting from waves. In deep waters,

the surface current response to wind can be considered to be inertial.

Therefore, there is a delayed lag response between wind and surface currents

(Stewart, 2008). The lag explains why currents can be observed traveling in

different directions to the overlying wind (Capodicasa, Foti, & Scandura, 1991;

Mao & Heron, 2008). The scale at which wave-induced currents flow,

generated in the nearshore, are considered to be unaffected by the planetary

forces, such as the Coriolis force (Jenter & Madsen, 1989; Ozkan-Haller, 2014;

Tang et al., 2014).

In deeper waters, physical layers within the water column can be delineated

from one another by a shifting angle of current direction. This is known as the

Ekman spiral (Garrison, 2013). The transference of stress through the water

column is direct and so water movement follows the direction of the stress

23

applied (Lentz, 1995). Currents in the Maltese Islands are generally weak, as

they are throughout most of the Mediterranean because of the negligible

significance of tides (Basterretxea et al., 2004; Jordi et al., 2011). Drago (1980)

shows that there is a consistency with the dominant large scale current flow

around the Maltese islands in a SE direction and this consistency is disrupted

in cases of large storm events. In shallow waters of Ramla Bay, strong winds

and wind shear at the surface are the main driven of mean flow, with some

negligible influence from tidal pressure gradients, whereby there is little

stratification of currents with depth (Jones & Monismith, 2008).

2.5.1 Turbulence and Radiation Stress

Turbulence occurs due to instability by the breaking process of waves on the

shore (Tang et al., 2014), with maximum turbulence occurring within the

breaker zone and swash zone (Bakhtyar et al., 2009). Swirling vortex of fluid

describes turbulence best and exists on different scales of length and time.

Small morphological variations in the seabed are responsible for the

development of small eddies, by which horizontal convection of eddies is driven

by waves following the bore (Peregrine & Bokhove, 1999). As turbulent eddies

lose mechanical energy, they decrease to smaller scales until the dissipated

energy eventually is transformed into heat by molecular viscosity (Brown et al.,

1999; Mohsin & Tajima, 2014; Svendsen, 2006). This gives rise to augmented

diffusivity, which in turn drive fluxes in momentum and energy that is referred

to as stress (Celik, 1999; Kraichnan, 1976). The eddy viscosity in association

with this turbulence, accounts for the process leading to the production,

advection and dissipation of turbulent flow in the surf zone (Inukai, Kuroiwa,

Matusbara, & Noda, 2001; Mohsin & Tajima, 2014).

Variation in radiation stress within the nearshore is a requirement for

generating currents, whether cross-shore or alongshore. This radiation stress

is the product of the net momentum flux forced by the dissipation of breaking

waves (Newell et al., 2005). The incident shoaling and breaking waves create

a bi-directional variation in the mean sea level, referred to as the set-up and

set-down. On open coasts, when incident waves approach the shore

24

perpendicularly, the radiation stress gradient is balanced by the set-up/set-

down variation (Stive & Wind, 1982) and so no longshore currents are created

(Yu & Slinn, 2003). This does not apply to headland embayments because of

the array of alterations in wave dynamics discussed before. When there is

differential breaking along the shore, then pressure and radiation stress

gradients develop within the surf zone. This is responsible for the momentum

transfer from waves to currents (Peregrine, 1998). Turbulent shear stress is

the mechanism by which the differences between radiation stress gradient and

pressure gradient (uniform with depth) are balanced, in turn driving currents

(Ting & Kirby, 1994). There is a linear decrease in the turbulent stress down

through the water column until reaching the bottom boundary layer (Cox &

Kobayashi, 1996), thusly disrupting the no-slip characteristics of the bottom

boundary layer surface (Garcez Faria, Lippmann, Stanton, & Thornton, 2000).

2.5.2 Longshore Currents

Longshore currents form within the nearshore zone. The mechanism driving

longshore currents, is the variation in radiation stress and wave set-up/set-

down along the shore, which are caused by variance in wave breaking along

the surf zone (Idier et al., 2011). As discussed throughout this Chapter,

differential wave dissipation concurs with (Johnson, 2004):

1. Topographic and bathymetric variations

2. Spatially varying approaching wave fields

3. Approaching high frequency surface waves with low frequency waves,

such as edge waves. This is related to effects of shoaling as described

in the previous section.

4. Wave-current interactions within the surf zone

This forms areas of high energy dissipation that produce a resultant mean flow

towards the zone low energy dissipation (Smith, 1993), brought about by

breaking waves of relatively smaller breaking wave heights. Longshore current

generation occurs exclusively in the surf zone; with maximum speeds occurring

in the middle of the surf zone (Davis Jr & Fitzgerald, 2004). These flows can

25

move beyond the nearshore zone and flow along the periphery of winding coast

(i.e. around headlands). Thus, follow the contours of the coastline. The

generated longshore currents, with speeds ranging from 0.3 – 1 ms-1, exhibit a

proportional relationship with the angle that the propagating wave field makes

with the shoreline and the orbital velocities of waves once within the breaker

zone (Brown et al., 1999).

2.5.3 Undertow

Undertow currents commonly occur under high energy wave conditions and/or

when there is the absence of a longshore bar. They result from the landward

moving water by waves that pile up and elevate the set-up. Momentum balance

is then achieved by means of seaward moving currents below the surface

moving water, i.e. concentrated close to the seabed (Davis Jr & Fitzgerald,

2004; Scandura, 2011). Balance is maintained by returning water by landward

moving waves above (Yu & Slinn, 2003). The set-up is responsible for vertical

imbalances in momentum flux and pressure gradient – the foundation for

driving undertow (Cox & Kobayashi, 1996). Ohlmann, Fewings, & Melton

(2012), used drifters to study how current velocities moving shoreward change

with decreasing depth. They found that under weak winds, drifters decelerated

as they move onshore. This decrease in velocity is brought about by seaward

moving undertow. Their study, however, was conducted on an open system

coast, characterized by long beaches and wide surf zones.

2.5.4 Rip Currents

Rip currents are jets of narrow, relatively fast flowing currents towards the sea

that occur throughout much of the world’s beaches (McCarroll et al., 2014;

Winter, van Dongeren, de Schipper, & van Thiel de Vries, 2014). Rip currents

are considered a danger to beach users, where numerous deaths are

associated with drowning when caught up by these relatively strong currents

(Castelle et al., 2014). The momentum flux generated by incoming breaking

waves within the surf zone creating an imbalance between the inside and

26

outside of the surf zone. The conservation of mass requires there to be balance

and this balance is brought about by the creation of currents that flow seaward

(Johnson, 2004). Topographic and bathymetric variations, particularly with

respect to variations in sand bar morphology can cause this variation in wave

breaking (Miles, Guza, Elgar, Feddersen, & Ruessink, 2001). Where breaks in

sand bars are present, wave breaking will not occur as much (locally) in that

portion, as it would over the rest of the bar. The piling of water behind the bar

will seek to maintain balance by flowing through the break, outwards to sea as

a rip current through the funnelled past of least resistance (i.e. the break)

(Murray & Reydellet, 2001).

Two types of rip currents can be associated with headland-bay embayments;

topographic and mega rips (Macmahan et al., 2009). The intensity of the rip

currents and longshore currents are inversely related, in respect to the factors

governing intensity, which are wave height, wave direction and directional

spread (Dusek & Seim, 2013). Storm events may lead to the formation of mega

rips, which are intensified versions of topographically controlled rip currents

that can cause severe beach erosion (Short, 2010).

Figure 2.7: The anatomy of a rip current (Source: Johnson, 2004).

27

A rip current consists of three integral parts (Figure 2.7). Rip currents develop

by means of feeder current. Feeder current refer to alongshore currents

generated within the surf zone as discussed before. Their existence disrupts

the longshore moving flow of alongshore currents (Johnson, 2004). Obtaining

data sets acquired in the field on rip current measurements is difficult because

of the shallow depths in which they originate and their transient nature, making

it hard to know where and when to take measurements (Haller, 2002). A fully

comprehensive computation of the complex circulation dynamics of rip currents

is plausible with numerical modelling, yet may require bathymetric and wave

data, which may not always be obtainable (Leatherman & Fletemeyer, 2011).

2.5.5 Embayment classification

Masselink & Short (1999) recognised the profound difference in hydrodynamic

circulation between an open and long beach coastal system with that of an

embayment, characterized with headlands or rocky outcrops. They designed a

formula to express this relationship. This design is mainly directed towards

classifying the degree of embaymentisation with the presence of headland rip

currents in relation to the incident wave field (Razak, Dastgheib, Surydai, &

Roelvink, 2014).

As proposed by Castelle & Coco (2012), certain issues arise with the original

design, as it disregards the fact that the wave energy dissipation will be less at

the headlands compared to the attenuating effect the sea bottom has on wave

energy as waves approach shallower depths (Garrison, 2013; Pickard & Pond,

1983) Therefore, for embayments receiving low to moderate energy waves

characterised with prominent headlands, the scaling parameter could be

deceptive.

Three types of embayment circulation may occur. Normal circulation typifies

open beaches, having no headlands or barriers (Razak et al., 2014). The

second type of circulation flow is described as cellular circulation. The

occurrence of cellular circulation is signified by strong headland control, in

which rip currents are formed at either side of the embayment or in less likely

28

instances, in the centre. This type of circulation typically results in the formation

of a small gyre that circulates within the confines of the bay. This has

consequential implications on the migration of the sand bar but also beach

shape (Castelle & Coco, 2012; Daly, 2013; Razak et al., 2014). Normal type

circulation can also be possible in embayments with headlands where the size,

length and shape of the beach is large enough for currents and waves not to

be powerfully affected by interfering topography. This may result in numerous

rips occurring across the beach. This is referred to as transitional circulation,

which may be assumed to be an intermediate of the prior two (Castelle & Coco,

2012).

The significance of the embayment characterisation and the hydrodynamic

processes involved is important when applied to integrated coastal zone

management, by the concept of sediment cells. Sediment cells can be

described as “spatially discrete areas of the coast within which marine and

terrestrial landforms are likely to be connected through processes of sediment

exchange… commonly identified as self-contained where little or no sediment

movement occurs across cell boundaries” (Stul, Gozzard, Eliot, & Eliot, 2015,

p. 5). This coastal cell concept aims to understand the sediment budget of a

closed system, in which studies on the dynamics of currents and wave climate

within a cell need to be understood, not only spatially but over short to long

term periods for future management of the coastal area (Montreuil & Bullard,

2012; Sedrati & Anthony, 2014).

2.6 Lagrangian Measurements

In operational oceanography, currents are measured by either Eularian or

Lagrangian methods. The Eularian approach primarily involves measuring

current vectors from a fixed point on the sea bottom, making it possible to

determine currents distribution and magnitude through the water column

(Sharples & Simpson, 2012). The Lagrangian method does the opposite. The

Lagrangian method tracks the current vectors freely, untethered to the seabed

by means of drifters that flow with the current on the sea surface or sub-surface

(Emery & Thomson, 2004). A drifter deployed in proximity to rip currents should

29

theoretically follow a similar trajectory. This has been recorded to occur in the

field by Schmidt, Woodward, Millikan and Guza (2003), when a drifter was

deployed within the surf zone of a rip channelled bay. Lagrangian

measurements from drifters are subject to the net movement of sub-surface

water movement in the direction of the travelling wave field, which is caused

by the underlying physics of wave orbitals (Capodicasa et al., 1991; Sharples

& Simpson, 2012), known as the Stokes Drift.

2.6.1 Drifters

Drifters can be simple in design and cheap, equipped with a low cost GPS

logger and be just as effective (MacMahan, Brown, & Thornton, 2009). The

accuracy of the equipped GPS can vary significantly depending on whether it

is differential or non-differential. Non-differential GPS trackers are more

accurate than the former, however, they are much larger. The added bulk

would, consequently, impair the drifter’s abilities, particularly when measuring

within and outside the surf zone (Sabet & Barani, 2011). A description of the

custom made drifter used in this project is provided in the Methodology

Chapter.

2.6.2 Rosario-SHYFEM Model

The SHYFEM model (Shallow Water HYdrodynamic Finite Element Model) is

a two-dimensional vertically integrated model, which solves shallow water

hydrodynamic equations of coastal areas, in which time integration is resolved

using a semi-implicit algorithm (Dinu, Bajo, Umgiesser, & Stănică, 2011). The

Rosario-SHYFEM model is a recently developed model specified to the

Maltese Islands. Consequentially, there is a lack of related literature. The

SHYFEM model is governed by the shallow water equation (Equation 2.1).

30

Equation 2.1

𝜕𝑈

𝜕𝑡+ 𝑔𝐻

𝜕𝜁

𝜕𝑥+ 𝑅𝑈 + 𝑋 = 0

𝜕𝑉

𝜕𝑡+ 𝑔𝐻

𝜕𝜁

𝜕𝑦+ 𝑅𝑉 + 𝑌 = 0

𝜕𝜁

𝜕𝑡+

𝜕𝑈

𝜕𝑥+

𝜕𝑉

𝜕𝑦= 0

Where, ζ, is the water level, g is the acceleration due to gravity; t, is time; H is

the depth of water. X and Y are substitutable components for other elements,

such as wind stress or non-linear terms. The U and V components represent

the transports in the horizontal dimension (x,y), which can be extracted from

the U and V velocities in the vertical dimension by means of integration (Desira,

2015; Umgiesser, Canu, Cucco, & Solidoro, 2004). Finite elements of the

model refer to an unstructured numerical grids that are generated by an

automatic mesh generator. The Rosario-SHYFEM model applies a triangular

finite element grid that is defined by nodes (Figure 2.8). The grid becomes

more refined closer to the coastline, resulting in a higher resolution to be

obtained where the variation in hydrodynamics is more complex. The depth is

specified for each element, with the velocities of the currents quantified at the

centre and the water level prescribed at the nodes (Dinu et al., 2010;

Umgiesser et al., 2004).

Figure 2.8: Rosario SHYFEM gridded mesh consisting of triangular elements and node, which become more refined closer to the coastline for a higher resolution (Source: Produced by PORG).

31

SHYFEM is also assembled by a number of models and equations which

compute different physical processes and features. Namely, these are wind

driven waves, wave-driven forces, wave-current interactions, sediment

dynamics, shear and frictional stresses, cohesive and non-cohesive

sediments, advection-diffusion equations, morphodynamics, amongst many

more. Respectively, these models include a hydrodynamic model, spectral

wave model, sediment transport model and bed model. When input into the

hydrodynamic model, the radiation stress gradient of the wave induced forces

produces results for the changes in wave set-up/down and correspondingly,

currents (Ferrarin et al., 2008).

2.6.3 SWAN Model

The SWAN Model is a coastal phase averaged, Eularian based model that

produces predictions of the development of energy within the wave spectrum

of waves approaching the coast (Gorrell, Raubenheimer, Elgar, & Guza, 2011;

Liau, Roland, Hsu, Ou, & Li, 2011). The third generation model, was developed

to produce outcomes for the spectrum of wave conditions under the influence

by indiscriminate wind, current and bathymetric conditions (Daly, 2013; Ris,

Holthuijsen, & Booij, 1999). The general equation (Equation 2.2) run in the

SWAN model is:

Equation 2.2

𝜕

𝜕𝑡𝑁 +

𝜕

𝜕𝑥𝑐𝑥𝑁 +

𝜕

𝜕𝑦𝑐𝑦𝑁 +

𝜕

𝜕𝜎𝑐𝜎𝑁 +

𝜕

𝜕𝜃𝑐𝜃𝑁 =

𝑆

𝜎

Whereby t, is time, x and y are the horizontal coordinates, 𝜃 is the direction

and 𝜎 is the intrinsic frequency. The action density is represented as a function

of all these parameters by means of N(𝜎, 𝜃; 𝑥, 𝑦, 𝑡). Through development of

numerical equations, it has been adapted for coastal shallow waters, so as to

simulate wave processes, such as refraction and shoaling (Ris et al., 1999).

Energy dissipation due to current and/or topographical interactions, as well as

wave breaking and bottom friction are computed. In the initial development of

the model, diffraction may have been omitted but is now possible to compute

32

by using a phase-decoupled refraction-diffraction approximation. Wave-current

interactions may be modelled to produce a more realistic output but requires

input of current information, generated from a current model (Choi & Yoon,

2011). The SWAN coastal model is run on data input from other models, such

as SCMR and SKIRON, which models wind. Therefore, if there is a deficit of

data from the component proxy models, then the data produced from SWAN

will also have data gaps.

The SWAN model in Malta has already been validated by Drago, Azzopardi,

Gauci, Tarasova and Bruschi (2012), using observational wave data collected

by the moored instruments, such as the Datawell Waverider buoy. Ideally,

highly accurate in-situ data is collected for all physical parameters (i.e. wave

climate and currents) but the long term measuring is restricted to a localised

area. Therefore, numerical models are often implemented to extrapolate data

to provide a synoptic interpretation that spans a wider spatial and temporal

range. The SWAN model has a spatial resolution of 0.001o, encompassing a

domain marked by a boundary between 14.040-14.700oE in longitude and

35.665-36.206oN in latitude (Azzopardi, 2012). The outputs of the model can

be generated in three hourly intervals, providing Significant Wave Height, Peak

Wave Period (of the variance density spectrum) and Mean Wave Direction

(Drago et al., 2012).

33

Chapter 3 Methodology

3.1 Materials Used

The field work for this project required the use of a main vessel to travel to the

location, as well as a smaller and easily manoeuvrable vessel, in order to move

around the bay with ease, to deploy and recover the drifters. A logbook was

also kept to take record readings.

3.1.1 Bathymetric Depth Equipment

A bathymetric map was produced for a more comprehensive understanding of

how the local topography and bathymetry may affect sea current flow. This

required the use of GPS application (Satellite Check by DS Apps) and a

pressure depth gauge (used by divers), which was tied to a weighted line.

Unfortunately, because the pressure depth gauge was designed as an

analogue measuring device, the readings were of a low accuracy of

approximately +/- 1m. The accuracy was found to be far higher in deeper water

than in shallower water. This was discovered when comparing the readings of

the pressure gauge with the depth sounder on the vessel (for deeper water)

and with a weighted measuring tape (in shallower water). The presence of the

waves also caused variations in the readings. A measuring tape had to be used

in shallower waters. The gauge consisted of two arms, both of which begin at

the 0m mark. One arm moves across the gauge in response to changes in

pressure. The other arm (orange) served as a marker that moved with the

response arm but remained in place at the deepest reading, even when

brought back to the surface (Figure 3.1).

34

A

B

C

Figure 3.1: Equipment used to measure bathymetric depths. (A) Line with weight attached at one end, (B) Diver’s analogue pressure depth gauge, (C) measuring tape with weighted end.

35

3.1.2 Drifters

The drifters used for this study have been custom designed for the application

of measuring surface currents. A consequence of surface water drifters, is the

inevitable influence of surface winds on the floating device. Therefore, the

design attempt to minimize this frictional interference as much as possible

(Poulain, Gerin, Mauri, & Pennel, 2009). The drifter possesses six components

(Figure 3.2). The buoyancy weight, which kept the structure of the drifter in an

upright position. The current vane is a wooden frame in the shape of a 3D

cross, which resembles the CODE/Davis drogue design. Its function is to

propel the drifter into movement by frictional drag from the surface area of the

vane. The floatation device kept the drifter at the sea surface, while a water

proof compartment was used to hold the GPS tracker. A flag was fixed so that

the drifter would be easily tracked from the vessel, particularly for retrieval. A

Figure 3.2: Diagram illustrating the components of the customised drifter and a photo of the drifter in the field whilst recording during a calm day (Source: Author).

36

1m long rope attached the current vane and the float/pole, as well as one

connecting the vane to the weight. The weights were made from concrete, the

current vane from wood, coated with protective paint and the float was made

from a pool noodle. The container was placed as low as possible on the pole

to reduce the friction forces from surface winds. Unfortunately, this

compromise resulted in the occasional submergence of the container, which

sometimes meant the GPS connection was lost and so, resulted in gaps in the

data for some track recordings.

A miniHomer GPS, funded by the European Union, was used for the drifters.

The miniHomer GPS Position Finder used had some beneficial features, ideal

for the drifter design. Apart from being light-weight and compact in size, it was

also accurate, with low power consumption. The minihomer was capable of

taking a single instantaneous reading or be set to log coordinates continuously,

with a pre-set time interval. Before the drifter was deployed, it was made sure

that the GPS was in sync with the satellites above (NAVIN Corporation, 2013).

The miniHomer is compatible with the Ntrip software, which imports

geographical coordinates, displays the logged points on a map and export files

in a number of formats. Ntrip was used to adjust the data recording setting of

the miniHomer GPS so that recordings were taken every ten seconds.

3.2 Data Collection

3.2.1 Bathymetric depth Data

The pressure gauge was tied to the weighted end of the line and lowered to

the seabed. A reading was marked on its analogue gauge, showing the

deepest point it descended to. Simultaneously, a GPS position was taken using

the smartphone app. The depth gauge was recovered and the reading marked,

was recorded. Since a smaller vessel was used to take measurements, in

cases when the wind was strong enough to cause the vessel to drift, a small

anchor had to be dropped for every reading taken, in order to remain in place

so that the GPS reading would correspond to the same position of the depth

measurement.

37

The diminished accuracy in shallower water mentioned before, required the

use of a measuring tape to be used in water, generally shallower than 5m. At

the end of each session the coordinates and depth readings were input into an

Excel spreadsheet and saved as a Comma Separated Value (CSV) file. A total

of 340 data points were taken.

Bathymetric data encompassing the wider extent of the area across 286 points,

was also obtained from the Physical Oceanography Research Group (PORG),

within the Department of Geosciences of the Faculty of Science. To rasterise

the soundings, Kriging interpolation was conducted on these two sets of data.

The scope of this was to contrast and compare the products of two different

methods of bathymetric surveys.

3.2.2 Drifter Data Collection

Two custom made drifters were supplied by the PORG. The drifters were

deployed from the smaller vessel within the study area. Prior to deployment,

the GPS logger was switched on and some time was allowed for the device to

sync with the satellite in orbit overhead. Data recording was started from the

main vessel and the time of activation was recorded. From the main vessel the

drifters, with the GPS logger already within the waterproof containers, were

taken out and deployed at a random position within the boundaries of the study

area. The time of deployment and retrieval of each drifter for every track was

recorded in a logbook. Whilst still recording, the drifter, was taken to a different

part of the bay for a following deployment. The same procedure was repeated.

During the deployment, the drifters were regularly monitored using a pair of

binoculars.

It was found to be easier not to cease recording of the GPS between

deployments because it would have increased the possibility for human error,

possible water damage from removing the GPS from the container or losing

the connection to satellites when switching the logger off and on. As a

precautionary practice, the GPS logger was taken back on board the main

vessel to download the tracks and view them in NTRIP, to ensure that

38

recordings were being logged. One drifter would have been deployed several

times within a single day and data collection period spanned from between July

till October of 2015 (Figure 3.3).

Figure 3.3: Histogram of the number of tracks taken on the days of fieldwork.

It was planned to record two hour tracks, or longer, if possible. However, this

often could not be done due to numerous interruptions stopping the drifter.

These interruptions were typically due to the presence of anchored boats,

reduced visibility after sunset, as well as other circumstances mentioned in the

Limitations section (Chapter 3). Using the digital wind anemometer on-board

the main vessel a single reading of the local wind direction was recorded in the

logbook that was representative of the general conditions of the day of the

deployments. The wind direction and the starting points (of certain tracks) were

colour coded for organising the final map products. (Table A-1 in Appendix A)

This method of keeping the GPS recording, whilst traveling with the drifter on

board the small vessel and during track recording resulted in excess track data.

Consequently, post data management was required to clean and remove the

excess track data, whereby two different methods were used. One involved

using Ntrip directly, where the entire track (track of current and of small vessel

transportation combined) was split up, using the “Split Track” function. The

4

1

4

1

2 2

7

2

1

4

6

1 1

0

1

2

3

4

5

6

7

8

Nu

mb

er o

f Tr

acks

Date of Fieldwork

Number of Drifter Tracks taken per day

39

necessary tracks of the drifters were kept and saved as CSV file. The second

method option, was to save the entire track as a CSV file and open it in

Textpad. From the documented start and end times recorded in the logbook,

the necessary data was kept and the excess removed. This process had to be

done for every individual track that was recorded in a single session.

3.3 Data Processing

3.3.1 ARCGIS

With the complete set of cleaned data from tracks and bathymetric depth

measurements in CSV format, ARCGIS was used to plot the output. The

WGS_1984 Geographical Coordinate System was used for all map layers.

3.3.2 Bathymetric map

The latitude, longitude and depth, recorded in the logbook, were input into a

Microsoft Excel spreadsheet. The spreadsheet was then saved as a CSV file.

To compute a bathymetric map using ArcGIS, the latitude and longitude

coordinates where placed in the x-axis and y-axis fields, respectively and depth

(in m) in the z field. It was required that the coordinates be in decimal degrees

format for ArcGIS to enable plotting each point. The CSV file was opened into

ArcMaps and converted into a point shapefile.

To interpolate the shapefile and illustrate the depth contours, the Kriging

Interpolation1 method was used because of its tested higher accuracy

compared to other spatial interpolation methods (Jang, Park, & Choi, 2015;

Shanshan, Meijian, Di, & Shaohui, 2015). The interpolated product could not

account for the perimeter of the coastline. The map layer was modified by

clipping the Kriging product using a polygon which outlines the boundaries of

the study area and coastline. The polygon was traced along the coastline in

1 The Kriging Interpolation method is a geostatistical spatial optimal estimator that utilizes a generalized linear regression (Ge & Cheng, 2014).

40

Google Earth and exported as a KML file. The KML file was converted into a

layer file using the conversion tool function. With the polygon boundary layer

on top of the Kriging output, the Image Analysis tool was used to clip out the

area covered by the polygon from the Kriging output.

3.3.3 Drifter Data

The tracks were input into ArcGIS as CSV files and converted into shapefile

files. Each track was illustrated by a series of points (i.e. those point taken

every ten seconds). Each track was formatted to be represented as a line with

an arrow bearing at the heading of travel. The drifter tracks were grouped into

maps according to the day of recording and colour coded according to the

direction of wind (Table A-1).

3.3.3.1 Calculations

Table 3.1 shows the structured model of the table used to process data and

perform the calculations.

Table 3.1: Model of the table of the procedures used to process drifter track data.

Latitude (Radians)

Longitude (Radians)

Distance/second

(m)

Bearing* 1-5

V Component

U Component

Pythagoras Equation

*Split into five separate columns.

The raw data from the GPS was processed to obtain the distance between the

series of recorded points, the bearing of travel between each set of points and

the V and U component of the corresponding current. This enabled the

quantification of the path, direction and velocity of travel for each drifter (i.e.

the current). For every drifter track data file, the latitude and longitude (in

decimal degrees) were inserted into an Excel spreadsheet. The angle in

degrees was converted into radians, which was the required form to be used

in subsequent equations.

41

Figure 3.4: Diagram of the recorded points of a track. The distance and bearing between each point was calculated using the haversine formulae.

The Haversine equation (Equation 3.1 ), which measures the shortest distance

between two points on the curved surface of the Earth (Bullock, 2007; Drago

et al., 2012), was used to calculate the distance between waypoints taken

every ten seconds. The distance was divided by ten in another column to obtain

the distance (in m) travelled in one second. Essentially, this spherical

trigonometric formula is designed for a perfect sphere and computes the plane

intersection of a sphere. Therefore, the Earth is assumed to have a perfect

spherical shape, rather a geoid shape. Between two points with geographical

coordinates (Figure 3.4), the change in latitude and longitude can be found.

The derivation of the Haversine formula requires the radius of the Earth, which

is about 6371km (Javale, Gadgil, Bhargave, Kharwandikar, & Nandedkar,

2014; Kifana, 2012).

42

Equation 3.1

∆𝑙𝑎𝑡 = 𝑙𝑎𝑡2 − 𝑙𝑎𝑡1

∆𝑙𝑜𝑛 = 𝑙𝑜𝑛2 − 𝑙𝑜𝑛1

𝑎 = 𝑠𝑖𝑛2 (∆𝑙𝑎𝑡

2) + cos(𝑙𝑎𝑡1) . cos(𝑙𝑎𝑡2) . 𝑠𝑖𝑛2 (

∆𝑙𝑜𝑛

2)

𝑐 = 2. 𝑎𝑡𝑎𝑛2(√𝑎. √(1 − 𝑎))

𝑑 = 𝑅. 𝑐

Where, d, is the distance between two points and R, is the radius of the Earth.

When input into Excel for computing, the formula has to be altered to be

recognised in Excel (Equation 3.2).

Equation 3.2

= 𝐴𝐶𝑂𝑆( 𝑆𝐼𝑁(𝐿𝐴𝑇1) ∗ 𝑆𝐼𝑁(𝐿𝐴𝑇2) + 𝐶𝑂𝑆(𝐿𝐴𝑇1) ∗ 𝐶𝑂𝑆(𝐿𝐴𝑇2) ∗ 𝐶𝑂𝑆(𝐿𝑂𝑁2

− 𝐿𝑂𝑁1) ) ∗ 6371000

The bearing along the straight path between two points on the Earth’s surface

was calculated using the Forward Azimuth formula (Equation 3.3) so as to

determine the direction of currents. The results were listed under the column

‘Bearing 1’. Equation 3.4 was input into Excel. There is no difference between

Equation 3.3 and 3.4 in terms of result calculated. However, the Excel

programme is designed so as to reverse the argument of the atan function.

Equation 3.3 produces a final output in the range between -180o and 180o,

which would have had to be adjusted to the appropriate compass range (0o-

360o).

Equation 3.3

𝜃 = 𝑎𝑡𝑎𝑛2(𝑠𝑖𝑛(𝑙𝑜𝑛2 − 𝑙𝑜𝑛1) ∗ 𝑐𝑜𝑠(𝑙𝑎𝑡2), 𝑐𝑜𝑠(𝑙𝑎𝑡1) ∗ 𝑠𝑖𝑛(𝑙𝑎𝑡2) − 𝑠𝑖𝑛(𝑙𝑎𝑡1)

∗ 𝑐𝑜𝑠(𝑙𝑎𝑡2) ∗ 𝑐𝑜𝑠(𝑙𝑜𝑛2 − 𝑙𝑜𝑛1))

43

Equation 3.4

𝜃 = 𝐴𝑇𝐴𝑁2(𝐶𝑂𝑆(𝐿𝐴𝑇1) ∗ 𝑆𝐼𝑁(𝐿𝐴𝑇2) − 𝑆𝐼𝑁(𝐿𝐴𝑇1) ∗ 𝐶𝑂𝑆(𝐿𝐴𝑇2) ∗ 𝐶𝑂𝑆(𝐿𝑂𝑁2

− 𝐿𝑂𝑁1), 𝑆𝐼𝑁(𝐿𝑂𝑁2 − 𝐿𝑂𝑁1) ∗ 𝐶𝑂𝑆(𝐿𝐴𝑇2))

The calculated bearing was converted back to degrees, under column labelled

as ‘Bearing 2’, for mathematical simplicity in further calculations. The positive

values were copied to the ‘Bearing 3’ column and the negative values obtained

were added by 360 (into column Bearing 3) to get a positive angle in a

clockwise direction. The resulting list of positive bearings were filtered between

the following ranges;

0 ≥ θ ≥ 90,

90 > θ ≥ 180,

180 > θ ≥ 270

270 > θ ≥ 360.

Figure 3.5: Diagram illustrating the quadrants with 0o representing North with the corresponding ranges of angles and the trigonometric element which determines how the V

and U components would be calculated.

44

It was necessary to filter results before calculating U and V according to the

quadrant in which the bearing lies. The sorted angles from column ‘Bearing 3’

were subtracted by 0, 90, 180 and 360, respective of the corresponding ranges

above and put into column ‘Bearing 4’. This made it possible to find the angle

between the Resultant and the axis. The results were then converted back to

radians under the ‘Bearing 5’ column. Using the appropriate, trigonometric

function, according to the region of the angle (Figure 3.5), the V and U

components were calculated. The sign for both components is an indicator of

the corresponding resultant region. In order to check that the solutions for the

V and U components were calculated correctly, Pythagoras Theorem was

applied to determine the length of the resultant component, which should have

equated to the distance travelled per second, calculated before.

3.3.4 SWAN Data

The SWAN model is run and maintained by PORG. The model produces a

forecast for three and a half days, supplying data with a resolution of 0.001o

and a temporal frequency of three hours. For this study the PRG supplied

monthly extracted data for Ramla Bay. Multi-columnar Point Files were

produced, which contained all the relevant data for a single point. This data

was input in ArcGIS. Each point contains the Latitude, Longitude and a time

series of the Significant Wave Height (SWH) and Mean Wave Direction (MWD)

(J. Azzopardi, 2012). The SWH and MWD, were represented in a grid boundary

(Figure 3.6), comprising of 433 points.

45

Figure 3.6: Point grid used in the SWAN model computations. The yellow border highlights the Transect taken and within in it are the highlighted points for the Time Series analysis.

3.4 Modelling Data

3.4.1 SWAN Model

The modelled data was produced for each point, extrapolated every three

hours for the duration of each corresponding month between August 2015 and

January 2016. For each month and for every grid point, the minimum, the

maximum and the average values of each parameter were calculated. The

geospatial analysis toolbox was used to interpolate the data using a natural

neighbour interpolation method. An interpolated map was produced to illustrate

the spatial distribution that represents the average conditions of the two

parameters of every month. (Zhou, Huang, & Zhang, 2015). Again, the domain

of the interpolated map extended onto land and so it had to be clipped, as was

executed for the bathymetric map.

The averages of all six maps, for the average SWH was computed with the

Raster Calculator function, which utilizes Python syntax to complete map

46

algebra expressions and produce a final raster product. The average had to be

computed for each parameter individually by adding the spectrum of monthly

average raster maps and dividing by six.

A map product was ultimately created, encompassing an area larger than the

intended project boundaries. It was decided to provide a map on a larger scale

because at the smaller scale of the bay area, the interpolated map of the

modelled data would have had a low resolution for proper analysis.

Additionally, it would be beneficial to foresee the external physical conditions

that ultimately influence the conditions within the study area. The map may

also prove advantageous for future studies of the surrounding area.

3.5 Statistical Analysis

The drifter tracks for currents were statistically analysed through a validation

of the SWAN model. The drifter tracks were plotted in ArcGIS across the grid

of the Wave Direction output from SWAN. Only a few tracks were taken, in

which the points along the track, which coincided as close as possible to the

SWAN grid points, spatially and temporally, were used. The selected drifter

tracks had to be individually paired with the 3-hourly Wave Direction output

from SWAN, so as to encompass the time the track was taken within the 3-

hour time range from SWAN. The bearing values of the SWAN grid point of

Wave Direction and the corresponding track points in closest proximity to one

another were recorded in a table for each track. The tabulated data of wave

direction and current direction (Table A-2) and a scatter plot was produced.

The two variables were correlated using Pearson Correlation. The Root Mean

Square Error (RMSE) was also determined to assess the level of association

between the wave and current direction. The process of subsequent to verify

the results is described in Chapter 4.

For current velocity, the U and V velocity components of a selected number of

tracks, grouped according to the day of deployment, were plotted on separately

into a time-series graph. So the individual tracks on the time-series could be

identified and linked to the maps, colour coded marks on the selected tracks,

47

were added at the start of each of the selected track. The colour coded legend

may be found on Table A-1 of Appendix A.

A time-series was drafted for the average SWH of the six months over the

same point in the centre of the bay (Point 2). Additional time-series were

conducted for each month across the five points along a transect of the grid

from the SWAN model (Figure 3.6). The selected grid points ran seawards,

perpendicular to the beach. More points concentrated within the bay were

taken and gradually reduced further out from the beach. Point 1 corresponds

to the point closest to the beach (i.e. shallowest) and every highlighted point

up to the last (Point 5), represents the deeper water. Daily data for the average

atmospheric pressure taken by a meteorological station in Rabat, Gozo, was

acquired (“Underground Weather,” 2016). The average atmospheric pressure

time-series was superimposed to each time-series for analysis.

3.6 Limitations

Ramla Bay is a popular bathing area for people to retreat to during the summer,

both on the coast and at sea. Unfortunately, the majority of deployments could

have only been done during the weekend (due to the availability of the vessel),

when the presence of people and recreational boats were highest. In cases

when interruptions were suspected of occurring, the track would have had to

be stopped and the drifter reset elsewhere. Similarly, a drifter deployment track

would have been ceased when the drifter became entangled in the float line

marking the boundary of the bather area, which was quite a common

occurrence. If the drifter was not removed before colliding with the line, the line

was otherwise raised to allow the drifter to pass and enter the surf zone that

was situated shoreward of the float line. At this point, it would have to be

stopped when the bottom weight of the drifter began caressing the sandy

seabed.

The loss of a drifter on the 18th of July 2015, when it was deployed around the

north-eastern area of the bay and possibly hit by a passing boat, hindered the

capacity of data collection. Consequently, the amount of drifter tracks that

48

could have been recorded, was reduced, in addition to losing the stored GPS

data already stored on the logger of the same day and the day before. The

GPS tracker sometimes failed to take full records, resulting in significant data

gaps for some track recordings. Unfortunately, a few track recordings had to

be discarded. This error was assumed to be the cause of the temporary

submergence of the GPS in rough conditions. A major limitation to the study

was the restricted timeframe in which the area could have been properly

studied. Ideally a more comprehensive study could have been undertaken,

were the annual and seasonal trends would have been represented.

The low accuracy of the pressure gauge used to acquire depth readings for the

bathymetric map entailed that the map product should serve as a reference for

descriptive purposes and analysis. Also, because the embayment’s

substratum is composed predominantly of sandy material, the seabed

morphology is subject to major variations, both spatially and temporally, from

when readings were taken. Therefore, the measurements taken represent the

morphology and bathymetry of the bay at a fixed period (mid-August to mid-

September). The Rosario-SHYFEM hydrodynamical model, which was to be

used for a comparative analysis with the drifter tracks taken and to validate the

model, was not successfully implemented on time and so could not be used for

the analysis. This was a major limitation, as it was significant component of this

dissertation. Accordingly, an alternative methodology was developed to

statistically analysis the data acquired, as discussed above.

49

Chapter 4 Results and Discussion

In this Chapter, the results from the data collected in the field and produced

and processed from models are presented. The study is also critically reviewed

and the link between the results and the material discussed in the literature

review, is made. Quintessentially, the research questions are answered in this

Chapter and the discussion deciphers whether the hypotheses made, are

correct or not. The bathymetric maps and drifter tracks were plotted separately

for descriptive analysis. The same was done for maps produced for the

average SWH and wave direction. The time series analytical method was used

to graphically illustrate the variability of the SWH over time and space. A time-

series was also plot for the U and V velocity components of selected current

tracks. The difference between current velocities in relatively deeper waters

outside the nearshore zone and those generated by wave breaking as

longshore currents, are discussed. To measure the relationship between the

wave and current direction for a selected number of drifter tracks, the Pearson

correlation coefficient was determined and Root Mean Square Error was

performed to check the level of association of the data with the line of best fit.

All maps produced and referred to in this Chapter can be found in the

Appendices.

4.1 Bathymetric Results

Two bathymetric maps of the study area were produced using data collected

in-situ (Figure 4.1) and by the Physical Oceanography Research Group

(PORG) (Figure 4.2). Despite using a low accuracy measuring device for the

in-situ data, the map produced, still proved to have a more detailed, higher

resolution than that of the PORG output. The PORG map does, however,

encompass a wider extent of the area.

The in-situ depth measurement map (Figure 4.1) shows two notable features

of the bathymetry that are not illustrated in the PORG map. The west-side of

the bay appears to have a more gradual slope and broader extent of the

50

shallow depth. On the east side of the bay, the gradient tends to be steeper,

with a narrower extent of sub-marine rock fields. From observations made in

the field at the time of data collection, this can be attributed to the extensive

rock field below sea-level, originating due the erosion of the Upper Coralline

Limestone escarpment on top of the Blue Clay slopes on both headlands. The

more extensive rock field on the west-side is characterised by smaller rocks,

which give the area a highly irregular and variable surface bathymetry. This

irregular surface is not represented properly in the map, which is a limitation of

the method used. The other side of the bay (east-side), was characterised by

fewer and larger boulders close to the shoreline with less variation than the

opposite side of the bay. Generally, along the periphery of the two sides of the

headlands within the bay, a higher rugosity can be observed than in the centre

of the bay, where there is a sandy seabed. The exception to this, are the

remnants of the submerged sea-wall and the patches of Posidonia oceanica

seagrass beds. Secondly, the shape/outline of the sand bar is clearly outlined

on the in-situ measured bathymetric map (Figure 4.1) and corresponds to the

satellite imagery of the bay, if superimposed on one another. This is another

clear advantage the in-situ map has over the PORG map. The sand bar during

the summer period between August and September (when measurements

were taken) has a crescentic shape, as opposed to a linear parallel sand bar

observed by Azzopardi (2015) after the winter period.

51

Figure 4.1: Bathymetric Map produced from in-situ measurements, with the shallowest

depths in red, graduating down to deeper depths in blue.

Figure 4.2: Bathymetric Map produced data obtained through numerical modelling performed by the PO-Unit, with the shallowest depths in red, graduating down to deeper depths in blue.

Source: Esri, DigitalGlobe, GeoEye, Earthstar Geographics, CNES/Airbus DS, USDA, USGS,AEX, Getmapping, Aerogrid, IGN, IGP, swisstopo, and the GIS User Community

¯LegendRamla BayBathymetry

-0.303 - 0

-0.718 - -0.304

-1.12 - -0.719

-1.54 - -1.13

-1.95 - -1.55

-2.37 - -1.96

-2.78 - -2.38

-3.2 - -2.79

-3.61 - -3.21

-4.02 - -3.62

-4.44 - -4.03

-4.85 - -4.45

-5.27 - -4.86

-5.68 - -5.28

-6.1 - -5.69

-6.51 - -6.11

-6.92 - -6.52

-7.34 - -6.93

-7.75 - -7.35

-8.17 - -7.76

-8.58 - -8.18

-9 - -8.59

-9.41 - -9.01

-9.83 - -9.42

-10.1 - -9.84

-10.6 - -10.2

-11.1 - -10.7

0 150 30075 Meters

Source: Esri, DigitalGlobe, GeoEye, Earthstar Geographics, CNES/Airbus DS, USDA, USGS,AEX, Getmapping, Aerogrid, IGN, IGP, swisstopo, and the GIS User Community

0 500250 Meters

¯LegendPORG Bathymetric Map 1

-1.14 - 0.452

0.453 - 2.04

2.05 - 3.63

3.64 - 5.22

5.23 - 6.8

6.81 - 8.39

8.4 - 9.98

9.99 - 11.6

11.7 - 13.2

13.3 - 14.7

14.8 - 16.3

16.4 - 17.9

18 - 19.5

19.6 - 21.1

21.2 - 22.7

22.8 - 24.3

24.4 - 25.9

26 - 27.4

27.5 - 29

29.1 - 30.6

30.7 - 32.2

32.3 - 33.8

33.9 - 35.4

35.5 - 37

37.1 - 38.6

38.7 - 40.2

40.3 - 41.7

41.8 - 43.3

43.4 - 44.9

45 - 46.5

46.6 - 48.1

48.2 - 49.7

52

4.2 Lagrangian Drifter Currents

A map of all the drifters track measurements of recorded currents was compiled

(Figure 4.3). Additionally, the sorted drifter track maps, according to the day of

deployments can be found in Appendix A. Also in Appendix A, is a table of all

the information about the tracks, including the wind direction of the day with

colour coded legend, the times of drifter deployments and retrieval and the

duration of each track. A total of 46 hours and 30 minutes of current recordings

were measured throughout the collection of data, with the average duration of

a single track lasting to approximately 76 minutes.

Figure 4.3: The complete set of drifter tracks recorded throughout the data collection period superimposed on a map with bathymetric contours extrapolated from the bathymetric map interpolation.

The plotted tracks presented, show that under north-westerly winds (red),

currents flowing from the NNW from deeper water and approach the

embayment obliquely, as was observed on the 5th of July 2015 (Figure A-1).

Under NNW winds, longshore currents, as were clearly identified on the 18th of

July 2015 and the 26th of September 2015. The directional flow of these tracks

mirrors the coastline and/or deviates slightly at some point. The same is true


0 60 120 180 24030Meters

¯

53

for the opposing direction from the NNE (yellow) and ENE (green), in which

longshore currents are clearly identified, flowing along the contours of the

coast. The exception being for currents measured on the 11th of July 2015,

whereby the longest track does not show directional preference to coastal

configuration but to the wind direction, largely because it was deployed in more

open water. Therefore, the results agree with the hypothesis stated, when

currents have direct influence from the shallower bathymetry.

4.2.1 Drifter Trajectories: Current Velocities

The extracted U and V velocity vectors, were initially intended to be used in the

Rosario-SHYFEM model. Instead, they have been presented as time-series

velocity graphs for four selected tracks. Only four tracks were chosen because

of the insurmountable amount of the data available for discussion. The data

not used has been made available with this dissertation.

For the duration of most tracks taken on the 5th of July 2015 (Figure A-14), the

drifter appeared to be stationary for short periods. The highest velocity reached

was during the 16:13-16:41 track, with a peak in the U vector velocity

exceeding 1m/s. The track 12:17-12:37 was the weakest, with velocity

fluctuations not exceeding 0.6m/s. The large peak at the end resulted whilst

retrieving the drifter and not the actual current. This could be observed for

several other tracks. Both tracks occurring between 12:15 – 12:52 and 16:10

– 16:38 were characterised by minor fluctuations in velocities not exceeding

1m/s.

On the 11th of July 2015 (Figure A-15), the strongest currents came from the

tracks 09:28-11:38 and 13:26-14:29, reaching velocities of over 0.8m/s and

1m/s, respectively, both in the westwards direction (signified by the negative

value in of the U component). Thusly, a dominant alongshore flow prevailed.

The remaining two tracks at 13:27-14:37 and 14:46-16:40 were much weaker,

with velocities not reaching more than 0.2m/s. The latter shows a stronger

velocity from the positive V component so the flow is dominantly cross-shore.

This may resemble a rip current but because of its low velocity, it may not

54

necessarily classify as a rip current, since rip currents are typically strong and

fast as explained by Thornton, MacMahan and Sallenger (2007). Interestingly,

track 13:26-14:29, deployed in shallower waters than track 13:27-14:37, was

significantly stronger in comparison. This is significant because both tracks

were taken at relatively the same time but at different depths.

Out of the four tracks selected on the 29th of August 2015 (Figure A-16), the

track between 09:27-11:10 exhibited the highest peak in velocity of 0.58 m/s,

travelling in the southerly, cross-shore direction. Surprisingly, this track

exhibited the highest velocity when it was in the shallowest waters compared

to the other three tracks, which were in much deeper water but all had lower

velocities. The track between 13:39-14:34, was slightly slower at 0.52m/s at its

peak when travelling westwards in the alongshore direction. This track was in

the deepest water of all four tracks.

On the 26th of September 2015 (Figure A-17), the track between 13:41-14:31

shows a highly variable velocity, strongly associated within the U vector rather

than the V vector, indicating a strong alongshore direction of travel. This track

is the strongest amongst all other tracks on this day, with velocities exceeding

0.2m/s. In contrast to previous tracks discussed, it is relatively weak. On this

day, this track, along with the track between 14:50-16:39 were much stronger

than the other two, which fluctuated below 0.1m/s. This is significant because

unlike the prior three cases, the strongest currents on this day (13:41-14:31)

occurred in relatively deeper water compared to other tracks.

The alternating spikes and dips are most likely the cause of strong gusts. The

dips in velocity to 0m/s indicate that the drifter was stationary. This could be an

error caused by the GPS logger, which may have lost connection, as

mentioned in previous chapters. The range of velocities of currents recorded

comply to the range presented in the literature reviewed. The general pattern

observed from drifter measurements submits to a higher degree of alongshore

current flow in shallower waters, flowing from direction of the wind. Some of

these longshore currents (such as between 17:50-19:12 on the 26th of

September 2015) are the products of wave breaking in the surf-zone and

although measurements directly in the surf-zone were not possible to obtain,

these resultant longshore currents are representative of the wave induced

55

current processes. Deployments and therefore, currents, initiated in deeper

water tend to follow the direction of the wind and not always reconfigure to the

coastal perimeter. From the selected current tracks for time-series comparison,

a general trend arose that suggests that the shallow water and nearshore

currents are stronger than those currents in the deeper portions of the bay. The

results presented do not support the hypothesis, which suggested that currents

in shallower water would be weaker than those of deeper waters because of

the significant dissipation in wave energy. The only track that complies with the

hypothesis was between 13:41-14:31 on the 26th of September 2015. This was

not statistically proven, however. From the results present, it may be construed

that with stronger currents in the shallow surf zone, greater transport of beach

sediments is likely to occur, largely in the longshore direction.

4.2.2 Drifter Trajectories: Current Direction

Despite attempting to record drifter tracks under as many environmental

conditions as possible in the field, rip currents were unable to be observed and

measured by the drifters during the summer period at Ramla Bay. This does

not conclude that rip currents do not occur indefinitely within the bay but infers

that they may be extremely rare events in the summer period when the wave

climate is drastically dampened in contrast to the higher energy during the

winter months. Therefore, the hypothesis with regards to the biophysical

configuration of Posidona oceanica due to a cellular rip current circulation was

incorrect.

The direction of current flow observed from field measurements show that

currents often flow along the contours of the coastline. The direction of current

flow is dependent on the wave direction to a certain extent. When plot on a

scatter plot (Figure 4.4), the outcome of the correlation reveals itself to distort

the true relationship by the added skewness incurred by three outliers.

56

Figure 4.4: First scatter plot of the measured current direction (y-axis) against the modelled wave direction (x-axis) with outliers included.

The R2 value calculated (0.0176) is closer to 0 than to 1. This suggests that,

although the correlation is positive, the relationship is weak. The Root Mean

Square Error (RMSE) was calculated for the two variables of the seventeen

sets of records listed in Table A-2. This measures the level of association of

the data with the line of best fit. The RMSE was computed to be 107.05o. This

indicates that typically, the points are around 107.05o off from the line of best

fit and because the RMSE value is so high, there is a weak association

between the variables.

The Pearson correlation was used to measure the strength of the relationship

between two variables. Let the null hypothesis (H0) be that there is no

relationship between the direction of current flow and the wave direction if the

p-value exceeds the 0.05 level of significance. The alternative hypothesis (H1)

states that there is a statistical relationship between the wave direction and

current direction if the p-value is less than the 0.05 level of significance.

y = 0.4037x + 100.82R² = 0.0176

0

30

60

90

120

150

180

210

240

270

300

330

360

0 30 60 90 120 150 180 210 240 270 300 330 360

Drift

er

Curr

ent

Direction (

deg)

SWAN Wave Direction (deg)

Wave Direction vs Current Direction

57

Table 4. 1: Table of Pearson correlation and level of significance of the relationship between wave direction and current direction with outliers. Produced in SPSS.

The Pearson Correlation coefficient, r, (Table 4.1) was computed in SPSS to

be 0.132, which indicates that there is a positive correlation between the wave

direction and the current direction. Since, the 0.132 mark is closer to zero than

one, it can be concluded that the proportional relationship between the two

variables is weak. This reaffirms the result of the R2 value. Furthermore, the p-

value of 0.612 is significantly greater than the 0.05 level of significance, hence

the null hypothesis is accepted. This indicates that there is no statistical

significance between wave and current direction.

The three outliers are the likely causes of the statistical insignificance of the

data. The outliers observed occurred on the 4th September 2015 from the 18:03

-19:51 track, with points taken at 19:01:52 and 19:06:33. Again these points

were taken because they were closest to the SWAN grid point (spatially and in

time at 18:00). The second set of outliers occurred on the 5th of September

2015 from the 11:02-12:48 track, with points taken at 12:27:06 and 12:42:26.

These points were temporally closest to the SWAN grid point at 12:00. To test

the alternative relationship that would otherwise be skewed by the outliers, the

outliers were removed and the same statistical analysis was repeated.

58

Figure 4.5: Second scatter plot of measured current direction against modelled wave direction without outliers included.

Table 4. 2: Table of Pearson correlation and level of significance of the relationship between wave direction and current direction without outliers. Produced in SPSS.

With the three outliers removed, the correlation remains positive but the

relationship is much stronger now (Figure 4.5). The null and alternative

hypotheses proclaimed for the first statistical test, still applies to this new test.

The Pearson correlation coefficient of 0.896 (Table 4.2) is now closer to 1

signifying a strong positive relationship between the two variables. Since the

p-value (0) is less than the 0.01 level of significance, the alternative hypothesis

(H1) is supported, whereby it can be established that there is a strong

associated relationship with wave direction and current direction.

y = 2.8497x - 328.5R² = 0.8022

0

30

60

90

120

150

180

210

240

270

300

330

360

0 30 60 90 120 150 180 210 240 270 300 330 360

Drifter

Curr

ent D

irection (

deg)

SWAN Wave Direction (deg)

Wave Direction vs Current Direction

59

To inspect the possible cause of the emergence of the outliers, a further test

was conducted for the data of the corresponding tracks from which the outliers

originated from. This was done to measure the statistical significance of the

wind vector velocities from SKIRON (a component model of SWAN) with the

outlier current vector velocities. The U and V vectors were used because of the

directional and magnitude components. The SKIRON model has a much lower

resolution than the SWAN model so a single grid point (36.05oN, 14.3oE) that

was closest to the bay was taken as a constant for the statistical analysis. By

taking the U velocity of sea currents and wind coinciding at the same time, a

scatter plot was produced, with the line of best fit added. The level of

association was calculated and found to be strong between these points.

Therefore, the line of best fit will serve as a baseline reference to compare the

U velocities of the outliers points in question. The same was repeated for the

V velocity component.

Figure 4.6: Scatter plot of U (top) and V (bottom) components of current velocity and wind speed on 04/09/2015 with the U and V components of the two points from the tracks at 19:01

(green) and 19:06 (yellow) to test the relationship of these possible outliers.

y = 0.0171x + 0.0977R² = 0.0437

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

-2.5 -2 -1.5 -1 -0.5 0

Curr

ent

(m/s

)

Wind( m/s)

U vectors of wind against current velocities (04/09/2015)

U component

19:01:52

19:06:33

Line of Best Fit

y = 0.0171x + 0.0448R² = 0.9695

0

0.02

0.04

0.06

0.08

0.1

0 0.5 1 1.5 2 2.5

Curr

ent

(m/s

)

Wind( m/s)

V vectors of wind against current velocities (04/09/2015)

V component

19:01:52

19:06:33

Line of Best Fit

60

For the 4th of September 2015, the R2 values for the U (0.0437) and V (0.9695)

scatter plots show the V vector having stronger relationship between the

current and wind velocities, than the U vector. The RMSE calculated for the U

and V vectors came to be 1.611m/s and 0.831m/s, respectively. The U

component RMSE is much larger than the V component RMSE, which

amalgamates the result of the R2 value. When comparing the outlier

components of 19:01:52 (Figure 4.6), the scatter plot shows a close association

of the outlier V components with the line of best fit. However, the outlier U

component for the same data is far from the line of best fit of the wind U vector

velocity (Figure 4.6). The exact opposite is the case with 19:06:33.

Figure 4.7: Scatter plot of U (top) and V (bottom) components of current velocity and wind speed on 04/09/2015 with the U and V components of the two points from the tracks at 19:01

(green) and 19:06 (yellow) to test the relationship of these possible outliers.

y = 0.1966x + 0.4903R² = 0.9905

-0.05

0

0.05

0.1

0.15

-3 -2.5 -2 -1.5 -1 -0.5 0

Curr

ent

velo

city (

m/s

)

Wind Velocity (m/s)

U vectors of wind against current velocities (05/09/2015)

U component

12:27:06

12:42:26

Line of Best Fit

y = 0.4464x + 0.2026R² = 0.676

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3

Curr

ent

velo

city

(m/s

)

Wind Velocity (m/s)

V vectors of wind against current velocities (05/09/2015)

V component

12:27:06

12:42:26

Line of Best Fit

61

The RMSE of the U and V velocities on the 5th September 2015 current and

wind velocities coinciding at the same time was calculated to be 2.3777m/s

and 0.2934m/s, respectively. Both indicate a relatively close association. This

shall be the base which to correlate the outliers with. The scatter plot (Figure

4.7) shows that the two outlier points have a stronger association between the

V vectors than with the U vectors. Unfortunately, since the points skew far from

the line of best fit of the U components, they must be considered as outliers.

This test has shown that since the points remain outliers in relation to the wind

velocity and direction, they are verified outliers on the wave- sea current

correlation and scatter plot.

Both sets of outlier points (4th and 5th September 2015) are themselves outliers

in either the U or V component fields within the SKIRON wind-sea current

velocity test and have no close association with the line of best fit. It can be

concluded that the SKIRON model is not the cause of the outliers through

incorrect modelled data. This was shown by the strong relationship formed by

the line of best fit. The drifter points themselves may have been erroneous due

to a GPS error. Therefore, the outliers observed in the wave-sea current scatter

plot can be taken to be valid. Furthermore, with the first scatter plot of the

wave–sea current direction correlation (i.e. with outliers included) being

accepted, the final determination would suggest that under general conditions,

represented by the selected drifter tracks, there is a positive relationship

between the wave-current direction, albeit weak. As determined from the first

statistical test (Table 4.1), there is no statistical significance between the wave

direction and the current direction. Therefore, the degree of variation in wave

direction is less likely to change current direction at the same extent.

By putting these results into context, one could determine that within the

shallow nearshore zone, the complex hydrodynamic processes statistically

distort the relationship between current and wave direction. However, the

second test, without outliers, may also be accepted for currents in deeper

waters, whereby the influence of the bathymetry (i.e. beyond the influence of

the depth of closure) is irrelevant.

62

4.3 SWAN Maps

4.3.1 Significant Wave Height

Figure 4.8: Spatial variation graph of the Significant Wave Height across the transect.

The average SWH across the transect taken from the SWAN grid runs from

0m at the shoreline to 4225m outside the embayment. A long transect was

taken to observe how the average SWH varied from deep waters to shallow

waters for each month. The results show that SWH decreases as water depth

decreases (Figure 4.8). August 2015 experienced the lowest range variation in

SWH between shallow and deeper points, with a maximum of 0.58m in deep

water and a minimum of 0.25m in shallow water. The extent of variation

between deep and shallow water increased with each subsequent month, in

which January 2016 experienced the highest variance of SWH, with a

maximum SWH of 4.16m and a minimum value of 0.28m. SWHs in December

were the exception of this observation, whereby SWHs were averaged

between August 2015 and September 2015.

On the larger scale, the interpolated maps of SWH (Figures B-1 to B-7) show,

not only a decrease in SWH with water depth but also re-orientation with the

coast. The results also reveal the processes of wave diffraction and refraction

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1000 2000 3000 4000 5000

Ave

rag

e S

ign

ific

an

t W

ave

He

igh

t (m

)

Distance from Shoreline

Average Significant Wave Height Monthly Spatial Variation

August September October

November December January

63

as the wave fields approaching at an oblique angle, converge around the

headland and approach the beach at an angle almost perpendicular to the

beach but still angled to facilitate minor longshore drift of sediment. The spatial

variation in SWH indicates that a directional spread of the wave energy across

the bay results in a gradient of radiation stress, which leads to the formation of

longshore current, as discussed before. Therefore, the directionality changes

in SWH can be linked to the wave direction.

The thickness of the graded bands of the interpolation can be seen to decrease

spatially from deeper to shallower waters. This represents the conversion of

long-crested to short-crested waves. Long-crested waves, as Sundar,

Sannasiiraj and Kaldenhoff (1999) explain, are those waves responding to the

decreasing bathymetric depth contours, resulting in the parallel orientation of

waves to bathymetric contours. Short-crested waves are the product of the

interactions of an irregular bathymetric and collective effects of wave refraction,

diffraction and reflections that the waves endure when approach the

embayment. Acknowledging the shift to short-crested waves is important for

estimating the radiation stresses in the nearshore area.

4.3.2 Wave Direction

During the time scale of the study across six months, the dominant monthly

average direction of wave fields propagating towards the coast was from the

general NE direction throughout August (Figure C-1), September (Figure C-2)

and November (C-4). This does not comply entirely with what was

hypothesized. It was expected that the dominant average monthly mean wave

direction was to approach from the NW, according to the dominant wind

direction from the NW, as mentioned in the Introduction. This may be of

significant importance as a means of identifying a possible shift in the general

trends of wave climate due to climate change. NW wave fields were observed

throughout the limited days of available data in October (Figure C-3). Wave

fields from the North and East were prevalent throughout December (Figure C-

5) and January (Figure C-6), receptively. When approaching from the North,

drastic changes in directionality occur, exhibiting an almost ideal theoretical

64

scenario (Figure C-5) whereby, the high-energy breaking occurring at the

headlands forces currents to flow along the peripheries of the headland into

the bay. During August, September, November and January when the

predominant mean wave direction propagates from the NE, sediments are

likely to be transported to the western side of the beach. Longshore sediment

transport during November and January may be more lateral because of the

more acute angle the waves break to the beach. With the mean wave direction

during October and December showing to propagate in from the NW direction

within the surf zone, longshore drift may be assumed to migrate sediments to

the eastern part of the beach. However, due to the significant data gap of

October and the seemingly erroneous results produced by the model for

December, this may not be representative of reality.

The directionality of the wave fields is observed to change, from a seemingly

unidirectional propagation in open waters to a highly variable nature within

shallower waters. This change is represented by the narrow, vibrant colour

array along the peripheries of the coastline within the bay (Figure C-1 to C-6).

This is because waves adjust due to decrease in water depths once reaching

the depth of closure and due to the boundary configuration of the coast causing

refraction and diffraction of the wave field. This aspect supports the hypothesis.

It can also be noted from the maps that after bending around the headlands,

the waves in actuality propagate within the surf zone at an obtuse angle. This

facilitate the longshore drift of sediments along the beach (Figure C-1 to C-6).

The longshore sediment transport within an embayed beach, which functions

within a semi-closed system, will tend fluctuate to and fro in the alongshore

direction. The average wave direction of each month may provide an estimate

of the direction of longshore transport of sediments. This is, speculative as

other processes may also be playing a role. This field deserves a study in itself.

4.4 Time Series Analysis: Significant Wave Height

A time series of the average SWH for every month was computed across the

five points along the transect running centre cross-shore of the bay (Figure D-

1 to D-6). Typically, the pattern of the temporal variation across each point (i.e.

65

different depths), remains relatively identical. However, there is a change in the

amplitude that distinguishes the variations across the points (depths), with

points in deeper water having a larger amplitude to that of the shallower points.

A high degree of seasonality is evident between the calmer summer period

comparable to the more intense winter SWHs (Figure 4.9). It is noteworthy to

point out the almost overwhelming overlapping similarity, in terms of pattern

and amplitude of SWH characteristics at points two and three, which

corresponds to a point in the centre of the bay and at the outer edge of the bay

mouth, respectively (Figure D-1 to D-6).

Figure 4.9: Time series of the SWH from August 2015 to January 2016 over point 2, with the

atmospheric pressure superimposed in dashed black line.

Since SWAN is the first high resolution coastal model to be applied to Malta,

there was a limited amount of data available for the model. The lack of data

input from proxy models, such as SKIRON (for wind), resulted in data gaps in

SWAN (Table 4.3). Of the six months, the greatest deficiency of output data

was for October (81.85%). An adequate analysis may not be conducted for that

month. Data for August and December were also considerably absent but a

decent representation could be achieved, nonetheless. September, November

and January all had almost complete sets of data to provide a truly meaningful

representation.

995

1000

1005

1010

1015

1020

1025

1030

1035

1040

1045

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Atm

ospheric P

ressure

(hP

a)

Sig

nific

ant

Wave H

eig

ht

(m)

Time

Significant Wave Height Time-Series

66

Table 4. 3 Tabulation of the amount of data available from the SWAN model and the percentage of missing data.

Aug Sept Oct Nov Dec Jan

Total 3-hourly Intervals 248 240 248 240 248 248 Missing 3-hourly Intervals 127 26 203 47 89 20

Percentage 51.21% 10.83% 81.85% 19.58% 35.89% 8.06%

The dashed line (black) superimposed on all time-series for every month

represents the daily average atmospheres pressure, in hPa. The plot of

pressure (Figure 4.9) shows variations throughout each month and a seasonal

rising trend in the average pressure from summer to winter. During the summer

months, the frequency of fluctuations is much greater than in the winter

months, whereby from November, variations become less frequent. The

opposite is true for the magnitude, in which summer months exhibit low

amplitudinal variations and range. This natural shift occurs in November when

intensive amplitudinal variations become more violent. These drastic dips in

pressure represent low-pressure storm events. Although some strong low

pressure storms occurred during the summer months, the sheer intensification

of winter storms is unparalleled in comparison. This has significant

ramifications to the nature of SWH.

During August, the average SWH and atmospheric pressure were both

contrastingly lower compared to other months. The offset between the

atmospheric pressure and the SWH time-series may be more significant in

August than for other months (Figure D-1). The inverse relationship can still be

observed however, whereby periods of low atmospheric pressure generally

resulting in slightly higher SWHs as opposed to when the pressure was lower.

The time-series of the SWH in shallower water remains quite well defined, as

opposed to the dampened temporal variation pattern experienced in other

months.

The SWH in September 2015 (Figure D-2) is characterised by a double peak

spectrum, which corresponds to two strong decreases in pressure around the

same time of the month. November (Figure D-4) begins with slightly higher

SWH and gradually levels out for the mid-term period of the month, with values

straggling below 1m, before dramatically increasing closer to the end of the

month, when it reaches it maximum SWH across all points. This pattern is

67

observable for all points (within the bay and outside) with exemption to point 1.

Across the shallowest point, there is minimal variation.

The absence of SWH data available for time-series analysis may alternatively

be assessed by means of the average atmospheric pressure. The average

atmospheric pressure during October 2015 (Figure D-3) is characterised by

two major dips in pressure, occurring around the 10th and 23rd of October.

Other dips in pressure occurred on the 15th and 31st but are not as powerful as

the latter two. The seemingly inverse relationship between pressure and SWH

allows for the presumption that during or around this time of the month SWH

would have peaked. Subsequent peaks in high pressure on the 4th, 13th, 17th

and 25th of October 2015 would have most likely resulted in a compressed sea

surface and reduce the SWH.

December (Figure D-5) is seemingly the exception to the trend on seasonal

increase in SWH. There are dramatic fluctuations between higher and low

SWHs across all points. The SWH never exceeded 0.8m across all points. This

is significant because the maximum SWH is considerably lower than the

minimum fluctuating range of November and January. When viewing Figure

4.9, where the scale of the average atmospheric pressure is not

misrepresented as is on Figure D-5, it is evident that SWH data modelled by

SWAN must be erroneous because of the disproportional amplitudinal

relationship between the average SWH and the average atmospheric

pressure.

The observable relationship from the time-series graphs leads to the actuality

that SWH in the deeper waters than in the shallower waters as was

hypothesized. The direct correspondence between maximum peaks of SWH

and dips in pressure appear to be offset by a few hours, or sometimes days.

This limitation may be caused by the distance of the meteorological station in

Rabat, Gozo and Ramla Bay but could also be due to a response lag between

the conditions of the atmosphere and the sea surface layer. The pressure may

be used as a tool to predict the possible nature and peaks in SWH, where there

are significant data gaps in the SWH data. During times of low pressure and

storm events, there is maximum variance between the SWH in deeper water

(point 5) and shallow water (point 1). When pressure is relatively high the

68

variance between SWH in deep and shallow water in minor. This incurs that

Ramla Bay is strongly protected during storms. This effectively, reduces the

scale of sediment transport and erosion of the dunes that would otherwise

occur if not for the protection of the headlands. This may also explain why the

SWH decreases with depth (Figure 4.8) instead of increasing as was

hypothesised. The severe attenuation of SWH between deep and shallower

water depths within the embayment caused by the level of protection offered

by the headland embayment.

The intensity on wave energy signified by large SWHs during winter periods,

in particular November (Figure D-4) and January (Figure D-6), corresponds to

sharp decreases in the general atmospheric pressure and in the peaks reached

in both November and January. It is during this period, when the beach and

morphology of the bathymetry and features, such as the sand bar are likely to

shift and change shape. Azzopardi (2015) conducted a study on the

morphological variation of the seabed and sandbar at Ramla and found that

there are distinctive shifts in the underwater morphology between the summer

and winter seasons. Storm events are the cause of this reset of the seabed

and sandbar resulting in the attenuation of the extreme curvature of the

sandbar (Figure 4.1), forcing it straighten, becoming more parallel to the beach

and move shorewards (Winter et al., 2014). The supplementary fluctuations in

SWH that are far more minor in terms of amplitude, may be due to the

superposition of two wave groups travelling in the same direction, which will

cause the wave heights to increase and consequently, the SWH to increase.

The study focused on the SWH conditions and not the regular wave conditions

because the SWH represents the average of the largest waves. This is

relevant, especially for coastal engineers and managers because larger waves

are more likely to have a consequential effect on structures and sediment

dynamics (Altunkaynak & Wang, 2012). The process of wave shoaling,

whereby the wave heights increase and the velocity of the wave orbitals

decrease should produce weaker currents measured within the centre or

slightly deeper portions of the bay, where wave shoaling of incoming waves is

likely to occur. Currents generated by wave breaking within the surf-zone of

originating from the surf-zone are expected to be stronger.

69

Chapter 5 Conclusion

A study was conducted to investigate and examine the nature of the

hydrodynamic processes, pertaining to current flow and wave climate at Ramla

Bay. By means of drifter measurements, the flow the circulation of sea-

currents within the bay between July and October were mapped. A time-series

analysis for a selected number of tracks revealed that the velocities of currents

are stronger in the nearshore zone than in deeper portions of the bay, with

velocities ranging from 0 to 1m/s. The general flow pattern of currents followed

the alongshore direction, i.e. along the contours of the embayment. Currents

in deeper waters were recorded to cross the bay in lieu of following the

contours. Attempts to record rip currents using the drifters were unsuccessful,

leading to the conclusion that during the summer months, rip currents are

virtually inexistent. However, the possibility of strong rip currents (mega rips)

during the winter months should not be excluded as a possibility. If this were

to occur, a strongly defined cellular circulation would most likely prevail. For

this reason, similar surveys should be conducted during both summer and

winter months. Laborious statistical tests to determine the relationship between

the current direction and the wave direction within the embayment proved to

be statistically insignificant in shallow waters. However, to fully understand this

relationship, the results would have to be input and compared to modelled

outcomes, as was initially intended for this dissertation.

By means of modelled data of the monthly mean wave direction showed that,

wave directionality is more variable within the shallower nearshore regions of

the bay and that the dominant mean wave direction on average (even in the

surf-zone) originates from the northeast direction. This signifies that, the more

likely accumulation of beach sediments during this six month period, was likely

to occur on the western side of the pocket beach. An inversely proportional

relationship between the atmospheric pressure and the SWH is evident across

the months. The peaks in SWH occurring throughout certain months,

correspond to strong decreases in pressure, i.e. possible storm events. This

shows that climatic variances have a strong influence on the nature of

significant wave height. The spatial variation of the significant wave height

70

appeared to dampen within the shallower depths of the embayment, typical

since wave energy in shallower wave is drastically dissipated due to wave

breaking.

The results acquired, presented and discussed show little support to most of

the hypotheses formulated. Some statistical ambiguity did arise with the further

testing in attempting to correlate wave direction and current direction. The fact

that uncertainties within the modelled data do exist, needs to be acknowledged.

These uncertainties arose, particularly with the SWH for December.

Additionally, working numerical models may sometimes be unreliable. For

instance, the absence of data in the SWAN model and the Rosario-SHYFEM

model not operating. Nevertheless, numerical models are sometimes

necessary for studies in physical oceanography and coastal management,

especially because many complex processes and interactions cannot be

measured in the field at all times or at all. Uncertainties in the low accuracy of

the methodology to collect in-situ data may be argued. However, the results

have showed contextual association of the bathymetric map with that of

satellite imagery, as well as previous studies from Azzopardi (2015). For a

higher resolution surface bathymetry map, remote sensing would ideally be

used.

This research project, has been a pioneering study on the physical

characteristics of current and wave climate dynamics at Ramla, in which no

such study or data existed prior. This study may now serve as a baseline of

such information for future works. Even without the complete inclusion of winter

months in this study, the information provided for the summer period, when

human activities are highest at Ramla, may still be successfully applied to

certain aspects of management. From this study, it is suggested that to further

better understand the hydrodynamic processes at Ramla, particularly, on the

nature of rip currents, that annual measurements are taken. This information

should be regarded in the management studies and decisions, especially those

related to sediment dynamics, public safety, project proposals and the

fragmentation of Posidonia oceanica seagrass beds. This newly acquired

knowledge can now be applied to Coastal Management Plans. Such plans,

may be implemented using the sediment cell concept, in which currents and

71

waves are defining boundaries. This approach will help utilise a study such as

this, to implement management strategies to defend the coast in a sustainable

manner, whilst accommodating for the conservation of the area, as Ramla is

part of the NATURA 2000 network.

72

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Appendices

Appendix A – Drifter Tracks

Table A- 1: Table of information of drifter tracks.

Date No. of Tracks

Time ** Duration of Tracks

Wind Direction *

Heading Angle

2015/07/05 1 12:15 – 12:52 37 mins NNW 330o

2 12:17 – 12:37 20 mins NNW 330o

3 16:10 – 16:36 26 mins NNW 330o

4 16:13 – 16:41 28 mins NNW 330o

2015/07/10 1 18:09 – 19:18 69 mins NW 300o

2015/07/11 1 09:28 – 11:38 130 mins ENE 60o

2 13:26 – 1429 63 mins ENE 60o

3 13:27 – 14:37 70 mins ENE 60o

4 14:46 – 16:40 114 mins ENE 60o

2015/07/17 1 18:09 – 19:42 93 mins NNW 340o

2015/07/18 1 11:24 – 13:21 117 mins NNW 340o

2 15:56 – 16:16 60 mins NNW 340o

2015/08/28 1 15:51 – 17:44 113 mins ENE 60o

2 17:52 – 18:55 63 mins ENE 60o

2015/08/29 1 08:45 – 09:18 33 mins ENE 65o

2 09:27 – 11:10 103 mins ENE 65o

3 11:22 – 13:17 116 mins ENE 65o

4 13:39 – 14:34 55 mins ENE 65o

5 14:38 – 14:55 17 mins ENE 65o

6 15:11 – 16:20 69 mins ENE 65o

7 16:27 – 17:07 40 mins ENE 65o

2015/08/30 1 11:18 – 13:20 122 mins NNE 35o

2 14:35 – 15:59 84 mins NNE 35o

2015/09/04 1 18:03 – 19:51 108 mins W 270o

2015/09/05 1 09:14 – 10:31 77 mins SW 220o

2 11:02 – 12:48 106 mins SW 220o

3 13:02 – 14:14 72 mins SW 220o

4 15:10 – 16:06 56 mins SW 220o

2015/09/26 1 12:06 – 12:33 27 mins NNW 335o

2 12:54 – 13:31 37 mins NNW 335o

3 13:41 – 14:31 50 mins NNW 335o

4 14:50 – 16:39 109 mins NNW 335o

5 16:50 – 17:40 50 mins NNW 335o

6 17:50 – 19:12 82 mins NNW 335o

2015/09/27 1 09:10 – 11:59 169 mins NNW 340o

2015/10/04 1 12:11 – 13:44 93 mins E 90o

Total 2755 mins

Average 76.52mins

*colour code according to the angle of the wind direction during the day track was taken. **colour code to identify the times of each drifter on the maps, illustrated at the start of each track.

89


0 70 140 210 28035Meters

¯

Figure A- 1: Drifter tracks on the 5th of July 2015 with wind direction from the NNW.

Figure A- 1: Drifter tracks on the 10th of July 2015 with wind direction from the NW.Figure A- 2: Drifter tracks on the 5th of July 2015 with wind direction from the NNW.

89

90


0 70 140 210 28035Meters

¯

Figure A- 2: Drifter tracks on the 10th of July 2015 with wind direction from the NW.

Figure A- 3: Drifter tracks on the 11th of July 2015 with wind direction from the ENE.Figure A- 4: Drifter tracks on the 10th of July 2015 with wind direction from the NW.

90

91


0 70 140 210 28035Meters

¯

Figure A- 3: Drifter tracks on the 11th of July 2015 with wind direction from the ENE.

Figure A- 5: Drifter tracks on the 17th of July 2015 with wind direction from the NNE.Figure A- 6: Drifter tracks on the 11th of July 2015 with wind direction from the ENE.

91

92


0 70 140 210 28035Meters

¯

Figure A- 4: Drifter tracks on the 17th of July 2015 with wind direction from the NNE.

Figure A- 7: Drifter tracks on the 18th of July 2015 with wind direction from the NNW.Figure A- 8: Drifter tracks on the 17th of July 2015 with wind direction from the NNE.

92

93


0 70 140 210 28035Meters

¯

Figure A- 5: Drifter tracks on the 18th of July 2015 with wind direction from the NNW.

Figure A- 9: Drifter tracks on the 28th of August 2015 with wind direction from the ENE.Figure A- 10: Drifter tracks on the 18th of July 2015 with wind direction from the NNW.

93

94

#


0 70 140 210 28035Meters

¯

Figure A- 6: Drifter tracks on the 28th of August 2015 with wind direction from the ENE.

Figure A- 11: Drifter tracks on the 28th of August 2015 with wind direction from the ENE.Figure A- 12: Drifter tracks on the 28th of August 2015 with wind direction from the ENE.

94

95


0 70 140 210 28035Meters

¯

Figure A- 7: Drifter tracks on the 28th of August 2015 with wind direction from the ENE.

Figure A- 13: Drifter tracks on the 30th of August 2015 with wind direction from the NNE.Figure A- 14: Drifter tracks on the 28th of August 2015 with wind direction from the ENE.

95

96


0 70 140 210 28035Meters

¯

Figure A- 8: Drifter tracks on the 30th of August 2015 with wind direction from the NNE.

Figure A- 15: Drifter tracks on the 4th of September 2015 with wind direction from the W.Figure A- 16: Drifter tracks on the 30th of August 2015 with wind direction from the NNE.

96

97


0 70 140 210 28035Meters

¯

Figure A- 9: Drifter tracks on the 4th of September 2015 with wind direction from the W.

Figure A- 17: Drifter tracks on the 5th of September with wind direction from the SW.Figure A- 18: Drifter tracks on the 4th of September 2015 with wind direction from the W.

97

98


0 70 140 210 28035Meters

¯

Figure A- 10: Drifter tracks on the 5th of September with wind direction from the SW.

Figure A- 19: Drifter tracks on the 26th of September with wind direction from the NNW.Figure A- 20: Drifter tracks on the 5th of September with wind direction from the SW.

98

99


0 70 140 210 28035Meters

¯

Figure A- 11: Drifter tracks on the 26th of September with wind direction from the NNW.

Figure A- 21: Drifter tracks on the 27th of September 2015 with wind direction from the NNW.Figure A- 22: Drifter tracks on the 26th of September with wind direction from the NNW.

99

100


0 70 140 210 28035Meters

¯

Figure A- 12: Drifter tracks on the 27th of September 2015 with wind direction from the NNW.

Figure A- 23: Drifter tracks on the 4th of October 2015 with wind direction from the E.Figure A- 24: Drifter tracks on the 27th of September 2015 with wind direction from the NNW.

10

0

101


0 70 140 210 28035Meters

¯

Figure A- 13: Drifter tracks on the 4th of October 2015 with wind direction from the E.

Table A- 2: Table of the selected drifter track points and SWAN model grid points that have been selected based on closeness of between the two sets of points, spatially and temporally.Figure A- 25: Drifter tracks on the 4th of October 2015 with wind direction from the E.

10

1

102

Time SWAN Drifter

No SWAN Drifter Time Lat Lon Wave θ +/- 180 Lat Lon Drifter θ

1 15:00 20150828_1551_1744 15-56-01 36.063 14.282 44.785 224.785 36.062697 14.281413 288.92

2 18:00 20150828_1551_1744 17-06-31 36.063 14.28 41.991 221.991 36.06323 14.280089 287.19

3 12:00 20150829_1122_1317 11-23-45 36.065 14.282 7.05 187.05 36.065006 14.281881 195.63

4 12:00 20150829_1122_1317 13-06-17 36.065 14.28 12.002 192.002 36.064434 14.279989 290.65

5 15:00 20150829_1511_1620 16-00-42 36.065 14.282 3.425 183.425 36.064466 14.282049 249.12

6 15:00 20150829_1511_1620 15-16-32 36.065 14.284 358.7 178.7 36.064552 14.283901 255.34

7 18:00 20150904_1803_1951 19-01-52 36.065 14.286 68.137 248.137 36.065053 14.285908 348.89

8 18:00 20150904_1803_1952 19-06-33 36.065 14.286 68.137 248.137 36.065065 14.285945 67.59

9 12:00 20150905_1102_1248 11-35-26 36.063 14.284 46.933 226.933 36.063365 14.284479 336.60

10 12:00 20150905_1102_1248 12-27-06 36.065 14.284 71.178 251.178 36.064646 14.284739 43.44

11 12:00 20150905_1102_1248 12-42-26 36.065 14.286 65.736 245.736 36.065023 14.285019 20.33

12 12:00 20150926_1341_1431 13-42-21 36.065 14.284 336.47 156.47 36.064552 14.283973 107.19

13 12:00 20150926_1341_1431 14-08-51 36.065 14.286 333.49 153.49 36.064307 14.28605 90.00

14 12:00 20150926_1450_1639 15-49-56 36.063 14.2824 344 164 36.062604 14.283873 98.32

15 12:00 20150926_1450_1639 15-08-37 36.063 14.282 352.1 172.1 36.06319 14.282091 118.41

16 09:00 20150927_0910_1159 09-48-16. 36.063 14.282 350.98 170.98 36.062999 14.281823 180.00

17 12:00 20150927_0910_1159 11-54-22 36.063 14.282 350.11 170.11 36.062347 14.282307 107.11

10

2

Table A- 2: Table of the selected drifter track points and SWAN model grid points that have been selected based on closeness of between the two sets of points, spatially and temporally.

103

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

0 50 100 150 200 250

Velo

city (

m/s

)

Time (seconds)

U velocity 05/07/2015

12:15 – 12:52

12:17 – 12:37

16:10 – 16:36

16:13 – 16:41

-2

-1.5

-1

-0.5

0

0.5

1

0 50 100 150 200 250

Ve

locity (

m/s

)

Time (seconds)

V velocity 05/07/2015

12:15 – 12:52

12:17 – 12:37

16:10 – 16:36

16:13 – 16:41

Figure A- 14: Velocity time-series of the U (top) and V (bottom) components of four drifters on the 5th of July 2015.

Figure A- 26: Velocity time-series of the U (top) and V (bottom) components of four drifters on the 11th of July 2015.Figure A- 27: Velocity time-series of the U (top) and V (bottom) components of four drifters on the 5th of July 2015.

10

3

104

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0 100 200 300 400 500 600 700 800 900

Velo

city (

m/s

)

Time (seconds)


0928-1138

1326-1429

1327-1437

1446-1640

-0.4

-0.2

0

0.2

0.4

0.6

0 100 200 300 400 500 600 700 800 900

Velo

city

(m/s

)

Time (seconds)


0928-1138

1326-1429

1327-1437

1446-1640

Figure A- 15: Velocity time-series of the U (top) and V (bottom) components of four drifters on the 11th of July 2015.

Figure A- 28: Velocity time-series of the U (top) and V (bottom) components of four drifters on the 29th of August 2015.Figure A- 29: Velocity time-series of the U (top) and V (bottom) components of four drifters on the 11th of July 2015.

10

4

105

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0 100 200 300 400 500 600 700 800

Velo

city (

m/s

)

Time (seconds)


09:27 – 11:10

11:22 – 13:17

13:39 – 14:34

15:11 – 16:20

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0 100 200 300 400 500 600 700 800

Velo

city

(m/s

)

Time (seconds)


09:27 – 11:10

11:22 – 13:17

13:39 – 14:34

15:11 – 16:20

Figure A- 16: Velocity time-series of the U (top) and V (bottom) components of four drifters on the 29th of August 2015.

Figure A- 30: Velocity time-series of the U (top) and V (bottom) components of four drifters on the 26th of September 2015.Figure A- 31: Velocity time-series of the U (top) and V (bottom) components of four drifters on the 29th of August 2015.

10

5

106

-0.2

-0.1

0

0.1

0.2

0.3

0 100 200 300 400 500 600 700

Velo

city (

m/s

)

Time (seconds)

U Velocity 26/09/2015

13:41 – 14:31

14:50 – 16:39

16:50 – 17:40

17:50 – 19:12

-0.2-0.15

-0.1-0.05

00.050.1

0.150.2

0.250.3

0.35

0 100 200 300 400 500 600 700

Velo

city

(m/s

)

Time (seconds)

V Velocity 26/09/2015

13:41 – 14:31

14:50 – 16:39

16:50 – 17:40

17:50 – 19:12

Figure A- 17: Velocity time-series of the U (top) and V (bottom) components of four drifters on the 26th of September 2015.

10

6

107

Source: Esri, DigitalGlobe, GeoEye, Earthstar Geographics, CNES/Airbus DS, USDA,USGS, AEX, Getmapping, Aerogrid, IGN, IGP, swisstopo, and the GIS UserCommunity

¯

0 1,000 2,000500 Meters

LegendSWH August Average

0.14 - 0.14

0.15 - 0.15

0.16 - 0.15

0.16 - 0.16

0.17 - 0.17

0.18 - 0.17

0.18 - 0.18

0.19 - 0.18

0.19 - 0.19

0.2 - 0.19

0.2 - 0.2

0.21 - 0.2

0.21 - 0.21

0.22 - 0.21

0.22 - 0.22

0.23 - 0.22

0.23 - 0.23

0.24 - 0.23

0.24 - 0.24

0.25 - 0.25

0.26 - 0.25

0.26 - 0.26

0.27 - 0.26

0.27 - 0.27

0.28 - 0.27

0.28 - 0.28

0.29 - 0.28

0.29 - 0.29

0.3 - 0.29

0.3 - 0.3

0.31 - 0.3

0.31 - 0.31

Figure B- 1: Average Significant Wave Height for August.

Ap

pe

nd

ix B

– S

WA

N S

ign

ifica

nt W

ave

He

igh

t Ma

ps

10

7

108

Source: Esri, DigitalGlobe, GeoEye, Earthstar Geographics, CNES/Airbus DS, USDA,USGS, AEX, Getmapping, Aerogrid, IGN, IGP, swisstopo, and the GIS User Community

¯

0 1,000 2,000500 Meters

LegendSWH Sept Average

0.15 - 0.16

0.17 - 0.17

0.18 - 0.18

0.19 - 0.19

0.2 - 0.2

0.21 - 0.21

0.22 - 0.22

0.23 - 0.23

0.24 - 0.24

0.25 - 0.25

0.26 - 0.25

0.26 - 0.26

0.27 - 0.27

0.28 - 0.28

0.29 - 0.29

0.3 - 0.3

0.31 - 0.31

0.32 - 0.32

0.33 - 0.33

0.34 - 0.34

0.35 - 0.35

0.36 - 0.36

0.37 - 0.36

0.37 - 0.37

0.38 - 0.38

0.39 - 0.39

0.4 - 0.4

0.41 - 0.41

0.42 - 0.42

0.43 - 0.43

0.44 - 0.44

0.45 - 0.45

Figure B- 2: Average Significant Wave Height for September.

10

8

109


¯

0 1,000 2,000500 Meters

LegendSWH Oct Average

0.25 - 0.26

0.27 - 0.27

0.28 - 0.29

0.3 - 0.3

0.31 - 0.31

0.32 - 0.33

0.34 - 0.34

0.35 - 0.35

0.36 - 0.37

0.38 - 0.38

0.39 - 0.39

0.4 - 0.41

0.42 - 0.42

0.43 - 0.43

0.44 - 0.45

0.46 - 0.46

0.47 - 0.47

0.48 - 0.49

0.5 - 0.5

0.51 - 0.51

0.52 - 0.53

0.54 - 0.54

0.55 - 0.55

0.56 - 0.57

0.58 - 0.58

0.59 - 0.59

0.6 - 0.61

0.62 - 0.62

0.63 - 0.63

0.64 - 0.64

0.65 - 0.66

0.67 - 0.67

Figure B- 3: Average Significant Wave Height for October.

10

9

110


¯

0 1,000 2,000500 Meters

LegendSWH Nov Average

0.22 - 0.24

0.25 - 0.26

0.27 - 0.28

0.29 - 0.3

0.31 - 0.31

0.32 - 0.33

0.34 - 0.35

0.36 - 0.37

0.38 - 0.39

0.4 - 0.4

0.41 - 0.42

0.43 - 0.44

0.45 - 0.46

0.47 - 0.48

0.49 - 0.5

0.51 - 0.51

0.52 - 0.53

0.54 - 0.55

0.56 - 0.57

0.58 - 0.59

0.6 - 0.6

0.61 - 0.62

0.63 - 0.64

0.65 - 0.66

0.67 - 0.68

0.69 - 0.69

0.7 - 0.71

0.72 - 0.73

0.74 - 0.75

0.76 - 0.77

0.78 - 0.78

0.79 - 0.8

Figure B- 4: Average Significant Wave Height for November.

11

0

111


¯

0 1,000 2,000500 Meters

LegendSWH Dec Average

0.17 - 0.17

0.18 - 0.18

0.19 - 0.19

0.2 - 0.19

0.2 - 0.2

0.21 - 0.21

0.22 - 0.21

0.22 - 0.22

0.23 - 0.23

0.24 - 0.23

0.24 - 0.24

0.25 - 0.25

0.26 - 0.25

0.26 - 0.26

0.27 - 0.26

0.27 - 0.27

0.28 - 0.28

0.29 - 0.28

0.29 - 0.29

0.3 - 0.3

0.31 - 0.3

0.31 - 0.31

0.32 - 0.32

0.33 - 0.32

0.33 - 0.33

0.34 - 0.34

0.35 - 0.34

0.35 - 0.35

0.36 - 0.36

0.37 - 0.36

0.37 - 0.37

0.38 - 0.38

Figure B- 5: Average Significant Wave Height for December.

11

1

112


¯

0 1,000 2,000500 Meters

LegendSWG Jan Average

0.23 - 0.25

0.26 - 0.27

0.28 - 0.29

0.3 - 0.31

0.32 - 0.33

0.34 - 0.35

0.36 - 0.37

0.38 - 0.39

0.4 - 0.41

0.42 - 0.43

0.44 - 0.45

0.46 - 0.47

0.48 - 0.49

0.5 - 0.51

0.52 - 0.53

0.54 - 0.55

0.56 - 0.57

0.58 - 0.59

0.6 - 0.61

0.62 - 0.63

0.64 - 0.65

0.66 - 0.67

0.68 - 0.7

0.71 - 0.72

0.73 - 0.74

0.75 - 0.76

0.77 - 0.78

0.79 - 0.8

0.81 - 0.82

0.83 - 0.84

0.85 - 0.86

0.87 - 0.88

Figure B- 6: Average Significant Wave Height for January.

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2

113


¯LegendSWH Total Average

0.216 - 0.231

0.232 - 0.241

0.242 - 0.251

0.252 - 0.262

0.263 - 0.274

0.275 - 0.285

0.286 - 0.296

0.297 - 0.308

0.309 - 0.319

0.32 - 0.33

0.331 - 0.341

0.342 - 0.353

0.354 - 0.363

0.364 - 0.373

0.374 - 0.384

0.385 - 0.395

0.396 - 0.406

0.407 - 0.418

0.419 - 0.429

0.43 - 0.44

0.441 - 0.452

0.453 - 0.463

0.464 - 0.474

0.475 - 0.485

0.486 - 0.497

0.498 - 0.508

0.509 - 0.519

0.52 - 0.532

0.533 - 0.545

0.546 - 0.555

0.556 - 0.565

0.566 - 0.576

0 2,0001,000 Meters

Figure B- 7: Average Significant Wave Height for the total period of study.

11

3

114

F

F F

F F F F F F F

F

F F F F F F F

F

F F F F F F F F F F F F F

F

F F F F F F F F F F F F F F

F F F F F F F F F F F F F F F

F

F


F

F F F F F F F F F F F F F F F F F F F F F

F F F F F F F F F F F F F F F F F F F F F F

F

F F F F F F F F F F F F F F F F F F F F F F F F

F F F F F F F F F F F F F F F F F F F F F F F F F

F F F F F F F F F F F F F F F F F F F F F F F F F F











¯

0 1,000 2,000500 Meters

LegendWD August Average

F29 - 35

36 - 42

43 - 48

49 - 55

56 - 61

62 - 68

69 - 74

75 - 81

82 - 87

88 - 93

94 - 100

110 - 110

120 - 110

120 - 120

130 - 130

140 - 130

140 - 140

150 - 150

160 - 150

160 - 160

170 - 160

170 - 170

180 - 180

190 - 180

190 - 190

200 - 200

210 - 200

210 - 210

220 - 220

230 - 220

230 - 230

240 - 240

Figure C- 1: Average Mean Wave Direction for August.

Appendix

C –

SW

AN

Me

an

Wa

ve

Dire

ctio

n

Ma

ps

11

4

115

F

F F

F F F F F F F

F

F F F F F F F

F


F



F F F F F F F F F F F F F F F F F


F F F F F F F F F F F F F F F F F F F F F FF














¯

0 1,000 2,000500 Meters

LegendWD Sept Average

F230 - 230

230 - 220

220 - 220

220 - 210

210 - 210

200 - 200

200 - 190

190 - 190

190 - 180

180 - 180

170 - 170

170 - 160

160 - 160

160 - 150

150 - 150

150 - 140

140 - 140

130 - 130

130 - 120

120 - 120

120 - 110

110 - 110

95 - 100

89 - 94

83 - 88

77 - 82

71 - 76

65 - 70

59 - 64

53 - 58

47 - 52

41 - 46

Figure C- 2: Average Mean Wave Direction for September.

11

5

116

FF F

F F F F F F FF

F F F F F F FF F F F F F F F F F F F F FF F F F F F F F F F F F F F F


F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F F F F F

F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F F F F F F F F






F F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F F F F F F F F F


¯

0 1,000 2,000500 Meters

LegendWD Oct Average

F32 - 36

37 - 39

40 - 43

44 - 46

47 - 50

51 - 53

54 - 57

58 - 60

61 - 64

65 - 67

68 - 71

72 - 74

75 - 78

79 - 82

83 - 85

86 - 89

90 - 92

93 - 96

97 - 99

100 - 100

110 - 110

120 - 110

120 - 110

120 - 120

130 - 120

130 - 120

130 - 130

140 - 130

140 - 130

140 - 140

150 - 140

150 - 150

Figure C- 3: Average Mean Wave Direction for October.

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117

Figure C- 4: Average Mean Wave Direction for November.

F

F FF F F F F F FF

F F F

F F F F

F


F



F F


F F F F FF F F F F F F F F F F F F F F F F


FF F F F F F F F F F F F F F F F F F F F F F F F













¯

0 1,000 2,000500 Meters

LegendWD Nov Average

F22.5 - 29.8

29.9 - 37.2

37.3 - 44.6

44.7 - 51.9

52 - 59.3

59.4 - 66.7

66.8 - 74

74.1 - 81.4

81.5 - 88.8

88.9 - 96.1

96.2 - 103

104 - 111

112 - 118

119 - 126

127 - 133

134 - 140

141 - 148

149 - 155

156 - 162

163 - 170

171 - 177

178 - 185

186 - 192

193 - 199

200 - 207

208 - 214

215 - 221

222 - 229

230 - 236

237 - 243

244 - 251

252 - 258

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7

118

F

F

FF F F

F F F FF

F F F F F F FF

F F F F F F F F F F F F FFF F F F F F F F F F F F F F

F F F F F F F F F F F F F F FF

F

F F F F F F F F F F F F F F FF

F F FF F F F F F F F F F F F F F F F F F

F F F F F F F F F F F F F F F F F F F F F FF


F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F F F F F F F F F


¯

0 1,000 2,000500 Meters

LegendWD Dec Average

F29 - 35

36 - 41

42 - 47

48 - 52

53 - 58

59 - 64

65 - 70

71 - 75

76 - 81

82 - 87

88 - 93

94 - 98

99 - 100

110 - 110

120 - 120

130 - 120

130 - 130

140 - 130

140 - 140

150 - 140

150 - 150

160 - 160

170 - 160

170 - 170

180 - 170

180 - 180

190 - 180

190 - 190

200 - 200

210 - 200

210 - 210

220 - 210

Figure C- 5: Average Mean Wave Direction for December.

11

8

119

F

F FF F F F F F F

F

F F F

F

F F F

F


F



F F F F F F F F F F F F F F F F F



F














¯

0 1,000 2,000500 Meters

LegendWD Jan Average

F23 - 31

32 - 39

40 - 47

48 - 54

55 - 62

63 - 70

71 - 77

78 - 85

86 - 93

94 - 100

110 - 110

120 - 120

130 - 120

130 - 130

140 - 140

150 - 150

160 - 150

160 - 160

170 - 170

180 - 180

190 - 190

200 - 190

200 - 200

210 - 210

220 - 220

230 - 220

230 - 230

240 - 240

250 - 250

260 - 250

260 - 260

270 - 270

Figure C- 6: Average Mean Wave Direction for January.

11

9

120

1010

1011

1012

1013

1014

1015

1016

1017

1018

1019

1020

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Atm

osph

eric P

ressure

(h

Pa

)

Sig

nific

ant W

ave

He

igh

t (m

)

Time

Average Significant Wave Height Time-Series of August

August pt 2 August pt 1 August pt 3

August pt 4 August pt 5 Pressure (hPa)

August pt 2

Figure D- 1: Time-Series for the Significant Wave Height during August across the five points from the transect.

Ap

pe

nd

ix D

– S

ign

ifica

nt W

ave

He

igh

t Tim

e S

erie

s

August pt 1

12

0

121

Figure D- 2: Time-Series for the Significant Wave Height during September across the five points from the transect.

1008

1010

1012

1014

1016

1018

1020

1022

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Atm

osph

eric P

ressure

(h

Pa

)

Sig

nific

ant W

ave

He

igh

t (m

)

Time

Average Significant Wave Height Time-Series of September

September pt 1 September pt 2 September pt 3

September pt 4 September pt 5 Pressure (hPa)

12

1

122

1004

1006

1008

1010

1012

1014

1016

1018

1020

1022

1024

0

0.2

0.4

0.6

0.8

1

1.2

Atm

osph

eric P

ressure

(h

Pa

)

Sig

nific

ant W

ave

He

igh

t (m

)

Time

Average Significant Wave Height Time-Series of Ocotober

October pt 1 October pt 2 October pt 3October pt 4 October pt 5 Pressure (hPa)

Figure D- 3: Time-Series for the Significant Wave Height during October across the five points from the transect.

12

2

123

1000

1005

1010

1015

1020

1025

1030

0

0.5

1

1.5

2

2.5

3

3.5

4

Atm

ospheric P

ressure

(hP

a)

Sig

nific

ant

Wave H

eig

ht

(m)

Time

Average Significant Wave Height Time-Series of November

November pt 1 November pt 2 November pt 3November pt 4 November pt 5 Pressure (hPa)

Figure D- 4: Time-Series for the Significant Wave Height during November across the five points from the transect.

12

3

124

1020

1025

1030

1035

1040

1045

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Atm

osph

eric P

ressure

(h

Pa

)

Sig

nific

ant W

ave

He

igh

t (m

)

Time

Average Significant Wave Height Time-Series of December

December pt 2 December pt 1 December pt 3December pt 4 December pt 5 Pressure (hPa)

December pt 2December pt 1

Figure D- 5: Time-Series for the Significant Wave Height during December across the five points from the transect.

12

4

125

1000

1005

1010

1015

1020

1025

1030

1035

1040

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Atm

osph

eric P

ressure

(h

Pa

)

Sig

nific

ant W

ave

He

igh

t (m

)

Time

Average Significant Wave Height Time-Series of January

January pt 1 January pt 2 January pt 3January pt 4 January pt 5 Pressure (hPa)

Figure D- 6: Time-Series for the Significant Wave Height during January across the five points from the transect.

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A study on the Physical Characteristics of Currents and Wave …€¦ · shallowest depths in red,...

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Transcript of A study on the Physical Characteristics of Currents and Wave …€¦ · shallowest depths in red,...