Hervey Bay - Insights from Numerical Modelling into the...

Hervey Bay - Insights from NumericalModelling into the Hydrodynamics of an

Australian Subtropical Bay

Von der Fakultat fur Mathematik und Naturwissenschaften der Carl

von Ossietzky Universitat Oldenburg zur Erlangung des Grades und

Titels eines

Doktors der Naturwissenschaften (Dr. rer. nat.)

angenommene Dissertation

von Herrn Ulf Grawe

geboren am 12. Juli 1974 in Stralsund

Erstgutachter: Prof. Dr. Jorg-Olaf Wolff

Zweitgutachter: Prof. Dr. Emil Stanev

Tag der Disputation: 11. September 2009

...Twenty years from now, you will be more disappointed

by the things you didn’t do than by the ones you did do. So

throw off the bowlines. Sail away from the save harbour.

Catch the trade winds in your sails. Explore. Dream.

Discover ... - Mark Twain

Abstract

Hervey Bay, a large coastal embayment situated off the central eastern coast of Australia, is

a shallow tidal area (average depth = 15 m), close to the continental shelf. It shows features

of an inverse estuary, due to the high evaporation rate (approx. 2 m/year), low precipitation

(less than 1 m/year) and on average almost no freshwater input from rivers that drain into

the bay.

The hydro- and thermodynamical structure of Hervey Bay and their variability are presented

here for the first time, using a combination of three-dimensional numerical modelling and

observations from field studies. The numerical studies are performed with the COupled Hy-

drodynamical Ecological model for REgioNal Shelf seas (COHERENS).

Due to the high tidal range (> 3.5 m) the bay is considered as a vertically well-mixed system

and therefore only horizontal fronts a likely. Recent field measurements, but also the numerical

simulations indicate characteristic features of an inverse/hypersaline estuary with low salinities

(35.5 psu (practical salinity units)) in the open ocean and peak values (> 39.0 psu) in the head

water of the bay. The model further predicts a nearly persistent mean salinity gradient of 0.5

psu across the bay (with higher salinities close to the shore). The investigation further shows

that air temperature, wind direction, and tidal regime are mainly responsible for the stability

of the inverse circulation and the strength of the salinity gradient across the bay. Moreover,

wind forcing is the main driver for exchange processes within the bay. The dominating easterly

Trade winds are important to maintain the hypersaline/inverse features of Hervey Bay and to

control the water exchange within the bay.

Due to a long-lasting drying trend along the subtropical east coast of Australia and a significant

change in local climate, rainfall has decreased by about 50 mm per decade and temperature

increased by about 0.1 °C per decade during the last fifty years. These changes are likely to im-

pact upon the hydro- and thermodynamics of Hervey Bay, which is controlled by the balance

between evaporation, precipitation, and freshwater discharge. During the last two decades,

mean precipitation in Hervey Bay deviates by 13 % from the climatology (1941-2000). In the

same time, the annual river discharge is reduced by 23 %. In direct consequence, the frequency

of hypersaline and inverse conditions has increased. Moreover, the salinity flux out of the bay

has increased and the evaporation induced residual circulation has accelerated. Contrary to

the drying trend, the occurrence of severe rainfalls, associated with floods, leads to short-term

fluctuations in the salinity. These freshwater discharge events are used to estimate a typical

response time for the bay, which are strongly linked to wind driven water exchange time scales.

Due to the inverse features and thus a density difference between the shore and open ocean

(with higher densities close to the coast), gravity currents are released. They occur mostly

during late autumn and have an average duration of 30 days. The integrated volume transport,

associated with these flows, is comparable with the total volume of Hervey Bay.

8

Zusammenfassung

Hervey Bay, eine ca. 4000 km2 grosse Bucht (durchschnittliche Tiefe = 15 m), befindet

sich in unmittelbarer Nahe der kontinentalen Schelfkante der zentralen Ostkuste von Aus-

tralien. Durch die hohe Verdunstungsrate (ca. 2 m/Jahr), geringe Niederschlage (weniger als

1 m/Jahr) und nahezu verschwindenden Susswassereintrag durch Flusse, kann eine inverse

Struktur/Schichtungen erwartet werden.

In dieser Arbeit wird erstmalig die hydro- und thermodynamische Struktur von Hervey Bay

und deren Variabilitat prasentiert. Es werden Ergebnisse numerischer Modellierung sowie Feld-

daten von Messfahrten benutzt. Die numerischen Experimente wurden mit dem Modell “COu-

pled Hydrodynamical Ecological model for REgioNal Shelf seas” (COHERENS) durchgefuhrt.

Da Hervey Bay ein starkes Gezeitensignal aufweist (Tidenhub > 3,5 m), kann die Bucht als

vertikal gut durchmischt klassifiziert werden. Die Ergebnisse der Messfahrten, als auch die

numerischen Experimente, bestatigen, dass Hervey Bay die charakteristischen Merkmale einer

inversen/hypersalinen Struktur aufweist. In der Bucht existiert einen nahezu konstanten Salz-

gradient von 0.5 psu (practical salinity unit), mit einem Salzgehalt von 35.5 psu im offenen

Ozean und Spitzenwerten von uber 39.0 psu im kustennahen Bereich. Die Untersuchung

zeigten, dass Lufttemperatur, Wind und Gezeiten die wichtigsten Einflussgrossen fur die Sta-

bilitat der inversen Schichtung und der Salzgradienten sind, wahrend die ostlichen Passatwinde

den Wasseraustausch in der Bucht dominieren.

Aufgrund von lang anhaltenden Durren weisen die subtropischen Gebiete an der Ostkuste Aus-

traliens eine Veranderungen in der Balance von Niederschlag und Verdunstung auf. Langzeit-

datenreihen zeigen wahrend der letzten funfzig Jahre eine Verringerung der Niederschlags-

menge von ca. 50 mm pro Jahrzehnt an, verbunden mit einem Temperaturanstieg um etwa

0.1 °C pro Jahrzehnt. Mit Hilfe der numerischen Experimente konnten die Auswirkungen auf

die Hydro- und Thermodynamik von Hervey Bay untersucht werden. Durch die Verschiebung

des Gleichgewichtes zwischen Verdunstung und Niederschlag treten hypersaline und inverse

Bedingungen in Hervey Bay haufiger auf. In den letzten zwei Jahrzehnten weist der mittlere

Niederschlag in Hervey Bay eine Abweichung von 13 % von der Klimatologie (1941-2000) auf.

Die Verringerung im Flusseintrag, im selben Zeitraum, kann mit 23 % abgeschatzt werden.

Eine direkte Folge ist, dass sich der Salzigkeitsfluss erhoht hat, sowie die verdunstungsges-

teuerte Residuenstromungen beschleunigt haben.

Im Gegensatz zu der langfristigen Reduzierung der Niederschlage fuhrt das Auftreten von schw-

eren Regenfallen und damit verbundenen Uberschwemmungen, zu kurzfristigen Schwankungen

im Salzgehalt von Hervey Bay. Die Untersuchungen dieser extremen Frischwassereintrage er-

gaben, dass die Frischwasseraustauschzeiten eng an die windgetriebenen Residuenstromungen

gekoppelt sind.

Die inversen Eigenschaften von Hervey Bay und die damit verbundene Dichtegradienten (mit

einer hoheren Dichte in Kustennahe als im offenen Ozean) konnen instabile Schichtungen erzeu-

gen. Diese aussern sich in Dichtestromungen und damit einem Ausfluss von dichtem Wasser

entlang des Grundes von Hervey Bay. Die Ausflussereignisse haben eine mittlere Dauer von

30 Tagen und sind meistens auf den Spatherbst beschrankt. Der dabei auftretende integrierte

Volumentransport ist vergleichbar mit dem Volumen von Hervey Bay.

10

Contents

1 Introduction 3

2 The Region and Data 8

2.1 The Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Model description 12

3.1 General features of COHERENS . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.3 Model design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4 Barotropic circulations 16

4.1 Tidal forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.1.1 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.1.2 Tidal mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.2 Residual circulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.3 Water exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.3.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.3.2 Flushing time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.3.3 Residence time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3.4 Origin of replacement water . . . . . . . . . . . . . . . . . . . . . . . . . 27

5 Baroclinic processes 29

5.1 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.2 Stratification within Hervey Bay . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.3 Inverse state and hypersalinity . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.4 Evaporation induced circulations . . . . . . . . . . . . . . . . . . . . . . . . . . 39

6 Impact of climate variability 43

6.1 The drying trend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.1.1 Trends in freshwater supply . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.1.2 Hypersalinity and inverse state . . . . . . . . . . . . . . . . . . . . . . . 44

6.1.3 Residual circulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

1

Contents

6.1.4 Salinity flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6.1.5 Impact of the East Australian Current (EAC) . . . . . . . . . . . . . . . 46

6.2 Short term variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6.2.1 Catchment area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.2.2 River discharge statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.2.3 Flooding events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.2.4 The flood of 1999 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6.2.5 Flood response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

7 Gravity currents 54

7.1 Release of gravity currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

7.1.1 Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

7.1.2 Pre-conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

7.1.3 Down-slope propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

7.1.4 Fate of the plume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

7.2 Impact of freshwater reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

8 Conclusion 59

A Particle tracking schemes 61

A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

A.2 The Lagrangian model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

A.2.1 Numerical approximation . . . . . . . . . . . . . . . . . . . . . . . . . . 63

A.2.2 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

A.3 Idealised test cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

A.3.1 1-D diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

A.3.2 1-D residence time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

A.3.3 2-D correlation test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

A.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

2

1 Introduction

Estuaries have always attracted human settlements. Sheltered harbours, good fishing grounds,

access to transport along rivers have been important reasons why people have set up cities

along the coastal shores for millennia. The various human uses of estuaries affect the water

quality and the health of the estuarine ecosystem. As the human population grew significantly

during the 19th and 20th century and is expected to grow further in the next centuries, human

settlements along estuarine shores increase in size. With about 70% of the global population

living within the coastal zone, distance to the shore less than 100 km (e.g. Cohen et al.

[1997]), the influence of human activity upon coastal marine environments is immense. More-

over, the challenges and potential threats due to climate change, as the expected rise in sea

level, the possible increase in frequency or magnitude of weather extremes put an enormous

pressure on the life in coastal regions.

The increase in knowledge and understanding of coastal hydrodynamics and water exchange

cannot prevent for instance the occurrence of oil spills, waste dumping, toxic algae blooms,

or climate change. However, the knowledge of the complex processes in coastal waters can

lead to the development of adoption strategies, construction of protected habitats, redirection

of fairways, or construction of coastal protections. Thus, we can reduce the impact of future

threats and challenges or can better cope with them.

The understanding of the interaction of the near shore region with the open ocean, the impact

of climate change but also the influence of freshwater discharge in the coastal zone is in particu-

lar important for Australia. The Intergovernmental Panel on Climate Change (IPCC) predicts

a decrease in precipitation over many subtropical areas such as the East coast of Australia,

American-Caribbean and the Mediterranean [IPCC, 2007]. The observed decrease in precip-

itation [Shi et al. , 2008a] along the east coast of Australia distorted the balance between

evaporation/precipitation. Moreover, due to an increase in sea surface temperature, coral

bleaching is a severe issue in the Great Barrier Reef [Berkelmans and Oliver, 1999; Glynn,

2006; Hoegh-Guldberg, 2009]. Further, heavy precipitation events are projected to become

more frequent over most regions throughout the 21 st century. This would affect the risk of

flash flooding and urban flooding. These floods are expected to flush huge amounts of water,

of urban/rural origin, into the coastal regions, with the consequence of severe stress on the

local flora/fauna. Thus, the subtropical regions of Australia offer an excellent research area,

to investigate the interplay between evapotranspiration, regional ocean circulations/response

and climate change.

3

1 Introduction

In these subtropical climates where evaporation is likely to exceed the supply of freshwater from

precipitation and river run-off, large coastal bays, estuaries and near shore coastal environments

are often characterised by inverse circulations and hypersalinity zones [Tomczak and Godfrey,

2003; Wolanski, 1986]. An inverse circulation/estuary/bay is characterised by sub-surface flow

of saline water away from a zone of hypersalinity towards the open ocean. This flow takes

place beneath a layer of inflowing oceanic water and leads to salt injections into the ocean

[Brink and Shearman, 2001]. Secondly, inverse circulations are characterised by a reversed

density gradient. The riverine fresh water input and therefore low densities control the coastal

zone in regular estuaries or bays. Inverse estuaries or bays on the other hand are characterised

by high salinities in the coastal zone with inverse gradients for salinity and density directing

offshore with minimal direct oceanic influence. Examples for such regions include the Gulf

of California [Lavin et al. , 1998], estuaries in Mediterranean-climate regions (Tomales Bay,

California; Largier et al. [1997]), Spencer Gulf [Lennon et al. , 1987], the Ria of Pontevedra

[de Castro et al. , 2004] and the Gulf of Kachchh [Vethamony et al. , 2007].

High evaporation during summer leads to an accumulation of salt in the headwater of these

inverse bays or estuaries. Following the season into autumn and winter, these water masses are

subsequently cooled and can become gravitationally unstable. Under certain circumstances,

they can evolve into gravity currents or plumes that flow out of the bay into the deeper ocean

adjacent to the continental shelf. Due to strong tidal and wind induced mixing (either vertically

or horizontally) these events should be of short duration. Efficient mixing homogenises the

water column and instead of a two-layer structure in the vertical, one observes a more horizon-

tally distributed frontal system [Loder and Greenberg, 1986]. These gravity flows are not only

restricted to the subtropical regions. They can also occur in mid latitudes [Burchard et al. ,

2005] or even in high latitudes [Fer and Adlandsvik, 2008]. In the latter cases, the triggering

is caused by inflow of high saline water in closed seas or accumulation of salt due to freezing.

Despite different mechanisms that lead to the creation of unstable stratifications and relax-

ation into gravity flows, they are all controlled by the interaction of earth rotation, friction,

topography and pressure gradient [Shapiro et al. , 1997].

The excess of evaporation over precipitation also induces a mass flux towards the shore. Due

to the net loss of water (by evaporation) and to maintain the water balance, an inflow of water

from the ocean is required and in the case of semi enclosed water bodies with restricted water

exchange with the open ocean, this can have implications for the accumulation of salt, organic

or inorganic tracers and pollutants.

In Australia, where climate is characterised by significant inter annual variability in rainfall

[Murphy et al. , 2004], longer lasting trends in annual rainfall have been observed since about

1950 [Shi et al. , 2008a]. Along the densely populated east coast, annual rainfall has declined

by more than 200 mm during the period 1951-2000. This reduction in total annual rainfall has

caused persistent drought conditions in the last two decades. These shifts have been attributed

4

to changes in large scale climate system processes such as the Southern Annular Mode, the

Indian Ocean Dipole and the El Nino Southern Oscillation [Shi et al. , 2008b]. These changes,

which are linked to a widening of the tropical belt, are projected to persist into the future.

The adjustments are associated with an increased heat transport by the southward flowing

East Australia Current (EAC) that has been attributed to atmospheric circulation changes

[Cai et al. , 2005]. The changes in rainfall are accompanied by a rise in near surface atmo-

spheric temperature that along the east coast of Australia is in the order of about 0.1 °C per

decade [Beer et al. , 2006].

The Southern Oscillation Index (SOI) is a simple measure of the status of the Walker Cir-

culation, a major wind pattern of the Asia/Pacific region whose variability affects rainfall in

Australia and other parts of the world. During El Nino episodes, the Walker circulation weak-

ens and the SOI becomes negative. Other changes during El Nino events include cooling of

seas around Australia, as well as a slackening of the Pacific trade winds which in turn feed less

moisture into the Australian/Asian region. There is then a high probability that eastern and

northern Australia will be drier than normal. Rural productivity, especially in Queensland and

New South Wales, is linked to the behaviour of the Southern Oscillation. When the South-

ern Oscillation Index sustains high positive values, the Walker circulation intensifies, and the

eastern Pacific cools. These changes often bring widespread rain and flooding to Australia -

this phase is called La Nina. Australia’s strongest recent examples were in 1973-74 (Brisbane’s

worst flooding this century in January 1974) and 1988-89 (vast areas of inland Australia had

record rainfall in March 1989).

In this thesis, a detailed description of the hydrodynamic and thermohaline structure of Hervey

Bay is presented for the first time, with the help of numerical simulations. Hervey Bay is a

coastal embayment at the central East coast of Australia, which has attracted only little atten-

tion from the physical oceanography community during the last two decades. Middleton et al.

[1994] lacked observational evidence in support of their hypothesis that Hervey Bay potentially

exports high salinity water formed through a combination of heat loss, high evaporation, and

weak freshwater input in shallow regions of the bay. Field observations by Ribbe [2006] sug-

gests, that Hervey Bay can be classified as an inverse bay and that indeed the excess of

evaporation over precipitation leads to a salinity flux out of the bay.

This study explores in detail the mechanisms that lead to sub-surface flow of high saline wa-

ters out of the bay (gravity currents) and the stability of these flows. Recent hydrographical

observations from Hervey Bay, Ribbe [2008] and a coastal ocean general circulation model are

used for this purpose.

The coastal bay is shown to be dominated by hypersalinity and an inverse circulation. Hy-

persalinity is a persistent feature and is more frequent in the last decade due to an ongoing

drying trend and the occurrence of droughts. These severe weather events and extreme high

river discharge, due to flash floods, led to a major seagrass loss in the region of Hervey Bay

5

1 Introduction

and impacted adversely upon the Dugong (sea cow) population in the past [Preen et al. ,

1995; Campell and McKenzie, 2004] highlighting the regions vulnerability to extreme physical

climatic events. Sea grass recovery was monitored for several years [Campell and McKenzie,

2004]. The subtropical waters of Hervey Bay are also a spawning region for temperate pelagic

fish [Ward et al. , 2003] and support the fishery industry worth several tens of millions of

dollars, with aquaculture recently developing into a significant industry. Furthermore, recent

studies showed how the reduction of river discharges and most likely precipitation, impacts on

the fish production on the East coast of Australia [Staunton et al. , 2004; Growns and James,

2005; Meynecke et al. , 2006]. Their findings indicate a reduction in catch due to a decline in

freshwater supply. In extreme cases, the reduction of freshwater can lead to hypersalinisation

[Mikhailova and Isupova, 2008] in estuaries or the headwater of gulfs. In combination with

severe floods and therefore highly variable salt content, the induced stress on species can in-

fluence their growing stage [Labonne et al. , 2009].

The thesis is organised as follows: In chapter 2 Hervey Bay, the surrounding region and local

features are presented. Further, the data and sources, used in this work, are given.

Because this work is based on numerical simulations, in chapter 3 the numerical model is in-

troduced and the parameterisations, that are essential for this study, are described. Moreover,

the boundary conditions to force the model and the model design are highlighted.

Chapter 4 deals with the barotropic processes, thus only wind and tidal forcing is considered.

Results are presented to show that the model can reproduce the tidal signal in Hervey Bay and

surroundings. Further, the impact of tidal mixing and wind induced mixing is investigated.

To quantify the water exchange within the bay, different exchange time scales are introduced.

These measures are used to understand the response of Hervey Bay to different forcing sce-

narios.

In chapter 5, additional temperature and salinity forcing is considered, thus the model is used

to investigate baroclinic processes. Data from field trips are used to validate the temperature,

salinity and density fields of the simulations. Because numerical models can produce long-term

time series, this fact is used to quantify the stratification in the bay. Further it will be shown,

that due to the high evaporation, the salinity fields in Hervey Bay show a reverse/inverse

pattern, than known for instance from the North Sea. The circulations, associated with these

salinity fields, are described and quantified.

Chapter 3-5 are published in Ocean Dynamics, [Grawe et al. , 2009a].

Whereas chapter 3-5 give an insight into the dominant circulation pattern of Hervey Bay and

the most important hydrodynamic processes, chapter 6 is intended to show how the first signs

of climate change affect the hydrodynamic and thermohaline state of the bay. The chapter is

separated into the description of long-term effects and also the short-term variability and is

based in the article [Grawe et al. , 2009b], that is submitted to Estuarine, Coastal and Shelf

Science.

6

In chapter 7, a special feature of Hervey Bay is described. Due to interaction of high evapo-

ration rate and atmospheric cooling, gravity currents are triggered, that lead to an outflow of

Hervey Bay water over the continental shelf. The model is used to track the fate of the plumes

and to quantify the mass transport related to these events.

Finally, in chapter 8 conclusions are drawn.

In the appendix a detailed description of a Lagrangian particle tracking scheme is given, which

is used in chapter 4. The appendix was derived from the article [Grawe and Wolff, 2009], that

is published in Environmental Fluid Mechanics.

7

2 The Region and Data

2.1 The Region

Hervey Bay (see Fig. 2.1) is a large coastal bay off the subtropical east coast of eastern

Australia and is situated at the southern end of the Great Barrier Reef to the south of the

geographic definition of the Tropic of Capricorn (23.5 °S). The bay covers an area of about

4000 km2. Systematic research into the circulation and hydrodynamics of Hervey Bay has

just started. Most recent studies focused on aspects that underpin the importance of the bay

as a marine ecological system and whale sanctuary. Hervey Bay is a resting place for several

thousand humpback whales that migrate between the southern and tropical oceans annually

[Chaloupka et al. , 1999]. Each year, during winter, humpback whales migrate from Antarctic

waters; pass through South Island New Zealand, to the warm waters of the tropics for calving.

Many of them arrive in Hervey Bay from late July and remain until November when they

begin their return to the southern ocean. Further, it is estimated that 800 Dugongs (sea cow)

live in Hervey Bay waters. The Dugong is a protected species in Australian waters. Moreover,

the bay acts as a living ground for sea turtles.

Based upon its sedimentary environment, Boyd et al. [2004] classified the bay as a shoreline

divergent estuary expanding on the now well accepted classification of Australian estuaries

[Roy et al. , 2001]. Mean depth is about 15 m, with depths increasing northward to more

than 40 m, where the bay is connected to the open ocean via an approximately 60 km wide

gap. A narrow and shallow (< 2 m) channel (Great Sandy Strait) links the bay to the ocean

in the south. Two rivers connect the catchments areas with the bay, the Burnett River at

Bundaberg and the Mary River at Maryborough. In the East/North-east of Fraser Island, the

continental shelf has an average width of 40 km. At the eastern shelf edge, the East Australian

Current (EAC) reattaches to the shelf to follow the coastline to the south.

Fraser Island, the worlds largest sand island, separates the bay to the east from the Pacific

Ocean. At the northern tip of Fraser Island, an enormous sand spit is located, to extend the

separation from the open ocean further 30 kilometres north. This sand spit, called Break-

sea Spit, has an average depth of 6 m and shows some dominant underwater dune features.

Spanning 124 kilometres and covering an area of 1800 km2 Fraser Island has developed over a

period of 800,000 thousand years, and it is still changing. Due to its uniqueness, Fraser Island

is now part of the UNESCO “World Heritage List”.

8

2.1 The Region

EAC

Longitude

Latit

ude

Brisbane

Bundaberg

Gladstone

Maryborough

100 km

100060

200

30

10

30

200601000

200

60

10

30

151.5 152 152.5 153 153.5 154 154.5−28

−27.5

−27

−26.5

−26

−25.5

−25

−24.5

−24

−23.5

Sydney

Figure 2.1: Model domain and location of Hervey Bay. The isolines indicate the depth below mean

sea level. The red dashed box marks the region of interest and also the location of the inner nested

model area (details are given in Fig. 3.1). The thick black line indicates the mean centre position of

the East Australian Current (1990-2008). The black dot-dashed lines show the minimum/maximum

offshore position of the stream. The location of the weather observation stations are denoted by

stars, the location of tide gauges by red diamonds. Insert: a map of Australia showing the location

of the model domain along the east Australian coast.

The climate around Hervey Bay is characterised as subtropical with no distinct dry period

but with most precipitation occurring during the southern hemisphere summer. The region is

influenced by the Trade Winds from the east with a northern component in autumn, winter,

and a southern one in spring and summer (Tab. 2.1).

An interesting feature of Hervey Bay is that its length to width ratio is close to 1, whereas for

example for Spencer Gulf, Gulf of California and Ria of Pontevedra this ratio is larger than

3. This has some implications on the water exchange in Hervey Bay and the maintenance of

salinity and density gradients as will be shown later in chapter 5.

9

2 The Region and Data

Table 2.1: Climatological data (1941-2008) of Hervey Bay (southern hemisphere seasons). The south-wards water transport of the EAC is computed along 25°S (1990-2008). 1 Sv (Sverdrup) is equivalentto a transport of 106 m3/s.

Summer Fall Winter Spring Annual

Evaporation [mm/year] 2580 1824 1308 2217 1980Precipitation [mm/year] 2100 1068 588 936 1173River discharge [mm/year] 494 456 173 95 305Wind speed [m/s] 6.4 6.2 5.6 6.6 6.2Wind direction [degree] 170 120 48 107 110Air temperature [°C] 25.1 22.2 16.8 21.9 21.5EAC [Sv] 18.9 14.8 12.9 17.8 16.2

2.2 Data

Hydrographic observations (CTD measurements - conductivity, temperature, depth), made

during several field trips into the bay (2004 [Ribbe, 2006], 2007 and 2008 [Ribbe, 2008]) are

available for model validation. Moreover, three day composite Advanced Very High Resolution

Radiometer (AVHRR) sea surface temperature (SST) data from 1999-2005 are utilised to val-

idate the performance of the model. The 2004 field trip, the sampling locations (see Fig. 3.1)

and an analysis of the hydrographical situation within the bay is presented by Ribbe [2006].

To be consistent with the 2004 field trip, the sampling locations for the subsequent cruises

(2007 and 2008) were on the same grid.

Hourly tidal observations for model validation were taken from seven tide gauges for the whole

year 2006. The data for Bundaberg and Brisbane were taken from the Joint Archive for Sea

Level of the University of Hawaii, which are integrated into the Global Sea Level Observing

System [GLOSS, 2009]. The data for the remaining five gauges were provided by the Bureau

of Meteorology, Australia [BOM, 2009]. The sea level data were analysed by using a least

squares method in MATLAB, referred to as the T TIDE program [Pawlowicz et al. , 2002].

For validation of the computed evaporation, time series of measured pan evaporation are used.

Available are daily observations for Bundaberg (1997-2008). Although the data were quality

checked, no information is given for the sampling error. It is known that evaporation from a

natural body of water is usually at a lower rate than measured by an evaporation pan. To

account for this, a pan correction coefficient is introduced. It can vary from 0.65 [Tanny et al. ,

2008] up to 0.85 [Masoner et al. , 2008]. Here a correction factor of 0.75 was chosen.

The model forcing consists of three hourly observations of atmospheric variables (10 m wind

(u,v), 2 m air temperature, relative humidity, cloud cover, air pressure and precipitation) of

weather stations located along the east coast (see Fig. 2.1), which were linearly interpolated

onto the model domain. The river forcing was taken from daily observations of river discharge

gauges. Because the salt load of the river was unknown, the salinity of the river discharge was

fixed to 2 practical salinity units (psu). To avoid numerical instabilities, the daily river dis-

10

2.2 Data

charge was interpolated onto 3-hour intervals and afterwards smoothed with a running mean

filter without changing the total integrated discharge.

In Tab. 2.1 climatological data for Hervey Bay are presented. To compare the river discharge

with the contributions of precipitation, the fresh water inflow from the Mary River has been

converted to a precipitation equivalent (i.e. the thickness of a virtual freshwater layer over

Hervey Bay).

The climatological volume transport of the EAC (Tab. 2.1) was computed using monthly aver-

age velocity field from the Ocean Circulation and Climate Advanced Modelling project (OC-

CAM, Saunders et al. [1999]) with a resolution of 1/4° and 66 vertical z-levels. The transect

to estimate the southward transport was placed at 25°S. The mean transport of 16.2 Sv and

the annual variations are in good agreement with the estimates from Ridgeway and Godfrey

[1997].

Sea surface height (SSH), anomalies (SSHA) and also the sea surface gradient causing the

EAC are from the TOPEX/Poseidon, JASON-1 altimeter data sets [AVISO, 2009].

Tab. 2.2 summarises the data used to force and validate the model.

Table 2.2: Listing of all data used. NODC - National Oceanographic Data Center [NODC, 2009].

Data Source resolution/coverage

Atmospheric forcing BOM three hourly, 1988-2008Tidal observation BOM/GLOSS hourly, 2006River discharge BOM daily, 1988-2008Evaporation BOM daily, 1997-2008AVHRR SST NODC three daily (4×4 km) 1999-2005Boundary conditions OCCAM five daily, 1988-2008SSH, SSHA Aviso seven daily, 1992-2008

11

3 Model description

3.1 General features of COHERENS

We employ the hydrodynamic part of the three dimensional primitive equation ocean model

COHERENS (COupled Hydrodynamical Ecological model for REgioNal Shelf seas) [Luyten et al. ,

1999]. Some basic features of the model can be summarised as follows: the model is based

on a bottom following vertical sigma coordinate system with spherical coordinates in the hor-

izontal. The hydrostatic assumption and the Boussinesq approximation are included in the

horizontal momentum equations. The sea surface can move freely, therefore barotropic shallow

water motions such as surface gravity waves are included. The simulation of vertical mixing is

achieved through the 2.5 order Mellor-Yamada turbulence closure [Mellor and Yamada, 1982].

The horizontal turbulence KH is taken proportional to the product of lateral grid spacing and

the shear velocity [Smagorinsky, 1963]:

KH = CSmag∆x∆y√

(∂xu)2 + (∂yv)2 + 0.5 (∂yu+ ∂xv)2 (3.1)

where CSmag is an empirical constant that should have a value between 0.1 ... 0.4 (0.25 used

here), ∆x,∆y is the grid spacing. Advection of momentum and scalar transport is imple-

mented with the TVD (Total Variation Diminishing, Chung [2002]) scheme using the superbee

limiting function [Roe, 1985]. These are standard configurations provided with COHERENS.

For further details of numerical techniques employed, see Luyten et al. [1999].

3.2 Boundary conditions

Because the simulations heavily rely on the proper calculations of air-sea fluxes, we modified

the bulk parameterisations in COHERENS by the COARE 3.0 algorithm (Coupled-Ocean

Atmosphere Response Experiment, Fairall et al. [1996], Fairall et al. [2003]). The standard

bulk expressions for the scalar fluxes and stress components of sensible heat HS , latent heat

HL, momentum τ and evaporation E are:

HS = ρa cpa CH S (TS − θ) (3.2)

HL = ρa L CL S (qS − q) (3.3)

τ = ρa CD S2 (3.4)

12

3.2 Boundary conditions

E = ρa CE S (QS −Qa) (3.5)

where ρa is the density of air, cpa the specific heat of dry air, TS the sea surface temperature, θ

the potential temperature of the air, S the wind speed relative to the surface (the sea surface

velocity is subtracted from the 10 m wind speed), L the latent heat of vaporisation, qS and

q the water vapour mixing ratio at the interface and in the air and QS and Qa the specific

humidity at the interface and air are. The COARE 3.0 algorithm now includes various physical

processes, relating near-surface atmospheric and oceanographic variables and their relationship

to the sea surface, to compute/estimate the transfer coefficients of latent heat CL, sensible heat

CS, momentum CD and moisture CE. The total exchange coefficient

Cx =√cx

√cD (3.6)

is decomposed into the wind dependent part cD and the bulk exchange coefficient of the tracer

x under consideration. Here x can be u, v wind components, the potential temperature θ,

the water vapour specific humidity q or some atmospheric trace species mixing ratio. These

transfer coefficients have a dependence on surface stability defined by the Monin-Obukov

similarity theory (MOST) [Monin and Obukhov, 1954].

√

cx(ζ) =

√cxn

1 −√

cxn

κψx(ζ)

(3.7)

√cxn =

κ

ln(z/z0x)(3.8)

where the subscript n refers to neutral (ζ=0) stability, z is the height of measurement of

the mean quantity x. ψx is an empirical function describing the stability dependence of the

mean profile, κ is von Karmans constant and z0x a parameter called the roughness length that

characterises the neutral transfer properties of the surface for the quantity x. The stability

parameter ζ is given by MOST. Moreover the algorithm includes separate models for the

ocean’s cool skin and the diurnal warm layer, which are used to derive the true skin temperature

TS . For details of the parameterisations and the iterative solution techniques employed see

Fairall et al. [1996].

The long wave back radiation flux is computed using the formulation of Bignami et al. [1995]:

HLW = ǫσBT4S − σSBT

4a (0.653 + 0.00535 Qa)(1 + 0.1762 TCC2) (3.9)

where ǫ is the emissivity of the sea surface, taken to be 0.98; σB is the Stefan-Boltzmann

constant (5.67*10−8 W m−2 K−4), TS and Ta are the water and air temperature in Kelvin and

TCC the fractional cloud cover. This choice was motivated by the comparison of different back

radiation parameterisations by Josey et al. [2003]. Here the formulation of Bignami et al.

13

3 Model description

[1995] showed the best performance in subtropical regions.

Amplitudes and phases of the five major tidal constituents (M2, S2, N2, K1 and O1) are

prescribed at the open boundary. These five principal constituents explain nearly 80% of the

total variance of the observations within Hervey Bay. Tidal elevations and phases are taken

from the output of the global tide model/atlas FES2004 [Lyard et al. , 2006] with assimilated

altimeter data. Sea surface height (SSH), anomalies (SSHA) and also the sea surface gradient

causing the EAC, are prescribed using satellite altimeter data [AVISO, 2009]. The lateral open

boundary conditions are implemented as radiative conditions according to Flather [1976]. A

quadratic bottom drag formula at the sea floor is used with a bottom roughness length of z0 =

0.002 m. At the open-ocean boundaries, we prescribe profiles of temperature and salinity that

are derived from the global ocean model OCCAM, which has a horizontal resolution of 1/4°and 66 vertical z-levels. Because the OCCAM model data set only provides five day averaged

fields, the open ocean boundary conditions are therefore updated every fifth day.

Lady Elliot Island

Bundaberg

Maryborough

Sandy Cape

25 km

Mary River canyon

Break Sea Spit

Fras

er Is

land

Longitude

Latit

ude

10

10

20

20

30

30

40

50

100

300

300

50

2030

4030

50

10

152 152.5 153 153.5

−25.5

−25

−24.5

−24

Figure 3.1: Inner domain and details of Hervey Bay. The isolines indicate the depth below meansea level. The solid line indicates the position of the salinity/density gradient transect. Locationof the weather observation stations are denoted by stars. The dashed line indicates the transect tocompute the salinity flux and residual circulation and marks the northern boundary of Hervey Bay.The black dots mark the sampling grid of the CTD measurements.

14

3.3 Model design

3.3 Model design

The model domain is resolved using a coarser grid for the outer area and a finer grid for

Hervey Bay (one-way nesting). The outer domain (see Fig. 2.1) is an orthogonal grid of

90×140 points. The mesh size varies and increases from 2.5 km within Hervey Bay to 7 km

near the boundaries of the model domain. The model bathymetry is extracted from a high-

resolution bathymetry, which provides a horizontal resolution of 250 m. The vertical grid uses

18 sigma levels with a higher resolution towards the sea surface and the bottom boundary.

The reason is to resolve accurately the upper mixed layer, but also to catch gravity currents

at the sea floor. Haney [1991] showed, that the usage of sigma coordinates in bathymetry

with steep gradients, can cause problems due to internal pressure errors. To minimize these

artificial geostrophic flows, caused by the use of sigma coordinates over bathymetry with steep

gradients [Beckman and Haidvogel, 1993; Martinho et al. , 2006], the model bathymetry has

been smoothed [Martinho et al. , 2006]. This reduced the artificial flows to less than 5 cm/s at

the shelf edge. The maximum depth within the model domain is limited to 1100 m in order to

increase the maximum allowable time step to 12 s and 360 s for the barotropic and baroclinic

modes, respectively.

The inner domain (indicated by the dashed box in Fig. 2.1) has a uniform grid spacing of 1.5

km and a size of 100×120 grid points and is shown in Fig. 3.1. To be consistent with the outer

domain, the maximum depth was again limited to 1100 m, although, the vertical resolution

remains the same. The time steps are then 7 s and 140 s for the barotropic and baroclinic

modes, respectively. The vertical profiles of velocity, temperature, salinity and SSH of the

outer model are interpolated onto the grid of the inner model domain.

To initialise the model a spin-up of two years (1988-1990) was used, starting from rest with

climatologically profiles for salinity and temperature. The numerical experiments analysed for

this study cover the period 1990-2008.

15

4 Barotropic circulations

4.1 Tidal forcing

4.1.1 Model validation

The barotropic tides (M2, S2, N2, K1 and O1) were calculated and compared with observations

at 7 tidal gauges (Fig. 2.1). The tidal range within Hervey Bay can exceed 4 m; therefore,

strong mixing dynamics can be expected. The single constituents are separated for Bundaberg

as; M2: 0.87 m, S2: 0.30 m, K1: 0.22 m, N2: 0.19 m, O1: 0.12 m. In Fig. 4.1 a time series of

40 days for Bundaberg is shown.

Table 4.1: Comparison of observed and modelled tidal elevation and phase at reference sites forced

by five tidal constituents. The deviations are computed as ∆=observation-simulation. The tidal

amplitude error ∆ζ is given in cm and the phase error ∆ψ in degree.

M2 S2 K1 N2 O1

Station ∆ζ ∆ψ ∆ζ ∆ψ ∆ζ ∆ψ ∆ζ ∆ψ ∆ζ ∆ψ

Gladstone 4.0 -3.2 -3.0 4.6 2.1 -7.5 1.8 5.5 -3.2 7.7

Bundaberg 3.2 -4.7 2.7 -2.2 -0.9 -10.7 -1.9 -3.2 -0.2 10.1

Urangan 3.5 -4.7 1.8 2.8 -0.4 -5.7 0.9 9.3 -0.5 8.4

Waddy Point -1.3 0.8 -2.0 -5.6 -0.1 -2.6 -1.3 -3.4 -0.1 -5.9

Noosa Head -2.8 -6.1 -2.1 -3.9 -1.4 1.9 0.1 -5.4 -1.2 3.2

Brisbane 5.7 -1.2 1.7 7.5 1.4 8.9 2.4 11.7 1.1 6.0

Southport 1.2 0.8 -2.0 -5.6 -0.1 -2.7 -1.0 5.6 -1.1 3.9

RMS 3.4 3.8 2.3 5.8 1.1 6.6 1.5 7.0 1.4 6.9

In Tab. 4.1 the differences in amplitude and phase for all observation stations are listed. The

root mean square error (RMS) for the amplitude does not exceed 3.4 cm and the phase error

is not bigger than 7°. In addition Tab. 4.1 also shows that some computed results are larger

than the observations whereas others are smaller, so it can be assumed that no systematic

error is present in the simulations.

This good numerical reproduction of the tidal signal in Hervey Bay and surroundings gives con-

fidence in the underlying computed velocities field, although no direct velocity measurements

are currently available for comparison.

16

4.1 Tidal forcing

4.1.2 Tidal mixing

The hydrodynamical model COHERENS allows to compute the bottom friction velocity and

therefore an estimate of the thickness of the bottom boundary layer or Ekman layer thickness

δ can be given for different flow regimes [Loder and Greenberg, 1986]. The Ekman layer

thickness is a measure to describe a region that is controlled by friction:

δ =c u∗f

(4.1)

where u∗ is the bottom friction velocity, f is the Coriolis parameter and c is a constant that

can vary between 0.1 and 0.4 . The friction velocity u∗ is calculated as√

τB/ρ0, the square root

of the bottom friction normalised by the water density. Therefore, the distribution pattern of

the bottom boundary layer thickness is similar to the bottom friction. Using a low/medium

range value of c = 0.2, the thickness of the tidal (M2) induced Ekman layer in Hervey Bay is

estimated to be of the order of the water depth.

This is a different approach than the usual h/u3 argument, where h is the water depth and u the

depth averaged current speed [Simpson and Hunter, 1974]. However, Simpson and Sharples

[1994] discussed that the Ekman depth should be prefered because it includes directly effects

of rotation on mixing and frontal position. Thus, the Ekman depth measure is chosen.

In Fig. 4.1c the ratio of the Ekman layer thickness divided by the local depth is shown. In the

southern part of Hervey Bay and at Breaksea Spit, the ratio exceeds values of one. Therefore,

the Ekman layer is much thicker than the local depth; hence, friction and turbulent mixing

dominate the whole water column. Thus, one can assume that in these regions, the water

column is well mixed and stratification is suppressed. Only in the central part of the bay and

on the North Western shelf the mixing ratio is smaller than 0.5, hence, only parts of the water

column are occupied by the bottom Ekman layer. Fig. 4.1b shows the maximum M2 induced

tidal currents and the tidal ellipses. It is visible that at Breaksea Spit the currents can reach 1.2

m/s. In the central part of the bay, these currents vary between 0.5 - 0.7 m/s. Here the tidal

ellipses collapse into straight lines and the water is moved only in the north/south direction. It

is assumed that the central part of the bay is also well mixed, because the surrounding regions

supply already well mixed water into the central part by tidal swash transport. Consequently,

tidal mixing, due to the M2-tide alone seems sufficient to completely mix the water column

in Hervey Bay. Hence, only horizontal gradients/fronts are likely to appear. Fig. 4.1a shows

a time series of tidal gauge data at Bundaberg. In the 40 days time series one can see the

fortnightly modulation of the tidal signal. Only during 4-5 days around neap tide the tidal

amplitude is less than the M2 component alone. Therefore, in this short time window, tidal

mixing is significantly reduced and stratification within Hervey Bay can develop.

In Fig. 4.1d the maximum tidal excursion is shown. The pattern is similar to Fig. 4.1a. Peak

values of 8 km are visible at Break Sea Spit and also in the estuary of the Great Sandy Strait.

17


0 5 10 15 20 25 30 35 40−2

0

2

time [days]

ampl

itude

[m](a)

(b)

1 m/s

Tidal currents [m/s]

152.4 152.8 153.2

−25.4

−25.2

−25

−24.8

−24.6

−24.4

−24.2

0 0.5 1

(c)

Mixing ratio

152.4 152.8 153.2

0 0.25 0.5 0.75 1 1.25 1.5

(d)

Tidal excursion length [km]

152.4 152.8 153.2

0 2 4 6

Figure 4.1: (a) Typical tidal time series for Bundaberg. Indicated by the red dashed line is theamplitude of the M2 component, (b) maximum tidal currents (M2) and plot of the tidal ellipse and(c) the ratio Ekman layer/local depth and (d) the tidal excursion. For visualisation purposes, themixing ratio is limited to 1.5. The averaging period is five tidal cycles.

In most parts of the bay and on the northern shelf, the horizontal displacement during a tidal

cycle is less than 2 km.

4.2 Residual circulations

Fig. 4.2 shows that the M2 induced residual transport is negligible. In most parts of the bay,

the residual currents are less than 1 cm/s. Only at Breaksea Spit and in the northern part of

the Great Sandy Strait they can reach values of 10-15 cm/s. The contributions of the other

four tidal constituents to the residual flow are negligible. The importance of rotation of the

flow is also negligible. In most parts of the bay, it is far less than 0.1 cycles/day. Only at

Breaksea Spit and in the mouth region of the Great Sandy Strait peak values exists of approx.

1 cycles/day. Therefore, the tide in Hervey Bay is mainly responsible for the vertical mixing,

but transport processes are dominated by wind and baroclinic forcing. This feature of Hervey

Bay is quite surprising. Due to the high tidal range, much stronger residual currents should be

expected. Furthermore, numerical experiments (not shown here) with barotropic conditions

and variations in bottom roughness did not change the residual circulation significantly. It

must be concluded that weak residual currents are an intrinsic feature of Hervey Bay.

The region of Hervey Bay is influenced by the Trade winds from the east with a northern

component (NE wind) in autumn and winter and a southern one in spring and summer (SE

wind) (Tab. 2.1) with an average strength of 6-7 m/s. Because both wind directions are

18

4.2 Residual circulations

dominant and represent different residual circulations, only these two directions are considered.

(a)

152.4 152.8 153.2−25.4

−25.2

−25

−24.8

−24.6

−24.4

−24.2

(b)

152.4 152.8 153.2−25.4

−25.2

−25

−24.8

−24.6

−24.4

−24.2

(c)

152.4 152.8 153.2−25.4

−25.2

−25

−24.8

−24.6

−24.4

−24.2

5 10 15

Figure 4.2: Depth averaged residual circulations and currents (in cm/s) for (a) M2, (b) idealised NE

wind (6 m/s) and (c) idealised SE wind (6 m/s). The magnitude is indicated by the colour code,

whereas the arrows are normalised to indicate the direction of the flow. Residual currents below 1

cm/s are marked white. The averaging period is one spring-neap cycle. The residual currents for the

wind forcing are detided by subtracting the tide induced residuals.

During SE winds a clockwise current exists in the bay (see Fig. 4.2c). Ocean water enters

the bay via Breaksea spit and leaves Hervey Bay along the western shore. Peak values of 15

cm/s are reached in the shallow waters in the western part of the bay. The average residual

transport is computed with 4 cm /s. Further east of Break Sea Spit the wind-induced currents

reaches peak values of 18-20 cm/s. Thus, during SE wind there exist a narrow near shore

current, which is trapped between Fraser Island and the 150 m depth contour. Break Sea Spit

shields Hervey Bay from this current. Water passing the spit enters the bay to leave past a

U-Turn at the western shore. Nevertheless, most of the water of this coastal current flows

19


northward, to turn at the northern end of Break Sea Spit to the west/north-west, to flow into

the direction of the Great Barrier Reef, without any water exchange with Hervey Bay.

For NE-wind conditions, the whole circulation pattern changes. Now the bay is dominated by

an anti-clockwise circulation. Further, the residual circulation velocity is reduced. Maximum

flow velocities are 8 cm/s and the averaged flow speed is 2-3 cm/s. Only at the eastern shore,

a 5 km narrow jet exists, where the flow speed reaches 15-18 cm/s. The coastal current at the

eastern side of Fraser Island also reverses its direction. At the northern end of Hervey Bay

a clockwise circulations cell exists, which is trapped between Break Sea Spit and Lady Elliot

Island in the north. Therefore, water is exchanged with the northern shelf. Interesting to note

is the stream that flows between Lady Elliot Island and the northern tip of Break Sea Spit. It

transports water as a bottom flow within the Mary River Canyon. This feature will be later

important for the baroclinic water exchange with the open ocean. At the northwestern part

of the shelf exists a secondary circulation cell that restricts the water exchange between the

northern shelf and the Bay.

To give a better understanding of the three dimensional circulation, in Fig. 4.3 a transect of

the residual meridional velocity component at the northern end of Hervey Bay is shown. Fig.

4.3b depicts that during NE wind a two-layered structure exists. Surface water flows into the

bay and leaves in a central jet at the seafloor. Surface current speeds can reach 15 cm/s,

whereas the flow speed in the central outflow jet is approx. 10 cm/s. For SE wind (Fig. 4.3b)

the bay shows a east/west separation. Water enters the bay at the eastern part and leaves

Hervey Bay at the shallow western shore. However, there exists also a thin northward-directed

surface flow in the eastern part. For completeness, also the residual current for the tide is

given in Fig. 4.3a. As expected, the currents are negligible small.

Combining Fig. 4.1b and Fig. 4.2b,c can indicate possible scenarios for stratification in Hervey

Bay. During SE wind, well mixed water at Break Sea Spit is flushed into the bay. This can

prevent the occurrence of stratification. During NE wind water from the northern shelf enters

the bay. Due to low mixing in this region, the water column can be stratified and therefore

this layered water is pushed into the bay and can therefore establish stratification in Hervey

Bay. Further, the bottom outflow of dense water, generated within the bay, can slide under

lighter water on the shelf. The residual circulation cell (Fig. 4.2b) and the two layered flow

structure (Fig. 4.3b) can lead to a positive feedback loop, which enhances the stratification

in the bay and at the shelf. Nevertheless, one has to keep in mind that NE wind is mostly

dominant during the southern hemisphere winter, where stratification is generally unlikely.

However, this feature will be later important for the release and triggering of gravity currents

(see chapter 7).

20

4.3 Water exchange

Dep

th in

m

b)

−40

−20

0

−10

−5

0

5

10a)

−40

−20

0

Longitude

c)

152.3 152.4 152.5 152.6 152.7 152.8 152.9 153 153.1 153.2−40

−20

0

Figure 4.3: Transect (Fig. 3.1) of the northward velocity component (in cm/s) for (a) M2, (b) idealised

NE wind (6 m/s) and (c) idealised SE wind (6 m/s). Positive values indicate a northward flow. The

averaging period is one spring-neap cycle. The residual currents for the wind forcing are detided.

The thick black line indicates the change in sign of the velocity components.

4.3 Water exchange

The water exchange time scale is an important quantity that facilitates the classification of the

environmental state of estuaries, large coastal embayment, shelf seas, but also ocean basins

from regional to global scales. Sometimes this time scale is also called flushing or ventilation

time scale (e.g. Wolanski [1986], Banas and Hickey [2005], Guyondet et al. [2005]).

The water exchange time of an estuary, or segment of it, is often loosely referred to as the

average time a water parcel or substance remains within the system or area of interest. The

time, this tracer remains within a system, depends on the location and time where the water

parcel is ’tagged’ or the substance is introduced van de Kreeke [1983]; Prandle [1984]. If all the

existing water parcels in a water body, or segment of it, are marked at some instant of time,

inevitably some of them will be flushed out of the system more quickly, while some may stay

for a longer period of time. Thus, a first definition of a water exchange time is the residence

time. In the following, the residence time of the system is defined as the average time these

initially existing water parcels resides in the system before they are flushed out. This time

scale is best described in a Lagrangian framework, because single particles are ’tagged’ and

then followed in time. A second quantity commonly used to quantify the water exchange is the

flushing time. The definition of the flushing time is based on Officer [1976] and Knaus [1978]

as the time required to replace a specified fraction of the water in an estuary or segment by

the volume flows of freshwater and/or new ocean water [Pritchard, 1960]. This time scale is

21


well suited for the Eulerian framework, because it is necessary to compute the concentration

at a specific point or region. Both definitions of water exchange are based on the displacement

concept, which gives the time required to displace all the water in the region under consider-

ation.

Using domain averaged time scales, they are single parameters representing the integral time

scale of all physical transport processes of the system at once, which may be used to be com-

pared to time scales of biological and chemical processes or baroclinic response. Zimmerman

[1988] also defined several local time scales, which are functions of location in estuaries. The

local time scales provide more detailed information, however they suffer from complication

when related to biogeochemical processes.

It is obvious that the residence time of an estuary will change with its flushing time. The longer

it takes to flush an estuary, the longer its residence time will be. The flushing of estuarine

waters is achieved by all the mechanisms effecting the transport or removal of water from the

estuary to the open sea. These transport mechanisms include tidal flushing, river discharge,

density induced estuarine circulation and those induced by meteorological events.

4.3.1 Setup

In the following three different scenarios are used which are identical to the setups of the

computation of the residual circulations. Therefore, the model is forced with the tide without

wind, tide and NE wind (6 m/s) and finally tide and SE wind (6 m/s). The duration of the

experiments is limited to 60 days of constant forcing. Although it seems unrealistic to consider

a constant NE wind for 2 months, these idealised experiments shall give a rough estimate of

the water exchange. At the southern boundary the flow rates, through the Great Sandy Strait,

from Tab. 4.2 are imposed. These values are taken from the outer model.

Table 4.2: Tidal averaged flow through the Great Sandy Strait in m3/s. Negative values indicate

southward transport.

Tide NE wind SE wind

transport -100 -1200 800

van de Kreeke [1983] further differentiated the phase of the tide when the particles/tracer

were initially released. Due to the weak tidal residual currents and the fact that the spatial

dimension of the bay is much larger than the tidal excursion (Fig. 4.1c), the dependence on the

tidal phase is insignificant. Further, the dependence of the water exchange on the spring-neap

cycle was neglected. Additional experiments (not shown here) where the release was at spring

tide and one experiment with a release at neap tide, showed that the differences are negligible.

22

4.3 Water exchange

Flushing time

To compute the flushing time, the bay is filled with a neutral buoyant passive tracer, where

in every grid cell within the bay the concentration is set to one. The northern boundary of

the bay is given in Fig. 3.1. Then for every grid cell, the time is computed until the local

concentration drops below a threshold. Thus

Tflushing = T (C(t) > Cthreshold) (4.2)

The threshold Cthreshold is set to 1/e, where e is the Euler number. Therefore, the flushing

time is equivalent to the e-folding time.

Residence time

To asses the residence time, neutrally buoyant particles (which shall represent water parcels)

are released within the bay. Particles were tracked entirely in post processing; using Fortran

code that integrates the 3D velocity fields from COHERENS saved every 15 min. A multistep

scheme (HEUN scheme) was used for the integration, with a time step of 60 s in the horizontal

and 3 s in the vertical. In addition to advection in all three dimensions, particles were subject

to horizontal/vertical diffusion, using the ’random displacement’ scheme described by Visser

(1997). This scheme adds a random velocity, scaled by the local diffusivity from COHERENS,

to the advective velocity at every time step, and further includes a correction based on the

local diffusivity gradient:

dX(t) = (u+ ∂x KH)dt +√

2KH dWx(t)

dY (t) = (v + ∂x KH)dt+√

2KH dWy(t)

dZ(t) = (w + ∂x KV )dt+√

2KV dWz(t)

(4.3)

where X,Y,Z is the position, dt the time step, u, v,w the advective velocity, dWx, dWy, dWz

independent noise increments with mean 0 and variance dt, and KH the horizontal diffusivity

and KV the vertical one. The gradient correction is essential to preventing particles from

accumulating unrealistically in low-diffusivity areas, as demonstrated by [Visser, 1997]. For

a detailed discussion on the underlying theory and the validation of the numerical particle-

tracking scheme, the reader is referred to appendix A.

23


(a)

152.4 152.8 153.2

−25.4

−25.2

−25

−24.8

10 20 30 40 50

(b)

152.4 152.8 153.2

−25.4

−25.2

−25

−24.8

(c)

152.4 152.8 153.2

−25.4

−25.2

−25

−24.8

0 20 400

0.5

1(d)

Tide

NE wind

SE wind

Figure 4.4: Depth averaged flushing time. The colour code indicates the time in days, for (a) tide, (b)

tide + NE wind, (c) tide + SE wind and (d) normalised bay averaged concentration. The critical

threshold Cthreshold is indicated by the black dashed line.

4.3.2 Flushing time

In Fig. 4.4a-c the local e-folding renewal time is shown. Clearly visible in Fig. 4.4a is that

the tide does not contribute to the water exchange. This was expected due to the very small

residual currents. During the two month of simulations, only the most north-eastern part

could be flushed.

The water exchange changes dramatically if additional wind forcing is imposed. During NE

wind (Fig. 4.4b) most of the bay water is flushed within 20 days. Especially the eastern part

of the bay shows flushing times of less than 10 days. Clearly visible is the impact of the costal

jet, at the eastern shore, on the water exchange. In the central northern part of the bay, the

flushing time yields values of more than 50 days. This is caused by the fact, that most of

the water leaves Hervey Bay through the bottom jet (Fig. 4.3b). Therefore, the concentration

remains high until all bay water has left. At the western shore, there also exists a narrow

24

4.3 Water exchange

region, which shows rapid response to NE wind forcing. The flushing time of the Great Sandy

Strait is approx 25 days. During NE wind, a southward flow exists in the strait system. Thus

bay water is flowing through the strait and keeps the concentration high.

During SE wind the water exchange in the Strait is much faster (Fig. 4.3c). Now a northward

flow pushes ’new’ water into the bay and leads therefore to a fast water exchange in the mouth

of the Great Sandy Strait. The U-styled residual circulation within the bay is also visible in

the flushing time pattern. Fresh water is entering the bay in the eastern part and leaving the

bay at a narrow coastal stripe at the western shore. A stationary eddy causes the high flushing

times in the eastern part. This circulation cell close to Fraser Island is also visible in Fig. 4.2c.

The water exchange in the southern part of the bay is much slower than for NE wind.

In Fig. 4.4d the bay averaged concentration for the three forcing scenarios is given. The critical

thresholf of 1/e was crossed for SE wind at around 20 days, for NE wind 43 days, respectively.

For only tidal forcing, the threshold was not reached during the two months of simulation.

For the case of NE wind, the impact of the large circulation cell at the northern shelf is cleary

vissible(Fig. 4.2b). The bay shows a rapid response to this forcing. After approx. 14 days,

waters that were flushed out of the bay due to this cell, enter the bay again and therefore keep

the concentration high.

To quantify the rapid response, it is assumed that for short timescales, the concentration in

the bay drops exponentially. Thus to the first 10 days of the concentration time series, an

exponential fit was applied of the form:

C(t) = exp

(

− t

τ

)

(4.4)

τ gives then the decay rate. The results are summarised in Tab. 4.3. With a decay rate of 12

days for NE wind, the response time is much faster than for SE wind with 25 days. The decay

rate for the tidal forcing is approx. 3 months.

Table 4.3: Water exchange times for three different forcing scenarios. Given are the flushing times in

days for the threshold method and the exponential decay rate.

Tide NE wind SE wind

Threshold - 43 20

Exp. decay 130 12 25

Fig. 4.4d shows, that there exist two different times scales for Hervey Bay. A fast mode,

covering exchange processes within 3 weeks and secondly a slow mode, for the response when

the fast mode decayed. The fast mode is only visible for the wind forcing, thus indicating ex-

change processes associated with wind-induced circulations. Within 3 weeks, the concentration

drops rapidly and can be described by an exponential decay, with a decay rate of approx. 20

days. After the three weeks, Hervey Bay enters into the slow mode. The drop in concentration

25


is much lower and comparable for the three forcing scenarios. The decay rate is reduced to

approx. 3 months.

4.3.3 Residence time

The residence time is defined as the time required for a particle to travel from a location,

within the system, to the boundary of the region [Prandle, 1984], therefore it is dependent of

the location where the particle is released. Sometimes the residence time is also called turn

over time. To compute this time scale, 107 uniformly distributed particles are released in the

bay. Then, every particle is followed over 2 months and the time is computed until the particle

crosses the northern/southern boundary of the bay.

(a)

152.4 152.8 153.2

−25.4

−25.2

−25

−24.8

−24.6

10 20 30 40 50 60

(b)

152.4 152.8 153.2

−25.4

−25.2

−25

−24.8

−24.6

(c)

152.4 152.8 153.2

−25.4

−25.2

−25

−24.8

−24.6

Figure 4.5: Depth averaged residence time. The color code indicates the time in days, for (a) tide,

(b) tide + NE wind and (c) tide + SE wind.

Because at every grid point, approx. 4000 particles are initialised in the whole water column,

the depth averaged residence time for these 4000 particles is calculated. The results are shown

in Fig. 4.5. Due to the weak tidal residual currents, also the tidal residence time is high. Only

at the northern end of the bay, particles leave the bay due to tidal excursion and diffusion.

In the mouth of the Great Sandy Strait, residence times are also low due to the southward

26

4.3 Water exchange

directed residual flow through the strait (Tab. 4.2). The central part of the bay is not affected

by the tide. This changes dramatically by imposing NE wind. Residence times in the western

part are approx. 5-15 days. In the eastern part, particles need 30-50 days to leave the bay.

Thus, the pattern of the residence time clearly reflects the residual circulation. Because water

enters the bay at the eastern part, it has to be carried the whole way trough the bay, to exit

at the central part.

For SE wind the pattern is similar. The residence times of the western part of the bay is less

than 10 days. Due to the strong northward-directed flow in the Great Sandy Strait, Hervey

Bay shows a clear east/west separation. Waters originating from the Great Sandy Strait are

effectively transported along the western shore. At the eastern shore, the trapping of particles,

due to a persisted circulation cell, is visible. Here, residence times can reach 50-60 days.

4.3.4 Origin of replacement water

The particle-tracking scheme further allows to asses the origin of the replacement water, thus

answering the question: Where do the waters, entering Hervey Bay, come from? This is

computed by inverting the setup of the residence time. Again 107 particles are released, but

now they are initialised outside the bay. Than the time is computed until the particles cross

the boundaries of Hervey Bay and thus entering the bay domain. In Fig. 4.6 only the results

for wind forcing are shown.

(a)

152.4 152.8 153.2−25.5

−25

−24.5

0 10 20 30 40 50

(b)

152.4 152.8 153.2−25.5

−25

−24.5

Figure 4.6: Depth averaged replacement time. The colour code indicates the time in days, for (a) tide

+ NE wind and (b) tide + SE wind.

For NE wind (Fig. 4.6a), only water from the northern shelf enters the bay. Due to the large

residual circulation cell, bounded by Break Sea Spit and Lady Elliot Island (see Fig. 4.2b), the

water is trapped and the water exchange with the open ocean is limited.

27


For SE wind conditions (Fig. 4.6b) open ocean water enters the bay via Break Sea Spit. The

simulations show that within 10 days, shelf water (east of Fraser Island) replaces water in

Hervey Bay.

28

5 Baroclinic processes

5.1 Model Validation

Because the simulations reveal that the bay is in parts vertically well mixed throughout most

of the year, the depth averaged salinity/temperature distribution is considered here for the

first model validation. The simulated temperature and salinity distribution within Hervey

Bay is consistent with the observations during all three field surveys (Fig. 5.1). The model

reproduces the salinity gradient with salinity decreasing in all three field trips from the south

west coast towards the northern opening of the Bay (Fig. 5.1).

observation

(a)

simulation

(b)

(c)

Salinity [psu]152.4 153

152.4 153

35 35.5 36 36.5

observation

−25.2

−24.6simulation

−25.2

−24.6

Temperature [°C]152.4 153

−25.2

−24.6

152.4 153

20 22 24 26

Figure 5.1: Comparison of the depth-averaged salinity and temperature distributions during (a)

September 2004, (b) August 2007 and (c) December 2007.

The comparison with the first survey shows that the salinity gradient is less sharp than

indicated by the model. In general, the agreement of the model output and the measurements

from each of the field trips is quite well. The model confirms that the coastal region is

occupied by a zone of hypersalinity with salinities well above 36 psu. The model reproduces

the observed temperature distribution as well. There are some deviations for the September

2004 field trip. The model seems to overestimate the temperature in the near shore region, but

29


both observations and simulated data show a similar pattern. The distribution of temperature

is matched by the model for both subsequent field trips.

For further validation, transects of temperature and salinity at the northern opening of Hervey

Bay are shown in Fig. 5.2. The coastal hypersalinity zone is somewhat wider than the model

indicates, but again the patterns are matched. The model also reproduces the bottom cold-

water pool for the first two field trips.

observation

(a)

−20

−10

0simulation

Dep

th in

m

(b)

−20

−10

0

(c)

Salinity [psu]152.6 152.9

−20

−10

0

152.6 152.9

35 35.5 36 36.5

observation

−20

−10

0simulation

−20

−10

0

Temperature [°C]152.6 152.9

−20

−10

0

152.6 152.9

20 22 24 26

Figure 5.2: Comparison of the salinity and temperature transects along 24.8°S latitude (a) September

2004, (b) August 2007 and (c) December 2007.

The temperature pattern for the September 2004 field trip, reflects the residual circulation

pattern for NE wind (Fig. 4.2b), which was observed during this field campaign. Cold water

leaves the bay in the central part and creates therefore the central cold-water pool. Further,

the two layered structure (Fig. 5.2a) agrees with the barotropic residual flows (Fig. 4.3b).

To show that the model also captures the dynamics on the shelf, transects of σt density in

the northern part of Hervey Bay are shown in Fig. 5.3. The model misses the proper timing

of the upwelling event, which is visible in the observation for December 2007. It seems that

this event is lagged by two days in the simulations. For the May and June 2008 field trips,

the agreement is quite well. The model reproduces the frontal structures and the vertical

well-mixed conditions on the shelf.

30

5.1 Model Validation

observation

(a)

−40

−20

0simulation

Dep

th in

m

(b)

−40

−20

0

(c)

152.2 152.6 153.0

−40

−20

0

Longitude

152.2 152.6 153.0

23 23.2 23.4 23.6 23.8 24 24.2 24.4 24.6 24.8 25

Figure 5.3: Comparison of σt density [kg/m3] transects; (a) along 24.5°S during December 2007, (b)along 24.4°S during May 2008 and (c) along 24.5°S during June 2008.

2 4 6 8 10

2

4

6

8

10

Esimu

Epa

n

y = 0.940*x + 0.384

R2 = 0.794

(b)

20 25 30

20

25

30

SSTsimu

SS

TA

VH

RR

y = 0.980*x + 0.451

R2 = 0.818

(a)

Figure 5.4: Scatter plot of a) simulated SST vs. AVHRR SST [K] and b) simulated evaporation vs.

measured pan evaporation [mm/day]. The red line indicates a linear fit.

In order to demonstrate the model performance to capture the dynamics on longer time

scales, satellite AVHRR SST data for the period 1999 - 2005 have been used for the model

validation. Fig. 5.4a shows the comparison of bay averaged model SST data and AVHRR

satellite data. The linear fit indicates that the model reproduces the measurements with a

vanishing bias. R2 with 0.82 is quite high.

The comparison between the measured and simulated evaporation is shown in Fig. 5.4b (for

31


Bundaberg (1997-2008)). Due to the expected higher sampling errors in the pan-evaporation

measurement the data scatter is wider. Again R2 with 0.8 is reasonably high. The linear fit

again indicates that the model tends to underestimate high evaporation rates and vice versa

overestimates low evaporation rates, but this systematic error is quite small.

The simulated southward transport of the East Australian Current is on average 7.1 Sv, which

is much less than the EACs seasonal average of 16.2 Sv (see Tab. 2.1). Further, the location of

the centre of the EAC is shifted in the simulations in the northern part of the model domain

towards the 1000 m depth contour by 30-40 km. However, given the unrealistic maximum

depth of 1100 m, this transport is assumed to be representative of a baroclinic EAC flow.

[Oke and Middleton, 1999] also used the same argument.

32

5.2 Stratification within Hervey Bay

5.2 Stratification within Hervey Bay

The stratification is expressed in terms of a scalar quantity φ [Simpson et al. , 1990], which is

defined as:

φ =1

H

∫ 0

−H(ρ− ρ(z))gz dz; with ρ =

1

H

∫ 0

−Hρ(z) dz (5.1)

where ρ(z) is the density profile of the water column of depth H. φ (units J/m−3) is the work

required to bring about complete mixing. Recently, this quantity has been also defined as a

potential energy anomaly (PEA) (see e.g. Røed and Albertsen [2007]).

1990 1992 1994 1996 1998 2000 2002 2004 2006−0.6

−0.4

−0.2

0d)

time [year]

∆ S

−0.4

−0.2

0

c)

∆ ρ

0

5

10

15b)

φ

0.10.20.30.40.5a)

τ

Figure 5.5: (a) Time series of wind stress - τ [Pa], (b) stratification index - φ [Jm−3], (c) difference

between surface and bottom density - ∆ρ [kgm−3] and (d) difference between surface and bottom

salinity - ∆S [psu]. Time series for (b), (c) and (d) are only computed in the bay where the depth

is greater than 15 m. Shown are daily averaged values.

φ is therefore an expression for the competition of stirring (wind stress, tides, waves and cur-

rents) and stratification (heating and buoyancy flux due to precipitation and river discharge).

Fig. 5.5 gives time series of daily averaged wind stress, surface to bottom density/salinity

difference and φ. The time series of ∆ρ yield that the maximum difference is of the order

0.4 kgm−3. These peak values appear mostly in spring and early summer. Cold “winter”

water resides at the bottom of Hervey Bay, whereas increasing solar heat flux increases the

temperature of the upper layers and hence establishes the density difference. It is interesting

to note that the time series is rather spiky. The time lag between the spikes is nearly an in-

teger multiple of 14 days and clearly shows the spring/neap cycle of the tide. Fig. 5.6 depicts

the spectral analysis of the bay averaged stratification index. The pronounced peaks at 14

and 28 days cleary show the influence of the spring/neap cycle on φ and thus the fortnightly

33


tidal modulations. Therefore during spring tide, tidal mixing almost completely removes any

stratification and only during neap tide a short-term stratification (< 6 days) can be seen.

Further the daily, annual cycles and the M2-cycle are visible,.

0.5 1 14 28 365 7300

0.05

0.1

0.15

0.2

Periode in days

PS

D

M2

daily

annual

Figure 5.6: Power spectral density (PSD) of the bay averaged stratification index φ (1990-2008). The

sampling frequency is 2 hours.

The following analysis is mainly focused on daily averages, excluding daily cycles and inter-

tidal effects (tidal straining). During winter, there is no stratification visible. The same signal

can also be seen in the time series of φ. Most of the time it is less than 2 Jm−3 and only in

spring and summer the required energy to bring about complete mixing can exceed 5 Jm−3.

In contrast, the time series of ∆S is nearly flat. Almost during the whole year, the surface to

bottom salinity difference vanishes and only during some rare events, the difference can reach

-0.4 psu. Negative differences are caused by rainfall events. Positive peaks are associated with

bottom flows of cold, “fresh” dense water because these peaks mostly occur during late au-

tumn. This rather flat time series indicates that the main contribution to stratification is from

thermal effects. A second reason for dominating thermal stratification is the short duration of

these events. There is not enough time that saline two layer structures can develop.

An additional source of mixing is energy input due to wind stress (Fig. 5.5a). Under light

wind conditions thermal stratification can develop (as expected) but the additional wind en-

ergy input during medium/high wind conditions, can completely mix the water column even

during neap tide.

34

5.3 Inverse state and hypersalinity


The hydrographic observations made during the three field surveys indicate that hypersalin-

ity is likely to be a reoccurring climatological feature characterising the bay. Climatological

data for evaporation, precipitation and river runoff (see Tab. 2.1) show that evaporation with

about 2 m/year by far exceeds the supply of freshwater into the bay from precipitation with

about 1 m/year and very low river run-off (see Ribbe [2006] for details). The application of

the ocean model allows investigating the distribution of salinity throughout time. In fact, the

time-averaged distribution of salinity in the bay (Fig. 5.7) and its surroundings confirms that

the hypersalinity zone is a climatological feature for the period 1990-2008. The climatological

mean value for the salinity gradient in the bay is in the order of about 0.5 psu with salinities

near the south west of > 36.1 psu and near the open ocean in the north east of about < 35.5

psu. The magnitude of these gradients correspond to those observed during the three surveys.

To describe the temporal evolution of the hypersalinity zone within Hervey Bay, the salin-

Longitude

Latit

ude

36

35.9

35.8

35.7

35.6

35.5

35.6

152 152.5 153 153.5

−26

−25.5

−25

−24.5

−24

Figure 5.7: Mean salinity distribution averaged over the period 1990-2008. Also shown is the positionof the three transects to compute the density and salinity gradients.

ity/density gradients along the indicated transects in Fig. 5.7 have been computed. Firstly,

the focus is on the transect that is placed at the northern end of Hervey Bay. The transect is

35


aligned perpendicular to the isolines of the climatological salinity distribution. Fig. 5.8 pro-

vides an indication of the temporal evolution of these gradients. They are plotted as psu/km

and kg/m3/km.

To quantify these gradients the approach of Largier et al. [1997] is followed in defining hy-

persalinity and the inverse state of an estuary/bay as: “... hypersaline is defined as salinities

significantly greater than that of the ambient and inverse as densities significantly greater than

that of the ambient... ”. By salinities significantly greater, the authors define a salinity S that

exceeds the ambient salinity S0 by more than typical synoptic (i.e. multi-day) fluctuations in

the salinity of the ambient coastal waters. The standard deviation of the ambient salinity over

the period of hypersalinity, serves as an appropriate index of the size of these fluctuations.

Thus, (S − S0) > σ defines hypersalinity. For the case of Hervey Bay these fluctuations are of

the order σ=0.15 psu and in terms of the salinity gradient σGrad ≈ 2 · 10−3 psu/km and there-

fore one third of the climatological gradient. This means that Hervey Bay can be classified as

a hypersaline bay.

To define the inverse state a dynamical approach is used here. To have a Hervey Bay specific

threshold for the inverse state, the density gradients are converted into geostrophic induced

velocities, serving as a rough indication. Because tidal mixing is quite high and therefore tur-

bulence is essential in this coastal environment as demonstrated above, this indicator should

be handled with care.

Computing the geostrophic residual velocity, caused by a mean density difference of 0.45 kg/m3

over a distance of 65 km (see Fig. 5.7), will result in a flow of approx. 3-5 cm/s. This is in

the range of the wind induced residual circulations (Fig. 4.2). Here a wind speed of 6 m/s is

assumed, which is the mean climatological average. Hence, a geostrophic flow could balance a

northerly wind induced circulation. Thus density gradients exceeding 0.01 kgm−3/km can be

dynamically important for Hervey Bay.

In Fig. 5.8ab the red dashed lines indicate these critical values. As stated in the description

of Hervey Bay, a special feature of it is an aspect ratio of nearly one, i.e. the width of the

connection to the open ocean is equal to the length of the bay itself. For Spencer Gulf, Gulf

of California and Ria of Pontevedra this ratio exceeds a value of three. Therefore Hervey

Bay is better described as an “open” coastal environment than to fit into a classical inverse

estuary type classification. Further due to its low aspect ratio the bay can not produce high

salinity/density gradients like for instance Spencer Gulf with peak salinities of > 50 psu in the

headwater of the gulf.

36


b)

∂ S

−0.02

0

0.02

a)

∂ ρ

−0.02

0

0.02

Year

Day

s

c)

1990 1995 2000 2005

50

150

250

350

Figure 5.8: a) Time series of density gradient - ∂ρ [kg/m3/km], b) salinity gradient - ∂S [psu/km].

Shown are daily averages. The red dashed lines indicate the thresholds given in the text and c)

depicts the number of days per year where hypersaline (stars)/inverse (circles) conditions are found.

To indicate the trend, linear fits are added. The grey bars show El Nino/La Nina events.

To understand if these gradients are Hervey Bay specific or if they reflect simply the varia-

tion in the usual subtropical near shore hypersalinity zone [Tomczak and Godfrey, 2003], two

additional transects (see Fig. 5.7) have been investigated in the model domain. One is situated

at the northern shelf of Hervey Bay and the other is placed approx. 80 km south of Fraser

Island.

Tab. 5.1 shows the comparison of the two additional transects with the gradients in Hervey

Bay. The density and salinity gradients are a factor of two higher than the ones computed at

the northern shelf. Interesting to note is, that the mean values for the southern transect are

nearly vanishing. Comparison of the standard deviation of the three transects demonstrates

37


that the dynamics within Hervey Bay are much higher than for the surrounding near shore

areas. The comparison of the time series correlation indicates that the exchange of water of

Hervey Bay with the northern shelf is much higher, than the exchange with the region south

of Fraser Island.

Concluding from Tab. 5.1: the dynamics and magnitude of the gradients in Hervey Bay are

higher than in the surrounding coastal waters and therefore these gradients are indeed estab-

lished by the local dynamics within the bay.

The time series of the salinity gradient exhibits a clear seasonal pattern (Fig. 5.8). The annual

Table 5.1: Mean and standard deviation of the salinity and density gradients along the transectsindicated in Fig. 5.7. Also, the correlation of the time series for Hervey Bay with the two additionaltransects time series are given.

North Bay South

∂ρCorrelation 0.63 1 0.4Mean [kgm−3/km] 0.0027 0.0059 0.0004Std [kgm−3/km] 0.0039 0.0054 0.0028

∂SCorrelation 0.67 1 0.39Mean [psu/km] 0.0024 0.0059 0.0002Std [psu/km] 0.0042 0.0069 0.0012

cycle is mainly caused by three mechanisms. At first, due to the annual variation in solar heat

flux the evaporation rate is triggered by this signal. During summer the evaporation reaches

a maximum (see Tab. 2.1). Because Hervey Bay is in the western part much shallower than

in the eastern part, the effective evaporation (E/H - the ratio of evaporation and depth) is

at the western shore higher and this leads to a strengthening of the salinity gradient. During

winter, the whole process is reversed and can weaken or even reverse the gradient. The second

mechanism that causes the annual variations is the different residual flow pattern in Hervey

Bay. During summer the dominant wind direction is southeast whereas during winter the re-

gion is controlled by northeasterly winds, averaged wind speed are approx. 6 m/s. During SE

winds a clockwise circulation exists in the bay (see Fig. 4.2c). Ocean water of “low” salinity

enters the bay via Breaksea Spit and leaves Hervey Bay along the western shore. Combined

with the higher effective evaporation in the western part, the gradient is strengthened. In con-

trast, under NE-wind conditions the whole circulation pattern reverses. Now saline western

shore water is pushed into the bay and the salinity gradient is weakened, even if there exists a

hypersalinity zone close to the shore. To quantify the impact of both contributions, a typical

evaporation time scale is computed as:

Tevap =H σ/S0

E − P −R(5.2)

38

5.4 Evaporation induced circulations

where H denotes the mean depth, σ the size of the salinity fluctuations around S0 and in the

denominator are the contributions of the fresh water balance (evaporation, precipitation and

river discharge).

This gives an average Tevap of 15 days. In Tab. 4.3 typical water exchange time scales for

Hervey Bay are given as 20-40 days. Therefore, the evaporation water loss dominates the

salinity gradient rather than the movement of saline water due to residual circulations.

A third, more random, mechanism is provided by significant rainfall events accompanied by

somewhat delayed higher river discharges, i.e. the salinity near the coast is lower than towards

the open ocean. This is for example the case during 1996 when the strongest reversal is

observed. Closer inspection of the time series (not shown here) for surface freshwater fluxes due

to rainfall and river discharges reveal that during this year a particular wet winter prevents the

maintenance of a hypersalinity zone from about April to November 1996. With the approach

of summer and an increase of evaporation and no further significant freshwater discharges, the

hypersalinity zone reforms (Fig. 5.8b).


Due to the net loss of water (by evaporation) and to maintain the waterbalance within the

bay, an inflow of water from the ocean is required. Tab. 2.1 shows that the annual loss of

water is approx. 800 mm or 130 m3/s (Hervey Bay covers approx. 4000 km2). This would

result in a balancing oceanic inflow of 0.1 mm/s. Much more important than this inflow are

the effects of the accumulation of salt within Hervey Bay. In the case, that Hervey Bay would

be an enclosed water body; this water loss would cause an increase of salinity of 2 psu per year

(assuming conservation of salt). Because there is no evidence that the salinities are generally

increasing in Hervey Bay, a process of salt removal has to be at work.

A simple water and salt balance is considered here. It is assumed that there are two components

of salinity-induced circulations. The first component (as stated above) is the volume loss due

to evaporation. This is a pure inflow, with average velocity uI . Thus, continuity of volume

requires:

uI b h = A (E − P ) (5.3)

where E is the evaporation rate, P the precipitation rate, b the width of the opening of Hervey

Bay, h the average depth and A the surface area of the bay.

The second component represents all the inflows/outflows, at velocity uC , which account for

the removal/entry of saline water. It is assumed that there exists a circulation that brings

shelf water of low salinity into the bay and removes water of higher salinity from Hervey Bay.

Therefore, salinity continuity requires:

h

2uC b SI + uI b h SI =

h

2uC b SO (5.4)

39


where uC is the circulation velocity, SI the salinity of the water entering the bay and SO is

the salinity of the outflowing water. Using (5.3) and (5.4) gives:

uC =2 (E − P ) A

bh

SI

SO − SI(5.5)

This simple model describes how, at a given rate of evaporation, water leaves the bay with

higher salinities than the salinities of the inflowing waters. Further if the salinity difference

increases, the circulation velocity uC has to decrease.

In Fig. 5.9 a transect through the opening of the bay at 24.8°S is shown. Fig. 5.9a shows

the average salinity distribution for the whole simulation time (1990-2008). This is used to

estimate SI with 35.5 psu and SO with 36 psu. b is taken as 60 km and h as 20 m. (E −P ) is

estimated with 0.8 m/yr (Tab. 2.1). This yields a circulation velocity uC of approx. 2 cm/s. To

compare the performance of this simple analytical model, Fig. 5.9b shows the average velocity

of the north/south component of the flow. All barotropic residuals have been removed here,

therefore, only the evaporation induced velocity fields are visible. The peak inflow/outflow

velocity is in the range of 3 cm/s and therefore the estimation of uC with 2 cm/s agrees

well with the model output. Also visible is that the residual flow shows a tilted east/west

separation. Therefore, Hervey Bay does not show the typical two-layered structure with a

clear separation of the inflow of low saline water in the surface layer and the outflow of dense

high saline water at the bottom. The bay shows a superposition of a horizontal circulation

and a weak two-layered structure in the vertical. This is the result of the strong tidal mixing

in and at the northern part of the bay (Fig. 4.1c). Because a classical vertical two-layer

structure cannot be established, the water exchange is realised by an inflow of ocean water in

the eastern part of the bay and an outflow at the western shore. The east/west component

of the velocity (Fig. 5.9c) shows the fingerprint of the inverse circulations. At the western

shore, there is a weak eastward flow close to the bottom. This agrees well with the salinity

distribution (Fig. 5.9). This tilting of the isolines indicates an outflow of saline water down

the slope. Therefore, Hervey Bay shows an inverse circulation pattern (in the zonal direction)

with inflow of fresh water at the surface and an outflow of dense/saline water at the bottom.

To quantify the overall residual mass flow, the salinity flux of the bay has been calculated

explicitly by computing the transport by advection and diffusion across the open boundaries

(Ω) of Hervey Bay. The northern boundary is defined in Fig. 3.1 and the southern boundary

is located in the Great Sandy Strait at 25.5°S.

FSalt(t) =

∫

Ω

[

v(x, z, t)S(x, z, t) + KH(x, z, t)∂

∂yS(x, z, t)

]

dΩ (5.6)

The first term represents the flux by advection (meridional velocity times salinity) whereas the

second term represents the diffusive fluxes. KH is the turbulent scalar horizontal diffusivity.

A first estimate, to quantify the importance of both contributions to the integral, can be given

40


Dep

th in

m

b)

−20

−10

0

−2

0

2

a)

−20

−10

0

35.5

36

Longitude

c)

152.5 152.6 152.7 152.8 152.9 153 153.1

−20

−10

0

−4

−2

0

Figure 5.9: (a) Average vertical salinity distribution at the northern opening of Hervey Bay in psu,(b) average north/south velocity distribution in cm/s. Positive values indicate a northward directedflow (out of the bay) and (c) average east/west velocity distribution in cm/s. Positive values indicatea eastward directed flow (directed to Fraser Island). The thick black line indicates the change in signof the velocity components. The transect is placed along 24.8°S latitude. The data are averaged forthe whole simulation period (1990-2008).

by estimating the average advective transport with 4 kgm/s, assuming a residual current of

0.1 m/s. The model predicts a bay average turbulent diffusivity of 30 m2/s. which is used to

estimate the diffusive transport. The salinity gradient is estimated from the climatology (10−5

psu/m). This results in an average diffusive transport of approx. 3·10−4 kgm/s. Therefore, the

advective transport is at least three orders of magnitude larger than the diffusive transport.

Integrating both fluxes explicitly along sigma-coordinates over the domain, the export of salin-

ity is estimated to be in the order of about 4.0 tons/s (Fig. 5.10a). Using the climatological

values (Tab. 2.1), the net loss of 800 mm would result in an outflow of 3.7 tons/s, which is in

good agreement with the numerical results.

Finally, the magnitude of these fluxes can be compared with estimates for Spencer Gulf, Aus-

tralia [Nunes Vaz et al. , 1990]. Both coastal embayments do not differ significantly in size and

atmospheric forcing. The estimated volumetric flux for Spencer Gulf is of the order of 0.05 Sv

[Ivanov et al. , 2004]. Converting the peak flux (Fig. 5.8b) into a volume flux, this is estimated

to be 0.006 Sv and therefore one order of magnitude smaller. This is not surprising, because

Hervey Bay only covers 1/5 of the area of Spencer Gulf. Secondly, the aspect ratio (length

to width ratio) of Hervey Bay is nearly one whereas for Spencer Gulf this is in the range of

three. Hence Hervey Bay is more an open environment than that of a classical gulf shape and

can therefore not support high salinity gradients and it is also much more affected by water

41


1990 1992 1995 1997 2000 2002 2005 2007

0

10

20

Sal

inity

flux

Year

Figure 5.10: Time series of salinity flux (daily averages) - [ton/s]. To indicate the trend, linear fitsare added. The red dashed lines indicate the standard deviation. The grey bars show El Nino/LaNina events.

exchange with the open ocean. Taking these factors into account (assuming linear scaling, by

multiplying the flow of Hervey Bay by an area correction of 5 and an aspect ratio correction

of 2-3), the relative volume transport is comparable with Spencer Gulf even if Hervey Bay is

smaller in size and constrained by the geometry.

42

6 Impact of climate variability

The climate along the subtropical east coast of Australia is changing significantly. Rainfall

has decreased by about 50 mm per decade during the last fifty years. These changes are likely

to impact upon episodes of hypersalinity and the persistence of inverse circulations which

are controlled by the balance between evaporation, precipitation, and freshwater discharge .

In this chapter it is investigated how current climate trends have affected upon the physical

characteristics of the Hervey Bay. During the last two decades, mean precipitation in Hervey

Bay deviates by 13 % from the climatology (1941-2000). Contrary to the drying trend, the

occurrence of severe rainfalls, associated with floods, lead to short-term fluctuations in the

salinity content of the bay.

6.1 The drying trend

6.1.1 Trends in freshwater supply

Tab. 6.1 shows the climatology of freshwater supply (river discharge and precpitation) for

the three observation stations surrounding Hervey Bay. The deviations from the climatology

(1941-2000) between 1941-1970 and 1971-2000 are less than 5%. The reduction in freshwater

supply during the last two decades varies between 10-20% and is therefore higher than the long

term variability. This is caused by severe droughts and the ongoing drying trend on the east

coast of Australia. Despite the general trend, the precipitation gradient between Bundaberg

and Sandy Cape remains nearly the same. To show the reduction in freshwater supply in detail,

Table 6.1: Detailed climatological data of precipitation and river discharge (precipitation equivalent)in mm/yr.

Bundaberg Sandy Cape Maryborough Mary River

1941-1970 1119.8 1172.7 1187.7 294.11971-2000 1029.7 1306.9 1221.8 315.9

1941-2000 1074.8 1239.8 1204.8 305.0variability 45.1 (4%) 67.1 (5%) 7 (1%) 10.9 (4%)

1990-2008 988.7 1052.4 1008.1 235.2

reduction 8% 15% 16% 23%

Fig. 6.1 depicts the deviation of freshwater input into Hervey Bay from the climatology. Shown

are the cumulative sum plots of monthly bay averaged precipitation and Mary river discharge.

43


Two major events are visible. During 1992 strong rainfalls and river floods occurred, caused

by an El Nino event. The classification into El Nino/La Nina are based on the Oceanic Nino

Index (ONI, [NOAA, 2009]). The floods and rainfalls in 1999-2000 occurred during a La Nina

event. In 1992, the freshwater supply recovered to the climatology. Although the rainfalls in

1999-2000 were significant, they could not replenish the water deficit. Due to long/persistent

droughts, the soil moisture in the catchments were low, thus a certain amount of rainfall

was needed first to recharge soil moisture and ground water, until significant runoff could be

released. The La Nina events 1996 and 2008 show a signature in the river discharge but are

in general of minor importance.

In the following, the numerical model is used to quantify, how this reduction affects Hervey

Bay.

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008−3

−2

−1

0

1

Year

Cum

mul

ativ

e pr

ecip

itatio

n [m

m/y

r]

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008−0.3

−0.2

−0.1

0

0.1

Cum

mul

ativ

e riv

er d

isch

arge

[mm

/yr]

PrecipitationMary River

Figure 6.1: Deviation of freshwater flow into Hervey Bay from the climatology (1941-2000). Shownare the cumulative sum plots of monthly bay averaged precipitation and Mary river discharge. Thegrey bars indicate El Nino/La Nina events. Note that the river discharge has a different scaling toemphasise details.

6.1.2 Hypersalinity and inverse state

The density (Fig. 5.8a) and salinity (Fig. 5.8b) gradient times series clearly show the impact

of the 1999 and 2008 La Nina and also the 1992 El Nino event. Further during the last decade

less frequent reversals of the salinity gradient occurred. To understand the impact of the

drying trend, the days in the year are computed, where the salinity gradient and the density

gradient exceed the critical thresholds. A year is defined from July to June and therefore

the complete southern hemisphere summer is included in one year. The results are shown in

44

6.1 The drying trend

Fig. 5.8c. A linear fit has been added to both time series. Hervey Bay is, on average, during

240 days of the year in a hypersaline state and for 108 days in the inverse state, respectively.

Interesting to note is that due to the reduction in freshwater supply, both time series show a

rising trend. The model simulations indicate an increase of 2.7 days per year, where Hervey

Bay is hypersaline and an increase of 1.8 days per year for inverse conditions. These trends

are clearly biased by the El Nino/La Nina events. The 1999 floods and rains lowered the mean

but only slightly biased the trend. The 2008 La Nina decreased the trend. Therefore, these

trends should be judged with care. If ignoring the 1999 La Nina, the observed trend would be

in the range of the inter-annual variations and indicates significance.

The time series indicate that Hervey Bay shows different behaviour before/past the 1999 La

Nina event. Before 1999, the bay was on average on 250 days in a hypersaline state. After the

1999 La Nina event this increased to 300 days on average. This switch is mainly caused by

the ongoing drought on the east coast of Australia.

6.1.3 Residual circulations

To understand the impact of the reduced freshwater supply, a time series of the evaporation

induced residual flow is given in Fig. 6.2. To remove any barotropic influence, a model run was

started, where temperature and salinity were switched off. The induced barotropic residual

flow was then subtracted from the baroclinic case. The mean flow is about 2 cm/s.

1990 1995 2000 2005

1

1.5

2

2.5

3

3.5

Year

Res

idua

l flo

w

Figure 6.2: Time series of residual circulation (fortnightly averages) - [cm/s]. To indicate the trend,

linear fits are added. The red dashed lines indicate the standard deviation. The grey bars show El

Nino/La Nina events.

45


A closer inspection of the time series shows that the flow is weaker during summer than

during winter. This seems puzzling but the weakening of the evaporation induced residuals

during summer is caused by the EAC.

In Tab. 2.1 the transport of the EAC is given (see also Fig. 2.1). The current is strongest

during summer (18 Sv) and weaker during winter (12 Sv). The EAC induces an anti clockwise

circulation within Hervey Bay. This residual flow is estimated to be in the range of 1-2

cm/s and therefore of the same order as the evaporation induced clockwise flow. Thus during

summer the EAC can slow down the evaporation induced flow. Furthermore, this flow shows

a rising trend. The increase during the simulation period is about 18%. Fig. 6.2 also shows

the standard deviation, which is in the same range as the estimated trend. Thus, during the

two decades of simulations the reduction of freshwater leads to an acceleration of the residual

circulation.

6.1.4 Salinity flux

The model indicates that since 1990, the salinity flux has increased by about 22 % (linear fit in

Fig. 5.10). This corresponds to a rise of approx. 0.9 ton/s during the simulation period. The

mean flux is estimated to be 3.95 ton/s. Again the standard deviation is indicated, which is

now with 4.1 ton/s the fourfold on the trend. Thus, the model indicates a trend, but to show

that this increase is significant, the simulation period has to be at least doubled.

The analysis of the simulations further showed that the annual mean heat content of the bay,

solar heat flux and air temperature remain nearly constant over the whole simulation period.

They are only responsible for the intra-annual variability. The most important factor influ-

encing the rising trend in the salinity gradient/salinity flux is therefore the positive difference

between evaporation and precipitation/river discharge.

6.1.5 Impact of the East Australian Current (EAC)

To quantify the importance of the EAC on the hydrodynamics in Hervey Bay, two additional

experiments were conducted. The aim was to reduce the southward transport of the EAC.

The average transport is approx. 7.1 Sv (Tab. 2.1). In the first experiment, the transport was

reduced to 3.5 Sv and in the second experiment; the EAC was completely switched off. These

modifications were implemented by reducing the background sea surface gradient, causing the

EAC. To preserve the dynamics, the sea surface height anomalies were left unchanged.

The comparison of the numerical results with the measurements from the field trips shows

that the impact on the temperature field was of minor importance. The variations in the

salinity field were noticeable. The impact of the EAC was further visible in the salinity and

the density gradient time series, shown in Fig. 6.3. The EAC acts as low pass filter and

smoothes the salinity and the density differences. By completely switching off the EAC, the

peak values of the salinity and density gradient increased by approx. 10%. Especially from

46

6.2 Short term variability

a)

∂ S

−0.02

0

0.02

b)

Year

∂ S

1990 1993 1996 1999 2002 2005 2008

−0.02

0

0.02

Figure 6.3: a) Time series of density gradient - ∂ρ [kg/m3/km], b) salinity gradient - ∂S [psu/km].Shown are daily averages. The red lines indicate the difference between the simulation and a run,where the EAC was completely switched off. The grey bars indicate El Nino/La Nina events.

2000 onwards, the shut down of the EAC lead to a systematic increase in the salinity and

the density gradient. The simulations further indicate that the interannual variations in flow

strength of the EAC are noticeable, but rather unimportant. The dynamics in Hervey Bay are

a local feature and the EAC causes only a weak modulation. A possible explanation is that

the stream reattaches south of 25°S to the shelf. Further, Break Sea Spit (Fig. 3.1) shields

Hervey Bay from the ocean. In conclusion, the EAC has no direct influence on Hervey Bay,

for instance due to eddy entrainment.

Finally, the southward transport was investigated to detect a possible trend in the volume

transport. The analysis showed that the EAC slightly accelerates, but the trend in the two

decades is less than 1/6 of the standard deviations and thus not significant and can not explain

the increase in salininity flux and residual circulation.


The IPCC predicts that heavy precipitation events become more frequent over most regions

throughout the 21st century [IPCC, 2007]. This would affect the risk of flash flooding and

urban flooding. Australia’s strongest recent examples were in 1973-74, 1988-89 and May 2009.

In this recent example, within some days, approx. 300 mm, in total, rain was measured along

the Sunshine Coast (Brisbane up to Hervey Bay). This is around one third of the annual mean.

Northern Brisbane had peak values of 330 mm/day. Unfortunately, these data could not be

47


compiled into the simulations (due to missing river gauge data). However, Fig. 6.4 shows

times series of the Mary River and Burnett River discharge. Two extreme flooding events are

visible, one in February 1992 and in February 1999. The latter one lead to significant loss of

seagrass in the Great Sandy Strait [Campell and McKenzie, 2004]. Because the peak values of

the Burnett River are only about one sixth of the maximum flow of the Mary River, the main

focus of the short term variability is on the impact of the Mary River.

Year

Riv

er d

isch

arge

1990 1993 1996 1999 2002 2005 20080

2000

4000

6000

8000

Mary River

Burnett River

Figure 6.4: Freshwater discharge of the Mary and Burnett River (1990-2008) in m3/s. The grey barsindicate El Nino/La Nina events.

6.2.1 Catchment area

The catchment area of the Mary River covers 5000 km2. It reaches from 25.2°to 27°S and from

152° to the coast (see Fig. 2.1), thus a stripe of 150×50 km2. The Mary River flows into the

northern region of the Great Sandy Strait draining modified catchment of dryland grazing,

agricultural crops, cleared land, forests and both sewered and unsewered urban development

areas [Rayment and Neil, 1997]. For an average rainfall year, 21% of rainfall is exported as

runoff into the Mary River and 268,000 tonnes of eroded sediments flow into nearshore regions

annually. The river further flushes nitrogen (1.7 kg/ha/y) and phosphorus (0.2 kg/ha/y) into

the Great Sandy Strait passage each year [Schaffelke, 2002].

48


6.2.2 River discharge statistics

The river discharge time series in Fig. 6.4 are rather spiky. The peak values for the 1992 and

1999 flood reached 7000 m3/s. In Fig. 6.5 the cumulative distribution functions (CDF) for

the Mary and Burnett Rivers are given. The mean flow for the Mary River is 30 m3/s and 10

m3/s for the Burnett River. The Median is 3 m3/s and 0.8 m3/s, respectively, and therefore

only a tenth of the mean. Thus, most of the time both rivers are almost dry. The rare extreme

events shift the mean to higher values. The CDF indicates, that the probability to exceed a

flowrate of 70 m3/s for the Mary river and 30 m3/s for the Burnett River is less than 5%. Fig.

6.4 further indicate that the high flow volumes are strongly linked to El Nino/La Nina events.

1 10 30 100 1000

0.01

0.1

0.5

1

River discharge

CD

F

Mary River

Burnett River

Median

Figure 6.5: Cumulative distribution functions (CDF) of the freshwater discharge (in m3/s) of theMary and Burnett River (1990-2008).The two dashed lines indicate the mean.

6.2.3 Flooding events

In Fig. 6.6 the response of Hevey Bay to flooding events is shown. Plotted are the depth aver-

aged salinity field and a transect in the southern part of the bay, 10 days past the peak flow of

the Mary River. The river discharge associated with these flooding events is 7100 m3/s (1992),

6700 m3/s (1999) and 900 m3/s (2008), see also Tab. 6.2. The peak value of 900 m3/s seems

rather low, compared to the 1992 event. However, the 2008 flood was preconditioned by three

750 m3/s peaks (in the 40 days before the flood) and puts it therefore in a comparable range to

the 1992 event. Fig. 6.6 indicates, that the outflow of the freshwater is restricted to a narrow

region along the western coast. The transects for 1992 and 1999 further indicate a pronounced

frontal structure (horizontal and vertical). Beside this narrow coastal freshwater strip, the

whole bay is mainly unaffected by the flood. Although the river discharges for the 1992 and

49


Table 6.2: Atmospheric condition and river discharge for three flood events.

Year River discharge Wind direction Wind speed

1992 7100 m3/s SE 6 m/s1999 6700 m3/s S 8 m/s2008 900 m3/s SE 3 m/s

1999 flood are comparable, the transects in Fig. 6.6 show a different behaviour. Whereas in

1992 the bay has a nearly uniform salinity distribution, strong salinity stratifications are visible

for 1999. These differences are mainly caused by the location of the strong rainfalls. For 1992,

they occurred mostly in the southern parts of the Mary River catchments combined with minor

precipitation in Hervey Bay. For 1999, the rainfalls were uniformly distributed over Hervey

Bay and the catchments. Thus, due to the heavy precipitation, a freshening of the surface

layer is visible (Fig. 6.6b) and thus explaining the vertical salinity stratification. This further

explains the greater width of the river plume. Both events are assisted by strong southerly

winds. Hence, a northward flow-through in the Great Sandy Strait prevents an outflow of the

Mary River discharge into the southern region of the Strait. This high flow-through further

pushes the riverine water quite effectively into the bay. This is not the case for the 2008 floods.

Due to the light winds, the fresh water remains in the northern part of the Strait. Moreover,

the saline water in the bay acts as a salt barrier, which prevents the transport of the riverine

fresh water into Hervey Bay. Further, the low river discharge leads only to a weak coastal

plume on the western shore (Fig. 6.6c).

(a)

−25.2

−24.8

(b)

−25.2

−24.8

(c)

152.6 153

−25.2

−24.8

35 35.2 35.4 35.6 35.8 36 36.2 36.4 36.6

−15

−5

−15

−5

152.6 153.0

−15

−5

Figure 6.6: Depth averaged salinity (in psu) for a) 4 Mar. 1992, b) 20 Feb. 1999 and c) 23 Mar.2008. In the left column the salinity transects along the red lines are shown.

50


6.2.4 The flood of 1999

In the following, the 1999 flood event (February 1999) [Campell and McKenzie, 2004] is used

to estimate typical exchange time scales associated with high riverine flow, and also a time

which is needed for Hervey Bay to recover to a “normal state”.

Two experiments are conducted. In the first one, called the flood run (FR), the river discharge,

atmospheric boundary conditions and open ocean boundary conditions are prescribed using

the forcing given in Sec. 2.2. At the same time, a neutral tracer with a concentration of 100

units was released into the river. In the second experiment, the control run (CR), the high

river discharge due to the flood is completely switched off. Both experiments start at the 1.

February 1999 and run for three months. Fig. 6.7 shows the impact of the 1999 flood event.

de

f

a)

152.6 153.0

−25.2

−24.8

0

2000

4000

6000

Riv

er d

isch

arge

b)

Feb Mar Apr May−0.03

−0.02

−0.01

0

∂ S

c)

20

25

30

35

Sal

inity

d)

10

20

30

40

Tra

cer

30

35S

alin

itye)

0

10

20

Tra

cer

30

35

Sal

inity

f)

Feb Mar Apr May0

20

Tra

cer

Figure 6.7: a) position of three virtual measurement stations to showing the impact of the 1999flood, b) river discharge in m3/s, c) salinity gradient ∂S in psu/km (see also Fig. 5.8). The bluecurve represents the flood run (FR) and the red curve the control run (CR). Pictures d-f shows thesalinity at the three stations d-f. The green curve indicates the tracer concentration.

The peak river discharge is approx. 7600 m3/s at the afternoon of the 9 February. In the

beginning of March a second minor flood occurred with a peak flow of 800 m3/s. In Fig. 6.7c

the impact of the flood on the salinity gradient is visible. The transect is positioned close to

station f. The minimum gradient has a delay of 6 days compared to the flood peak. This

corresponds to a plume velocity of 10 cm/s. Taking the wind conditions for this event into

account (Tab. 6.2), clearly shows, that the plume is advected along the western shore, due to

the wind induced currents (Fig. 4.2). Fig Fig. 6.7c further indicates that, although the salinity

gradient shows a significant minimum, Hervey Bay completely recovers to the undisturbed

state (CR) within two months.

51


Fig. d-f depicts the change in salinity and tracer concentration at the three stations. A closer

inspection of the time series yields, that the minimum in the salinity and the maximum in

concentration appear simultaneously. Thus, both are advected with the same velocity. More-

over the further north the station is situated, the weaker the flood impact. This seems quite

reasonable, because the freshwater plume is much longer exposed to entrainment and tidal

mixing. Nevertheless, the salinity time series show the same recovery time of 2 months to the

undisturbed state.

5 10 15 20 25 30 35 40 45 50−1

−0.5

0

0.5

1

1.5

2

2.5

3

3.5

Days past peak flow

log(

salin

ity d

iffer

ence

)

Point d)Point e)Point f)

Figure 6.8: Time series of the logarithmic salinity difference (CR-FR) for the three virtual measure-

ment stations (see Fig. 6.7a). The dashed lines indicate a linear fit. For visualisation, the time series

are shifted along the y-axes

To compute a second time scale, it is assumed that the salinity time series of experiment FR

recovers exponentially to experiment CR. Fig. 6.8 depicts the logarithmic salinity difference

between the experiment FR and experiment CR. The linear fits indicate that the exponential

recovery is a valid assumption. Further, the exponential decay is nearly the same for all three

stations. The linear fits indicate a decay constant of approx. 20-24 days. This time scale is

similar to the flushing time of the western part of Hervey Bay under SE wind (Tab. 4.3). Thus,

the flushing of the riverine freshwater is strongly affected by wind conditions at the time.

6.2.5 Flood response

In the previous section a detailed analysis of the 1999 flood was given. The same exercise

was repeated with the events of 1992 and 2008. In Tab. 6.3 the results are summarised. The

52


simulation indicates, that although the flood related river discharges differs significantly, the

recovery times vary only slightly. For all three events, Hervey Bay shows a decay rate of the

disturbance, of approx. 22 days. This recovery time scale to the experiment CR is seen in the

salinity and in the salinity gradient. The simulations further indicate, that the flood response

is closely related to the wind induced residual circulations. The exponential decay with approx.

22 days, can also be seen in the residence time for SE wind (Tab. 4.3).

Table 6.3: Exponential recovery time for the three flood events in days. The salinity recovery is

averaged over the three stations. The salinity gradient ∂S is computed along the transect indicated

in Fig. 3.1. For 2008, this measure could not be computed.

Year River discharge salinity recovery ∂S recovery

1992 7100 m3/s 26 d 20 d

1999 6700 m3/s 22 d 18 d

2008 900 m3/s 20 d -

53

7 Gravity currents

7.1 Release of gravity currents

The density gradient time series in Fig. 5.8a show, that the density at the shore is higher

than on the shelf. This leads to the establishment of an inverse circulation. Because the

positive density gradient is a gravitational unstable state and therefore gravity induced flows

are triggered. This flow of dense water originating from cooling, evaporation, or salinisation

on the shelf, spills over the shelf edge and can develop as near-bottom gravity current or

an intermediate-depth intrusion. Quite often, it is difficult to observe them in nature due

to their intermittent character. It is worth mentioning that until now no observations of

the gravity flows in Hervey Bay are available. The main research focus was on Hervey Bay

itself; therefore, no field measurements were taken on the northern shelf. Middleton et al.

[1994] lacked observational evidence in support of their hypothesis that Hervey Bay potentially

exports high salinity water formed through a combination of heat loss, high evaporation, and

weak freshwater input in shallow regions of the bay. ... Thus, a second hypothesis is that

the high nutrient, low-oxygen waters that constitute the anomalous water masses observed at

both the Sandy Cape and Double Island Point sections consist partly of cooler, saltier ’winter

mangrove waters’ exported both north and south of the Great Sandy Strait on each flood and ebb

tide. The exported waters would subsequently sink off the continental shelf to their own density

level, progressively mixing with ambient waters... Thus the common assumption was, that tidal

flushing would lead to constant export of this dense water to the continental shelf. Further due

to its low aspect ratio and therefore the lack in supporting high density gradients, significant

gravity currents ( [Tomczak, 1985; Lennon et al. , 1987; de Silva Samarasinghe, 1998] were not

expected.

Fig. 7.1a shows such a flow event in June-July 1995. The density within Hervey Bay reaches

values of greater than σt=26.2 kg/m3, which is equivalent to a depth of approx. 300 m. During

its way down the shelf, the plume is channelled in the Mary River Canyon, to finally reach a

depth of 200 m.

7.1.1 Formation

To describe the four different stages in the development of the gravity flows, the classification

54

7.1 Release of gravity currents

a)

26.2

25.2

25

152 152.5 153

−25

−24.8

−24.6

−24.4

−24.2

−24

17

20

b)

152 152.5 153

−25

−24.8

−24.6

−24.4

−24.2

−24

c)

35.6

36

152 152.5 153

−25

−24.8

−24.6

−24.4

−24.2

−24

Distance [km]

Dep

th [m

]

d)

0 50 100−200

−150

−100

−50

0

24.5 25 25.5 26

Figure 7.1: a)bottom density σt [kg/m3] on the 28 July 1995, b) bottom temperature - [C], c) bottom

salinity - [psu] and d) σ-density along the black line in b) [kg/m3]. The thick dashed lines in a,b and

c are the 40 m, 100 m and 300 m depth isolines.

proposed in Shapiro and Hill [2003] is used. The pre-conditioning is the stage when dense

water accumulates on the shelf and a density front is formed. The short active stage corre-

sponds to the period when the leading edge of the dense water accelerates down-slope. The

main stage relates to a quasi-steady flow with a noticeable down-slope component. These two

stages can also be combined in a down-slope propagation stage. The final stage is reached when

the water spreads isopycnically off the slope, but traces of the cascade may still be detected

by inclined isopycnals over the slope.

7.1.2 Pre-conditioning

To trigger gravity currents in Hervey Bay, three conditions are necessary. First, the density

gradient has to exceed 0.008 kg/m3/km. This is a rather moderate gradient and the same

as the threshold to define inverse circulations. The second condition, which is necessary, is

that the SST in Hervey Bay has to drop below 20°C. This condition is mostly fulfilled during

June/July. The salinity gradient is of minor importance. The dependence on the SST indicates,

that Hervey Bay has a temperature driven cascade [Shapiro and Hill, 2003], with a response

55

7 Gravity currents

to surface cooling assisted by advection of salinity. The third mechanism is the tidal forcing.

The initialisation of the plume coincides with the occurrence of neap tide. During this time

tidal mixing is sufficiently reduced and a two layered flow structure can develop.

Wind forcing is not directly involved into the triggering of the plumes. It is only important

to maintain the gradients across the shelf. The wind forcing is important to restrict the path

of the plume between Breaksea Spit and Lady Elliot Island (see Fig. 3.1). Such an event

is shown in Fig. 7.1. In the northwestern part of the shelf, water of low density and higher

temperature is situated. This acts as an effective barrier for a northward flow of the plume.

Hence, the whole flow is directed into the Mary River Canyon. This is a typical situation

during northeasterly wind. Relative warm water from the southern part of the Great Barrier

Reef is pushed southwards onto the northern shelf of Hervey Bay. Further, the saline water

from the northern shelf is advected into the bay. This mechanism supports the intensification

of the flow but is not necessary to actually release the plume.

7.1.3 Down-slope propagation

The flow of the plume is mainly controlled by the steepest decent into the Mary River Canyon.

Therefore, topography suppresses the effects of earth rotation until the plume reaches the

100 m depth isoline. Although the flow is disturbed by the bathymetry, a good estimate to

compute the frontal velocity uNof is given by Nof [1983].

uNof = g′tanα

fwith g′ =

∆ρ

ρ0(7.1)

where g′ is the reduced gravity within the plume, f is the Coriolis frequency and α is the

bottom slope. To compute this theoretical velocity f is taken to be 3·10−5 s−1 and α is

estimated with 0.0016. To compute the reduced gravity, the density gradient (see Fig. 5.8a)

is used. The transect to calculate the gradient is aligned with the flow path of the plume and

has a length of 60 km. Using a density gradient of 0.008 kg/m3/km, equivalent to a density

difference of 0.5 kg/m3, leads to a maximum frontal speed of 0.25 m/s. This velocity is also

seen in the simulations. The average flow velocity in the steady state is approx. 5-7 cm/s.

Inspection of the time series shows that the plume front passes the 100 m isolines approx. 5-8

days past neap tide. This can be explained by simple geometry. The gravity current needs

on average 6 days to travel 150 km, which is approx. the shelf width. Therefore, the reduced

mixing during neap tide is necessary to trigger the release of the plumes.

If the plume has passed the 60 m isoline, the slope of the shelf nearly doubles (see Fig. 7.1d).

According to Eq. (7.1) this would cause a doubling of the frontal speed, which is not seen in

the simulations. Due to dispersion and intrusion, the density gradient across the plumes starts

to weaken, reduces therefore g′ and balances thus the change in bottom slope.

After passing the 60-80 m isoline, the plume is no longer restricted in its flow path by the

56

7.2 Impact of freshwater reduction

bathymetry. Using the distribution of salinity (see Fig. 7.1c), the deviations of the front to the

left are visible. Hence, there exists a balance of Coriolisforce and the component of gravity in

the cross-flow direction. The angle θ at which the current is deflected down slope by friction

can be estimated [Bowers and Lennon, 1987] as

tan θ =(ks + kb) u

f h(7.2)

where kb is the bottom friction coefficient, ks is an interfacial friction coefficient, uNof the

frontal speed and h the thickness of the plume. The only unknown here is the interfacial

friction ks. Using kb=0.0025, u = uNof , f=3·10−5 s−1, h=10 m (Fig. 7.1d) and estimating

θ=25°, yields ks=0.002, which is of the same order as the bottom friction coefficient. This is

in broad agreement with observations [Pederson, 1980].

7.1.4 Fate of the plume

After the head of the cascading plume has reached its equilibrium density level (which can be up

to 280 m), it detaches from the bottom, intruding into the ambient water as an isopycnal layer.

Heat and salt exchange with the surrounding water causes transformation of cascading water

and levelling salinity and temperature differences. The whole mixing process is enhanced by

the strong ambient currents (EAC) which additionally facilitates distant spreading of cascading

water from the source area. This was also observed by Tomczak [1985].

7.2 Impact of freshwater reduction

To quantify the impact of the freshwater reduction it is first necessary to define an outer

envelope for the gravity current. For Hervey Bay the isopycnal surface σt = 25.4 has been

taken for this purpose. This density contour is equivalent to depths of approx. 150-180 m. A

gravity flow starts if the σt = 25.4 contour crosses the 100 m depth line between Lady Elliot

Island and Break Sea Spit (Fig. 3.1). The same argument holds to define the termination

of the flow. During the occurrence of the gravity flow, the duration and the total volume,

transported down the shelf, is computed. Fig. 7.2 shows the duration and the volume flow for

each year. The gravity flows occur only once a year, mostly during June/July.

The average duration is 29 days (Fig. 7.2a) but can range from one week up to two months.

The average water transport associated with the plumes is comparable with the volume of

Hervey Bay. Peak values of twice the bay volume are observed.

It is rather difficult to identify a possible trend. It seems that there is an increase in duration

and magnitude of these outflow events, especially when comparing the first 10 years with the

last decade. Given the noisy signal, a firm conclusion cannot be given at this time.

57

7 Gravity currents

1990 1995 2000 20050

10

20

30

40

50

60

Flo

w d

urat

ion

in d

ays

Year

(a)

1990 1995 2000 20050

0.5

1

1.5

2

2.5

Nor

mal

ised

flow

vol

ume

Year

(b)

Figure 7.2: a) duration of gravity flows [days] and b) down shelf transport normalised by the volume

of Hervey Bay. The gravity flows are tracked between Lady Elliot Island and Break Sea Spit. A

gravity plume is defined to be bound by the σt=25.4 [kg/m3] isoline. This is equivalent to a depth of

approx. 150 m. The duration and the down shelf transport are only counted past the 100 m depth

isoline.

58

8 Conclusion

In this study the ocean model COHERENS has been applied to compute, amongst the usual

hydrodynamic variables, the temperature and salinity distribution within Hervey Bay, Aus-

tralia. A model validation and calibration has been carried out using recent in-situ field,

satellite AVHRR SST data, and pan evaporation measurements. Observations and model re-

sults show that the bay is in parts vertically well mixed throughout the year. The absence of

longer lasting stratification is caused by the tidal regime within Hervey Bay. The tidal range

can exceed 3.5 m. Due to the tidally induced bottom shear, the whole water column is con-

trolled by the bottom Ekman layer most of the time. Therefore only horizontal fronts appear.

Only during a short time around neap tide, a temperature induced stratification can develop

and the bottom to surface density difference can exceed 0.3 kg/m3. The dominant mechanism

forcing residual circulations in the bay is provided by the Trade winds from the east, with a

northern component in autumn and winter, and a southern component in spring and summer.

The wind-induced currents are in the range of 5-10 cm/s. The contribution of the tides to the

residual currents is negligible. Hence, the tides are only responsible for mixing.

To quantify the impact of the residual circulations on the water exchange of Hervey Bay with

the northern shelf/open ocean, the concept of flushing time and residence time was introduced.

Because both measures are defined in different frameworks (Eulerian/Lagrangian), different

aspects of the water exchange could be investigated. The weak tidal residual currents lead to

flushing/residence times of approx. 3 months. During SE wind conditions (Trade winds), the

water exchange times were in the range of 20 days. The clockwise circulation pattern yield

faster flushing times for the western part of the bay compared to the eastern part. During NE

wind, the exchange time scales are comparable to SE wind, only the pattern changed. Due to

the large-scale circulation cell, that connects Hervey Bay with the northern shelf (during NE

wind), the central part of the bay showed the fastest response. This outflow of Hervey Bay

water through the central part of the bay could also be observed in the temperature pattern

of the September 2004 field trip.

Climatological data indicate that Hervey Bay is a hypersaline bay that also exhibits features

of an inverse estuary, due to the high evaporation rate of approximately 2 m/year, a low pre-

cipitation rate of less than 1 m/year and an on average almost absent freshwater input from

the two rivers that drain into the bay. As in other inverse estuaries, the annual mean salinity

increases towards the shore to form a nearly persistent salinity gradient. The region therefore

acts as an effective source of salt accumulation and injection into the open ocean. The high

59

8 Conclusion

evaporation is leading to a loss of freshwater and increases salinity within the bay. The aver-

age salinity flux into the open ocean is estimated to be about 4.0 tons/s. This study showed

that this transport is mainly caused by advective transport, whereas the diffusive transport

is on average three orders of magnitude smaller. Furthermore, the evaporation loss and the

accumulation of salt within the bay leads to evaporation induced residual circulation of the

order of 2-4 cm/s.

The numerical modelling that was carried out made it possible to understand in detail, how

the actual drying trend on the east coast of Australia impacts on the hydrodynamics of Her-

vey Bay. During the last two decades the drying trend has manifested itself in a reduction of

precipitation by 13 % and a reduction in river discharge by 23 %. This is much higher than the

long-term variability suggested and shows the impact of severe droughts during the last two

decades. As a direct consequence, hypersaline/inverse conditions are more persistent but they

did not increase in magnitude. Further the baroclinic residual circulation accelerated by 18 %

due to the disturbance of the evaporation/precipitation ratio. The signal visible in the salinity

flux shows an increase by 22 % but the annual variations are higher than the trend. Thus,

longer simulation times should give more confidence. Due to the lack in boundary conditions

and forcing data, the simulations could only run from 1990 onward.

Due to the inverse conditions and thus gravitational unstable conditions, gravity currents are

released. These flows have a duration of approx. 30 days and are associated with a volume

transport comparable to the total volume of Hervey Bay. The signature of these outflow events

can be found up to depths of 280 m. A clear signal due to the reduced freshwater supply is

not visible, but the model indicates a slight increase in volume transport and duration.

Despite the drying trend, two major flood events occurred in Hervey Bay 1992 and 1999. The

riverine freshwater flow is restricted to an approx. 10-15 km narrow band along the western

shore of the bay. The simulations yield that essentially most of Hervey Bay is unaffected by the

floods. The recovery time, to an undisturbed state, follows an exponential law with a typical

decay time of 22 days. This time scale is similar to a flushing time for the western bay due to

SE winds. Thus, the export of the freshwater is strongly affected by the wind conditions at

the time of the event.

Due to the lack of validation data for biology/chemistry, only the impact on the hydrodynam-

ics could be investigated. Therefore the understanding of the influence of the drying trend on

the local flora/fauna would be of great interest but is at this stage of rather speculative nature.

Although the simulation time span is with 18 years rather short and is biased by severe El

Nino/La Nina events, the simulations demonstrate that recent climate trends impacted on

physical marine conditions in subtropical regions of eastern Australia and are likely to do so

in the future if current climate trends, especially drying, are to continue.

60

A Particle tracking schemes

A.1 Introduction

The behaviour of particles in turbulent flows has been studied for many years, ranging for me-

teorology [Brickman and Smith, 2001; Cencini et al. , 2006] to ocean dynamics [North et al. ,

2006; Visser, 1997, 2008]. Extensive literature exists on the treatment of Lagrangian trajec-

tories, ranging from highly idealised flows to situations as complex as the unstable convective

boundary layer or frontal zones. The level of understanding of these types of models has

greatly increased over the years. In the same time the need to predict the transport of parti-

cles, pollutants, or biological species has resulted in a rapid rise in the use of these numerical

models.

The random walk simulation model enables the observation of phenomena on scales much

smaller than the grid size, as well as the tracing of the movement of individual particles,

thereby describing the natural processes more accurately. Furthermore, information on inte-

grated properties like: residence/settling time or individual tracks are easily extracted from

the simulations. Concentrations of particles can be directly calculated from the spatial posi-

tions of the particles and, more importantly, when and where required. Additionally, errors

due to numerical diffusion inherent in methods such as finite differences or finite elements,

are avoided, particularly in areas where high concentration gradients exist, such as close to

point sources or frontal zones. Although there are methods to circumvent these difficulties

[Chung, 2002], their implementation is problematic in complex geometries, where it is difficult

to control the potential sources of error.

The development of particle tracking methods (or random walk / random dispersion methods)

started by tracking neutrally buoyant particles, i.e. water parcels [Maier-Reimer and Sundermann,

1982; Visser, 1997]. Hunter et al. [1993] and Visser [1997] also showed that due to the high

spatial variability of turbulence, the tracking algorithms need special modification to avoid

numerical artefacts. In recent years, a catalogue of test cases was developed to compare

the performance of tracking schemes but also to validate the models [Brickman and Smith,

2001; Deleersnijder et al. , 2006a; Spivakovskaya et al. , 2007]. Deleersnijder et al. [2006a]

extended the test catalogue to particles that have a finite sinking velocity. By this, particle

tracking schemes dealing with sediment or buoyant particles could be validated against an ana-

lytical solution. The random walk schemes for modelling suspended particulate matter (SPM)

dynamics are quite attractive, because they give a straightforward physical interpretation of

61


the processes and automatically account for suspension and bed load.

Because of these advantages, Lagrangian schemes have also become more common in the SPM

modelling community [Charles et al. , 2008; Krestenitis et al. , 2007; Rolinski et al. , 2005].

Nevertheless most of these models used only small number of particles O(104). Nowadays

with easy access to high performance computer clusters, the tracking of individual particles

can be parallelised with high efficiency and therefore makes huge particle numbers feasible

[Charles et al. , 2008]. This means to deal with particles in the order of > 107. This is still

negligible, by realising that a bucket of muddy water contains more individual particles, com-

pared to the ability of state of the art Lagrangian schemes. Nonetheless increasing the number

of particles leads to a better statistical description and makes the answers, a Lagrangian model

can give, more reliable.

A.2 The Lagrangian model

Dealing with concentration fields (SPM, pollutants, biology, etc.), the time evolution of these

fields is usually formulated as partial differential equations (PDEs) in an Eulerian framework.

∂tC = −∇ · (u C − K · ∇C)

∇ · u = 0(A.1)

The first equation is an advection-diffusion equation for the concentration field C of a passive

tracer, that is coupled to a 3D velocity field u, that shall be divergence free. The diffusivity

tensor K is symmetric and positive definite. In the following only diagonal diffusivity tensors

are considered

K =

KH 0 0

0 KH 0

0 0 KZ

(A.2)

where KH is the horizontal and KZ the vertical diffusivity. Hence, the three spatial dimensions

are decoupled. Instead of solving the PDE, one can transform the whole solution process

into the solution of a system of stochastic differential equations (SDEs) also called Langevin

equations. The basic idea is to interpret the concentration field C(x, t) as a transition density

field and reinterpret Equation (A.1) as a Fokker-Planck equation, i.e. a deterministic PDE

with regard to transition density functions. This can be solved by the following system of

SDEs defined in the Ito sense [Arnold, 1974]:

dX(t) = (u+ ∇ ·K)dt +√

2K dW(t) (A.3)

Here X(t) is the position vector of the particles and dW(t) is a Wiener noise increment with

the following properties. W(t) is a Gaussian process with independent increments for which

62


holds

〈W(t)〉 = 0 ; Std (W(t) − W(s)) =√

|t− s|I (A.4)

where I is the identity matrix. Therefore the noise process has a vanishing mean 〈·〉, its stan-

dard deviation scales as√dt and the increments are uncorrelated.

The first term on the right hand side of Equation (A.3) represents the deterministic part,

whereas the second term is the stochastic term. In the case of vanishing turbulent diffusiv-

ity, the system of equations reduces to a system of ordinary differential equations (ODEs).

Because the ocean is a turbulent environment, turbulent diffusion has to be included. This

is incorporated via the stochastic term. The particles experience a random displacement due

to eddies of average size√

2Kdt. Because the turbulent diffusivity K = K(x, t) is spatially

highly variable, the term ∇ ·K needs to be added to the deterministic part. This corrects for

an artificial noise induced drift [Hunter et al. , 1993; Visser, 1997].

A.2.1 Numerical approximation

Because the diffusivity tensor is diagonal, the three spatial directions can be treated separately

in developing a numerical approximation to the 3D Langevin equation. Focussing for simplicity

on the vertical dimension the following equation needs to be discretised.

dZ(t) = (w + ∂zKZ(z)) dt +√

2KZ(z) dW (t) (A.5)

This equation can further be simplified to

dZ(t) = a(z) dt + b(z) dW (t) (A.6)

where a = w + ∂zKZ(z), represents the deterministic part and b =√

2KZ(z) is the stochastic

part. Again Eq. (A.6) and (A.5) are only valid in the Ito interpretation [Arnold, 1974].

Instead of writing Equation (A.6) in differential form, it is also common to use the integral

representation

Zt = Z0 +

∫ t

0a(Zs) ds +

∫ t

0b(Zs) dWs (A.7)

A straightforward translation of Equation (A.6) into a numerical scheme, is simply to replace dt

by ∆t and dW by ∆W . This is equivalent to assuming that a(Zs) and b(Zs) in Equation (A.7)

are constant and can be taken out of the integrals. Therefore, the lowest order approximation

reads as

Zn+1 = Zn + a ∆t + b ∆Wn (A.8)

This is also known as Euler scheme. In the following, this approximation is named EULER.

This scheme is commonly used [Brickman and Smith, 2001; North et al. , 2006; Spivakovskaya et al. ,

2007; Visser, 1997]. Although this is a straightforward approach, some difficulties arise in the

63


case of SDEs. To define the accuracy or order of convergence for stochastic scheme two cases

have to be distinguish. For SDEs the order of convergence is separated into weak and strong

[Arnold, 1974; Kloeden and Platen, 1992]. A method is said to have weak/strong order of

convergence of γ if there exists a constant Λ such that

|〈p(Zn)〉 − 〈p(Z(τ))〉| ≤ Λ ∆tγ : weak

〈|Zn − Z(τ)|〉 ≤ Λ ∆tγ : strong(A.9)

for any fixed τ = n∆t ∈ [0, T ] and ∆t sufficiently small. Zn represents the true solution and

Z(τ) is the approximation. p(·) is an arbitrary function (in most cases a probability density

function). The weak criterion asks for the difference in a distribution, whereas the strong

criterion accounts for the difference in the trajectory.

As discussed after Equation (A.4) the increment ∆W scales as√

∆t, hence the whole EULER

scheme is only of order√

∆t in the strong convergence. Since we are interested in the time

evolution of a sediment distribution rather than individual trajectories of single sand grains,

the weak convergence is used. In this case the EULER schemes is or order ∆t in the weak

sense.

To develop higher order schemes, that have a higher accuracy in the strong definition, the as-

sumption that a(Zs) and b(Zs) in Equation (A.7) are constant is not valid any more. Using the

appropriate Taylor approximation for the integrals, see e.g. Arnold [1974]; Kloeden and Platen

[1992], the next higher order approximation reads as

Zn+1 = Zn + a ∆t + b ∆Wn +1

2bb′[

(∆Wn)2 − ∆t]

(A.10)

where b′ is the spatial derivative. This is also known as the MILSTEIN scheme. This scheme

is of order ∆t in the weak and strong convergence. Additional accuracy is gained by including

information of the derivative of the noise term b. If this scheme is used in numerical algorithms,

the term bb′ can cause problems due to round off errors. To avoid this, a symmetry property

of Equation (A.6) can be used. By replacing b again by√

2KZ(z) and computing the term

bb′ explicitly it turns out that it is equal to ∂zKZ(z). After some rewriting, the schemes read

as follows

Zn+1 = Zn + w∆t + ∂zK ∆t +√

2K∆W : EULER

Zn+1 = Zn + w∆t + ∂zK(∆W )2+∆t

2 +√

2K∆W : MILSTEIN(A.11)

As stated above the EULER scheme is commonly used, but it is easily appreciated that a

higher accuracy is gained here by a simple multiplication with ∆W · ∆W and one addition.

There are no approximations involved and the extra computational cost is negligible.

To further improve the accuracy of the numerical schemes, more terms in the Taylor approxi-

mations have to be included [Kloeden and Platen, 1992]. Due to the slow convergence of the

64


numerical schemes for SDEs, the extra computational costs are so far prohibitive. Therefore,

a multi step scheme is proposed, similar to Runge-Kutta schemes for ODEs.

Zn+1 = Zn +1

2

(

a(Z) + a)

∆t + b ∆Wn (A.12)

with

Z = Zn + a∆t + b ∆Wn (A.13)

Equation (A.12) is a stochastic version of the trapezoidal method also known as HEUN

scheme. Note that the predictor step (A.13) is only applied to the deterministic part, the

stochastic part is not corrected to keep the numerical approximation consitent with Eq. A.6

[Kloeden and Platen, 1992]. The HEUN scheme, like the MILSTEIN scheme, is of order ∆t

in the strong and weak convergence.

At this stage, the question might arise, why three algorithms are presented with the same

accuracy. All three algorithms should behave identical in predicting the time evolution of an

initial concentration, because they have the same order of convergence. Assume the limit of

vanishing diffusivity, here the MILSTEIN scheme becomes identical to the EULER scheme.

This is not the case for the HEUN scheme. Due to the predictor-corrector step, the accuracy

is higher. Therefore, in the case of advection-dominated problems, differences will be visible.

This should not be the case if diffusion dominates. However, especially Sec. A.3.3 will show the

limitation of the EULER scheme. Moreover, near boundaries, the proper approximations of

the particle trajectories become important to resolve for instance the bottom boundary layer.

A.2.2 Boundary conditions

The treatment of boundary conditions is always a critical issue in ocean modelling, especially

in coastal regions. The moving sea surface, the sea bottom and lateral boundaries like islands

or beaches have to be considered appropriately. E.g., in the framework of PDEs the sea

surface is an impermeable boundary and a no flux condition is normally imposed (at least for

suspended particulate matter). This no flux condition can be easily violated by overshooting of

the trajectories of simulated particles, due to either too large time steps or the random nature

of the stochastic increment ∆W . This can lead to a crossing of the boundary. To correct this,

a straightforward approach would look like this: When a particle crosses the boundary (due to

a too large random displacement), it is simply reflected back into the domain by the amount

it penetrates into the boundary domain. It would be advantageous in general to minimise the

number of particles that crosses the boundaries in the first place. The first solution that comes

to mind is to reduce the time step of the particle displacement. Nevertheless, this would also

lead to additional computation time in ’open water’. A more expensive method is the use of

a higher-order numerical scheme. This may perhaps not completely prevent the crossing from

happening, but it will at least reduce the number of times that it does occur. This was also

65


mentioned by Stijnen et al. [2006].

In the following all boundaries are treated as reflective boundaries (no flux condition), if not

stated otherwise.

A.3 Idealised test cases

In the following section two simple 1-D test cases are described and a 2-D test is considered.

Because the equations which need to be solved are SDEs, special care is taken for the stochas-

tic increment ∆W . A state of the art random number generator computes the increments:

the Mersenne Twister [Matsumoto et al. , 1998]. This generator produces uniform random

numbers in the interval [0, 1]. Because the particle numbers are quite large, standard gener-

ators are limited by their periodicity. Moreover the Mersenne Twister produces uncorrelated

random numbers in higher dimensions. These random numbers are transformed to Gaussian

random numbers by the Box-Muller algorithm [Press et al. , 1986].

A.3.1 1-D diffusion

Firstly, the numerical algorithms are applied to a diffusion test in a bounded region. This can

be visualised as an one dimensional water column that is bounded by the sea surface and the sea

floor. The model is discussed in detail in Deleersnijder et al. [2006a] or Spivakovskaya et al.

[2007]. The governing PDE for this case is written as

∂C

∂t=

∂

∂z

(

KZ(z)∂C

∂z

)

(A.14)

This describes a simple diffusion equation. The diffusivity KZ(z) has the following form

KZ(z) = 6 z (1 − z) (A.15)

This parabolic profile is a good approximation of the diffusivity profile in the upper mixed layer,

but it is also a good description for a shallow, well-mixed, coastal region [Burchard et al. , 1998;

Warner et al. , 2005]. For simplicity, time dependence is not considered. The boundary (BC)

and initial conditions (IC) are

BC:

[

KZ(z)∂C

∂z

]

z=0,1= 0 ; IC: C(0, z) = δ(z − z0) (A.16)

i.e. “no flux” boundary conditions are imposed at the boundaries of the normalised domain

[0, 1]. The initial condition is a delta like concentration peak. The Langevin equation for the

particle trajectories takes the following form

dZ(t) = ∂zKZ(z) dt +√

2KZ(z) dW (t) (A.17)

66


0.5 1 1.50

0.10.20.30.40.50.60.70.80.9

1

z

Concentration

A)

t=0.036t=0.072t=0.108t=0.144 .

0 0.2 0.4 0.6 0.8 10

0.10.20.30.40.50.60.70.80.9

1

Residence time

z

B)

Figure A.1: Analytical solution of A) the 1-D diffusion test for different moments of the simulationusing Equation (A.18) and B) the residence time for the parabolic diffusivity profile Equation (A.15)for ws=5.

Using this setup, an explicit solution for the dispersion of the initial peak is

CA(t, z) = 1 +∞∑

n=1

(2n + 1)Pn(2z − 1)Pn(2z0 − 1) exp(−6n(n+ 1)t) (A.18)

where Pn(z) denotes the n-th order Legendre polynomial. Figure A.1A presents the analytical

solution for different time steps obtained for z0 = 0.5. To compare the performance of the

three numerical algorithms (EULER, MILSTEIN, HEUN) the root mean square error (RMS)

is computed

RMS =

√

√

√

√

1

4

4∑

n=1

1

100

100∑

i=1

[CA(zi, tn) − CP (zi, tn)]2 (A.19)

the four time steps tn are given in Figure A.1. CA(tn) is the analytical solution (A.18) and

CP (tn) is the prediction of the Lagrangian models. To estimate CA(tn) the water column

is binned into 100 equally sized boxes and the concentration is obtained by a box counting

approach. The results are shown in Figure A.2. All three schemes converge to the analytical

solution if either the step size is decreased or the number of released particles is increased. The

HEUN scheme shows the smallest error whereas the EULER scheme has the largest deviation.

All three algorithms converge to the true solution, by decreasing the step size, with the same

rate, because they have the same order of convergence (see Sec. A.2.1). Further by increasing

the number of particles N , the approximated solution comes closer to the analytical one. This

is due to the intrinsic nature of random processes, because the results include statistical errors

proportional to N− 1

2 .

67


10−5

10−4

10−3

10−2

10−3

10−2

10−1

Timestep in s

RM

S

A)

104

105

106

107

10−3

10−2

10−1

Number of particles

RM

S

B)

EULERMILSTEIN .HEUN

Figure A.2: RMS of the dispersion test: A) for fixed particle number N=106 and B) for fixed timestep ∆t=10−4

A.3.2 1-D residence time

In the previous test, the settling velocity ws was set to zero to obtain an analytical solution.

This might be appropriate for tracking water parcels, for buoyant particles, this assumption is

no longer valid. However, imposing a finite sinking velocity makes it impossible to formulate

an analytical solution. Nevertheless, an exact solution for the adjoint problem of finding the

residence time θ(z) is known [Deleersnijder et al. , 2006a]. To obtain the residence time θ(z0)

a number of particles are released at a distance z0 from the bottom, and then the time is

tracked until all particles have crossed the bottom. The boundary and initial condition read

again as

BC:

[

(KZ(z)∂C

∂z

]

z=1= 0 ; IC: C(0, z) = δ(z − z0) (A.20)

The boundary condition at the sea floor is now modified. The sea floor is no longer a rigid

boundary, but represents for instance the pycnocline. The boundary condition changes from

no flux condition to an absorbing type. This means that if a particle reaches the boundary it

is immediately removed from the computational domain. Thus

BC: C(t, 0) = 0 (A.21)

The diffusivity profile remains the same (A.15). The analytical solution can be written as

θ(z) = z +

(

z

1 − z

)µ

B1−z(1 + µ, 1 − µ) (A.22)

where B1−z(1+µ, 1−µ) is a generalised incomplete beta function and µ = ws/6. The analytical

solution is shown in Figure A.1B.

68


10−5

10−4

10−3

10−210

−4

10−3

10−2

10−1

Timestep in s

RM

SA)

103

104

105

10610

−4

10−3

10−2

10−1

Number of Particles

RM

S

B)

EULERMILSTEIN .HEUN

Figure A.3: RMS of the residence time test: A) for fixed particle number N=106 and B) for a fixedtime step ∆t=10−4 s.

The Langevin equation for the particle trajectories takes now the following form

dZ(t) = (ws + ∂zKZ(z)) dt +√

2KZ(z) dW (t) (A.23)

To compare again the performance of the three algorithms a non-dimensional sinking velocity

of ws = 5 is applied. To approximate the residence time, the average time is computed until

all particles have left the domain. The results are shown in Figure A.3. Again, the HEUN

scheme performs best. The difference between the EULER and MILSTEIN scheme is nearly

vanishing.

A.3.3 2-D correlation test

One of the most important properties a Lagrangian stochastic model must fulfil is to maintain

an initially uniform distribution of particles for all time (in the absence of an advection field)

- the well mixed condition (WMC). The test is based on the fact that if a WMC does not

exist, then a significant correlation would exist between the perturbation field C ′(x, y, t) =

C(x, y, t) − C and the perturbation diffusivity field K ′H(x, y) = Kh(x, y) − KH , where C is

the initial well mixed concentration and KH is the xy-averaged diffusivity field. By this, the

approach of Brickman and Smith [2001] is adopted to demonstrate the WMC. Contrary to

their work, the following diffusivity field is chosen

KH(x, y) = K0

[

cos

(

2π n

Lxx

)

+ 1

]

[

cos

(

2π n

Lyy

)

+ 1

]

(A.24)

69


where K0= 20 m2/s, Lx=Ly = 40 km and n an integer number. The domain has a resolution

of ∆x=∆y = 200 m. The time step is set to ∆t = 30 s. In the experiments 106 particles are

released and uniformly distributed in the computational domain. Further, the diffusivity field

is chosen to have a vanishing gradient at the boundaries (which are again reflective).

The SDEs aredX(t) = ∂xKHdt +

√2KH dWx(t)

dY (t) = ∂yKHdt +√

2KH dWy(t)(A.25)

Although the diffusivity field has an analytical formulation, the diffusivity field is only given

at the discrete grid points. The spatial derivatives are computed using a second order approx-

imation of the gradient. The values are bilinear interpolated to the position of the particle. n

is now the test parameter. By increasing n, the spatial variation in the diffusivity field is also

increasing. It is expected that for higher n the numerical schemes start to fail, due to errors in

the approximation of the ∂xKH and ∂yKH terms. To show that the schemes really fail due to

discretisation, a fourth scheme is applied. This is called EULER-analytic. Here the diffusivity

field as well as the spatial derivatives are provided by analytical functions (A.24).

To test now for the WMC, the normalised correlation coefficient is calculated as

ρ(t) =1

σC σK ′H

i∑

j∑

C ′ij K

′Hij (A.26)

where σ is the standard deviation of the perturbation fields. To compute significance levels at

a given time step, the C ′ field was repeatedly randomised and the test statistic ρ recalculated.

A histogram of 5000 ρ values was constructed and ±ρ values corresponding to 95% of the

histogram area were computed. If the actual ρ is outside the ±ρ95 range, then it is deemed

significant and if this is true for all time steps and number of particles, then it is considered

that the WMC is not satisfied.

70

A.4 Conclusion

0 12 24 36 48

10−2

10−1

Time in hours

|Cor

rela

tion

coef

ficie

nt|

A)

0 12 24 36 48

Time in hours

B)

0 12 24 36 48

Time in hours

C)

EULERMILSTEINHEUNEULER−analytic95% significance .

Figure A.4: Absolute value of the correlation coefficient ρ(t) of the WMC test: A) n=3, B) n=8 and

C) n=11 and the ρ95 significance level. Plotted are the averages of 5 independent runs.

In Figure A.4 the performance of the schemes is shown. Here, for the first time, clear

differences are visible. The EULER scheme starts to fail the WMC test for n=3, the MILSTEIN

scheme follows at n=8 and the HEUN scheme starts to deviate from a uniform distribution for

n=11. The excellent performance is due to the predictor-corrector step of the HEUN scheme.

By this the ∇KH term is better approximated. The same holds for the MILSTEIN scheme.

The first order correction terms to the EULER scheme (see Equation A.11) is a modification of

the ∇K term and can therefore be better estimated. The performance of the EULER-analytic

scheme shows, that the failure of the EULER scheme is indeed caused by the insufficient

estimation of the ∇KH term. This algorithm starts to fail for n=11 and is therefore similar to

the HEUN scheme. This performance boost, by providing analytical functions to the schemes,

was also expected by Brickman and Smith [2001].

A.4 Conclusion

In the first part of the appendix A the underlying theory to translate SPM dynamics from

the Eulerian framework to the Lagrangian picture are present and summarised. The particle

tracking schemes for modelling single particle dynamics are quite attractive, because they give

a straightforward physical interpretation of the processes involved. Moreover, due to the easy

parallelisation of the Lagrangian schemes, this approach is well suited to run on massive par-

allel computers, to improve the reliability and accuracy of the results.

Various stochastic numerical schemes are presented to find the best suitable scheme for imple-

mentation in a three-dimensional particle-based transport model. To validate the schemes and

show their performance, analytical test cases with a spatially varying diffusion coefficient have

71


been investigated. All of the three idealised test cases were performed with different numerical

schemes: EULER, MILSTEIN and HEUN. Even though the MILSTEIN scheme only requires

a minor additional effort compared with the EULER scheme, the changes in terms of higher

accuracy and faster convergence are rewarding. A two-step scheme like the HEUN scheme

leads to a further improvement of the results. The set of experiments that was carried out

indicates that any improvement over the EULER scheme is welcome. Even though this is not

trivial, and some care needs to be taken in the choice and application of the scheme, such

a scheme does not necessarily need to be complicated or expensive. As advanced as higher

order Lagrangian particle transport models for dispersion in turbulent flow sometimes are,

it is surprising to see how many of these models still use the EULER scheme, while minor

adaptations may greatly improve the accuracy of the model. The analysis also showed, that

especially the term ∇ · K in Equation (A.3) needs special care. The effort, to improve the

estimates of the gradient, results in performance gains. Further the validation of the three

tracking schemes revealed that although they have by definition the same order of convergence,

differences showed up.

72

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Acknowledgements

At the end of this 3-year journey, leading to these final pages of my thesis, it is time to take

a bow and to acknowledge all the helpful people who pampered me with their kind support

along the way.

First, I am indebted to my supervisor Jorg-Olaf Wolff who invited me to work with him.

He was also ensuring fair funding for the years of my study. Further, I would also like to

express my gratitude for his friendly and permanent advice, guidance, the comfy working en-

vironment, the possibility to travel to Australia, to take part in summer schools and finally to

offer me the chance to discover parts of the ocean.

I would like to thank Joachim Ribbe for his help and to offer me the possibility to stay in Oz.

I am grateful to Emil Stanev for his kind support and to be finally my second supervisor.

I would also like to acknowledge the Wolfgang Schulenberg-Programm, the Universitats-

Gesellschaft Oldenburg (UGO), the Deutsche Forschungs Gesellschaft (DFG) and the Burnett

Mary Regional Group, Australia, for travel grants and financial support.

I really have to express my admiration and gratitude to the developers of COHERENS and

GETM for making their code available to the scientific community. I would also like to thank

the Mathworks Company for their excellent product MATLAB, the Linux community for

their fine OS and Intel for their breathtaking fast compilers.

A warm “thank you” goes to all my colleagues at the ICBM especially those mates (sorry, there

is no female version for mate) being members of the Theoretical Physics/Complex Systems

and Theoretical Physical Oceanography working group, the numerous coffee breaks, jokes and

laughing, discussions, cakes, music and motivation.

I would like to acknowledge Klemens for his selflessly care for the IT environment.

I further would like to thank Laird, Dave, Wes, Luc, and Spongebob for reminding me, that

the ocean is more than a discrete grid and that a wave is much more than a bump of water.

Further, I want to thank Oliver, who showed me how to shape a surfboard, ride a wave and

thus initiated an endless (summer) love story.

Special thanks goes to Pebbi and Carsten for offering me a second home in Oldenburg, Helmut

for being the most astonishing landlord I ever meet, Bastian and Antje for coffee, cake and

support and finally, Jens for help and motivation.

A special thanks goes to Maike, for the past, the present and the future.

Ultimately, I would like to mention my parents, but they know what I owing them.

CV

Ulf Grawe

born in Stralsund, July 12, 1974

Professional life

2005-2006 Researcher at ForWind - Wind Energy Research Insti-

tute/Oldenburg; modelling of the lower atmospheric boundary

layer and improvement of wind power predictions

1998-2002 4 years of travelling than a rolling Carpenter/Journeyman; work-

ing stays in Tunisia, Israel, Italy, Hungary, Switzerland, Austria,

France, Ireland, Germany, Estonia, Netherlands

Professional training

since October 2006 PhD student at the University of Oldenburg/ICBM - physical

oceanography (theory)

10/2005-08/2006 Student at the University of Oldenburg - Master of Science En-

gineering Physics (Thesis “Uncertainty estimation in wind power

predictions”), specialisation in turbulence, dynamical systems and

oceanography

10/2002-08/2005 Student at the University of Oldenburg - Bachelor of Engineering

Physics

1996-1998 Apprenticeship as carpenter, Carpentry Vifan GmbH Buschen-

hagen

Schooling

1981-1991 Herder-Realschule Stralsund

1991-1994 Technical Gymnasium Stralsund

Publikationsliste

Teile der vorliegenden Arbeit wurden bereits veroffentlicht oder eingereicht.

Grawe U, Wolff JO, Ribbe J (2009) Mixing, Hypersalinity and Gradients in Hervey Bay,

Australia. Ocean Dynamics DOI: 10.1007/s10236-009-0195-4 Grawe U, Wolff JO (2009) Suspended particulate matter dynamics in a particle frame-

work. Environmental Fluid Mechanics DOI: 10.1007/s10652-009-9141-8 Grawe U, Wolff JO, Ribbe J (2009) Impact of climate variability on an east Australian

bay. Estuarine, Coastal and Shelf Science eingereicht bei: Estuarine, Coastal and Shelf

Science

83

Selbstandigkeitserklarung

Hiermit erklare ich, dass ich die vorliegende Dissertation selbststandig verfasst und nur die

angegebenen Hilfsmittel verwendet habe. Teile der Dissertation wurden bereits in [Grawe et al. ,

2009a] und [Grawe and Wolff, 2009] veroffentlicht, bzw. sind zur Verweltlichung eingereicht

[Grawe et al. , 2009b]. Die Dissertation hat weder in Teilen noch in ihrer Gesamtheit einer an-

deren wissenschaftlichen Hochschule zur Begutachtung in einem Promotionsverfahren vorgele-

gen.

Oldenburg, September 16, 2009 Ulf Grawe

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