Hervey Bay - Insights from Numerical
Modelling into the Hydrodynamics of an
Australian Subtropical Bay
Von der Fakult¨
at f¨
ur Mathematik und Naturwissenschaften der Carl
von Ossietzky Universit¨
at Oldenburg zur Erlangung des Grades und
Titels eines
Doktors der Naturwissenschaften (Dr. rer. nat.)
angenommene Dissertation
von Herrn Ulf Gr¨
awe
Erstgutachter: Prof. Dr. J¨
org-Olaf Wolff
Zweitgutachter: Prof. Dr. Emil Stanev
...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.
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.
Zusammenfassung
Hervey Bay, eine ca. 4000 km2 grosse Bucht (durchschnittliche Tiefe = 15 m), befindet sich in unmittelbarer N¨ahe der kontinentalen Schelfkante der zentralen Ostk¨uste von Aus-tralien. Durch die hohe Verdunstungsrate (ca. 2 m/Jahr), geringe Niederschl¨age (weniger als 1 m/Jahr) und nahezu verschwindenden S¨usswassereintrag durch Fl¨usse, kann eine inverse Struktur/Schichtungen erwartet werden.
In dieser Arbeit wird erstmalig die hydro- und thermodynamische Struktur von Hervey Bay und deren Variabilit¨at pr¨asentiert. 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) durchgef¨uhrt. 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, best¨atigen, 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 k¨ustennahen Bereich. Die Untersuchung zeigten, dass Lufttemperatur, Wind und Gezeiten die wichtigsten Einflussgr¨ossen f¨ur die Sta-bilit¨at der inversen Schichtung und der Salzgradienten sind, w¨ahrend die ¨ostlichen Passatwinde den Wasseraustausch in der Bucht dominieren.
Aufgrund von lang anhaltenden D¨urren weisen die subtropischen Gebiete an der Ostk¨uste Aus-traliens eine Ver¨anderungen in der Balance von Niederschlag und Verdunstung auf. Langzeit-datenreihen zeigen w¨ahrend der letzten f¨unfzig 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 h¨aufiger 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 % abgesch¨atzt werden. Eine direkte Folge ist, dass sich der Salzigkeitsfluss erh¨oht hat, sowie die verdunstungsges-teuerte Residuenstr¨omungen beschleunigt haben.
Im Gegensatz zu der langfristigen Reduzierung der Niederschl¨age f¨uhrt das Auftreten von schw-eren Regenf¨allen und damit verbundenen ¨Uberschwemmungen, zu kurzfristigen Schwankungen
im Salzgehalt von Hervey Bay. Die Untersuchungen dieser extremen Frischwassereintr¨age er-gaben, dass die Frischwasseraustauschzeiten eng an die windgetriebenen Residuenstr¨omungen gekoppelt sind.
Die inversen Eigenschaften von Hervey Bay und die damit verbundene Dichtegradienten (mit einer h¨oheren Dichte in K¨ustenn¨ahe als im offenen Ozean) k¨onnen instabile Schichtungen erzeu-gen. Diese ¨aussern sich in Dichtestr¨omungen 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 Sp¨atherbst beschr¨ankt. Der dabei auftretende integrierte Volumentransport ist vergleichbar mit dem Volumen von Hervey Bay.
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
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
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.
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 rotrelax-ation, 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
to changes in large scale climate system processes such as the Southern Annular Mode, the Indian Ocean Dipole and the El Ni˜no 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 Ni˜no episodes, the Walker circulation weak-ens and the SOI becomes negative. Other changes during El Ni˜no 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 Ni˜na. 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
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, [Gr¨awe 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 [Gr¨awe et al. , 2009b], that is submitted to Estuarine, Coastal and Shelf Science.
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 [Gr¨awe and Wolff, 2009], that is published in Environmental Fluid Mechanics.
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”.
2.1 The Region EAC Longitude Latitude Brisbane Bundaberg Gladstone Maryborough 100 km 1000 60 200 30 10 30 200 60 1000 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.
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 equivalent to a transport of 106
m3
/s.
Summer Fall Winter Spring Annual
Evaporation [mm/year] 2580 1824 1308 2217 1980
Precipitation [mm/year] 2100 1068 588 936 1173
River discharge [mm/year] 494 456 173 95 305
Wind speed [m/s] 6.4 6.2 5.6 6.6 6.2
Wind direction [degree] 170 120 48 107 110
Air temperature [°C] 25.1 22.2 16.8 21.9 21.5
EAC [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-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, 1988-2008 Tidal observation BOM/GLOSS hourly, 2006
River discharge BOM daily, 1988-2008
Evaporation BOM daily, 1997-2008
AVHRR SST NODC three daily (4×4 km) 1999-2005
Boundary conditions OCCAM five daily, 1988-2008
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
q
(∂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 = ρacpa CH S (TS− θ) (3.2)
HL = ρaL CLS (qS− q) (3.3)
3.2 Boundary conditions
E = ρaCE S (QS− Qa) (3.5)
where ρais 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].
q cx(ζ) = √c xn 1 −√cxn κ ψx(ζ) (3.7) √c xn= 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 = ǫσBTS4− σSBTa4(0.653 + 0.00535 Qa)(1 + 0.1762 T CC2) (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), T
S and Taare the water and air temperature in Kelvin and
T CC 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.
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
Fraser Island Longitude Latitude 10 10 20 20 30 30 40 50 100 300 300 50 20 30 40 30 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 mean sea level. The solid line indicates the position of the salinity/density gradient transect. Location of the weather observation stations are denoted by stars. The dashed line indicates the transect to compute 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.
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 high-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.
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.
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 asp
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/u3argument, 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.
4 Barotropic circulations 0 5 10 15 20 25 30 35 40 −2 0 2 time [days] amplitude [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 the amplitude of the M2component, (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, the mixing 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
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
4 Barotropic circulations
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).
4.3 Water exchange Depth in m b) −40 −20 0 −10 −5 0 5 10 a) −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
4 Barotropic circulations
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.
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
Tf lushing = 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 + ∂xKH)dt +√2KH dWx(t)
dY (t) = (v + ∂xKH)dt +√2KH dWy(t)
dZ(t) = (w + ∂xKV)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.
4 Barotropic circulations
(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
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(c)
152.4
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−25
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0
20
40
0
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
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
4 Barotropic circulations
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
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.
4 Barotropic circulations
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.
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 −24.6 simulation −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
5 Baroclinic processes
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 0 simulation Depth 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 0 simulation −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.
5.1 Model Validation observation (a) −40 −20 0 simulation Depth 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 Epan y = 0.940*x + 0.384 R2 = 0.794 (b) 20 25 30 20 25 30 SSTsimu SST AVHRR 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.
5 Baroclinic processes
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.
