Estuarine, Coastal and S h elf Science. A m ulti-scale m odel of the hydrodynamics of the w hole Great Barrier Reef

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1 Estilarme, Coastal and Shelf Science 79 (2008) ELSEVIER C ontents lists available at ScienceD irect Estuarine, Coastal and S h elf Science journal homepage: C O A ST A L ;h e l f s c i e n c e B. A m ulti-scale m odel of the hydrodynamics of the w hole Great Barrier Reef Jonathan Lambrechtsa *, Emmanuel H anertb, Eric Deleersnijder3, Paul-Emile Bernard3, Vincent Legat3, Jean-François R em ad ec a, Eric W olanskie,d 1 Université catholique de Louvain, Centre for Systems Engineering and Applied Mechanics, B-1348 Louvain-la-Neuve, Belgium b The University o f Reading, Department o f Meteorology, Earley Gate, P.O. Box 243, Reading RG6 6BB, UK c Université catholique de Louvain, Département de Génie Civil et Environmental, B-1348 Louvain-la-Neuve, Belgium d Australian Institute of Marine Science (AIMS), PMB No. 3, Townsville MC, Queensland, 4810 Australia 0James Cook University, James Cook Drive, Townsville, Queensland 4811, Australia A R T I C L E I N F O A B S T R A C T Article history: Received 2 October 2007 Accepted 21 March 2008 Available online 1 April 2008 Keywords: Great Barrier Reef hydrodynamics shelf dynamics finite elem ents unstructured mesh East Australian Current An u n stru ctu red -m esh parallel hydrodynam ic m od el o f th e w h o le Great Barrier R eef is presen ted. This m od el sim u ltan eou sly sim ulates m ost scales o f m otion. It allow s interactions b e tw e e n sm all- and largescale processes. The d ep th -averaged eq u ation s o f m otion are d iscretized in space by m eans o f a m ixed finite ele m e n t form ulation w h ile th e tim e-m arch in g procedure is based o n a third order exp licit A d a m s- Bashforth sch em e. The m esh is m ad e up o f triangles. Their size and shape can be m od ified easily so as to resolve a w id e range o f scales o f m otion, from th o se o f th e regional flow s to th o se o f th e ed d ies or tidal jets th at d evelop in th e vicin ity o f reefs and islands. The forcings are th e surface w in d stress, th e tid es and th e in flow from th e Coral Sea (East A ustralian Current, Coral Sea Coastal Current), th e latter tw o forcings b ein g applied along th e op en boundaries o f th e com pu tation al dom ain. The num erical results com pare favourably w ith observations o f b oth longshore currents and th e local perturbations du e to narrow reef passages. C om parisons are also perform ed w ith th e sim u lation s o f a th ree-d im en sion al m od el app lied to a sm all dom ain cen tered o n Rattray Island, sh o w in g th at both m od els produ ce sim ilar horizontal flow fields. For a stru ctu red -m esh m od el to y ield results o f th e sam e accuracy, there is no dou bt th at th e com putational cost w ould be m uch higher Elsevier Ltd. All rights reserved. 1. Introduction The Great Barrier Reef is on the continental shelf of the Australian northeastern coastline as illustrated in Fig. 1. There are over 2500 coral reefs in a strip th at is about 2600 km in length and 200 km in w idth. Due to recent hum an activities, these ecosystem s deteriorate at an alarm ing rate. Land use contributes to the degradation of the Great Barrier Reef health and to an increased frequency and intensity of crow n-of-thorns starfish infestations (W olanski and De ath, 2005; Richmond et al., 2007). Therefore, there is a strong need for accurate hydrodynam ical simulations allowing to b etter understand and analyse the interactions betw een ecological processes and hum an im pacts (Richmond, 1993; Veron, 1995; Birkeland, 1997; W ilkinson, 1999; Wolanski, 2001; W erner et al., 2007). Today, developing a high resolution, efficient and realistic m odel of the hydrodynam ics of the w hole Great Barrier Reef is still a difficult task in view of the com plex bathym etry * Corresponding author. address: jonathan.lambrechts@ udouvain.be Q. Lambrechts). and topography. Taking up this challenge is th e objective of the present study. The circulation over th e Great Barrier Reef shelf is m ainly controlled by the com plex topography, the local wind, the tidal m o tions and th e shorew ard South Equatorial Current in the w estern Coral Sea. On m eeting the continental slope of the Great Barrier Reef, this current splits at a bifurcation point betw een 14 S and 18 S into th e northw ard-flow ing Coral Sea Coastal Current and the southw ard-flow ing East Australian Current (Wolanski, 1994). These longshore currents are m odulated and deviated by th e wind, the tides and the topography, w hich can strongly deflect th e m ean current aw ay from areas of high-reef density. The m ean current is an essential ingredient of th e ecosystem as it flushes the shelf and controls the dom inant spreading direction of m aterial em anating from reefs (W olanski and Spagnol, 2000; Brinkman et al., 2001; W olanski et al., 2003b; Luick et al., 2007). In other words, it controls the connectivity of reef populations as a result of the transport of w ater-borne larvae betw een reefs (W olanski et al., 1997, 2004; A rm sw orth and Bode, 1999) or th e transport of nutrients and pollutants by w ater currents (Done, 1988; Bell and Elmetri, 1995; W olanski et al., 1999). Moreover, tidal jets and eddies occur in the wake of islands and also have a significant im pact on the /$ - see front m atter 2008 Elsevier Ltd. All rights reserved, doi: /j.ecss

2 144 ]. Lambrechts et al. / Estuariae, Coastal and Shelf Science 79 (2008) km Cairns Australia Townsville 10 km Whitsunday Islands Rockhampton Fig. 1. Map of the whole Great Barrier Reef complex topography. The model computational domain is located between the coastline and the continental shelf break defined by the isobath of 200 m. ecosystem. Their length scales range from about a 100 m to a few kilometres. In situ m easurem ents, satellite im agery and num erical sim ulations show th at those small-scale phenom ena are mainly confined to the neighbourhood of small reefs, islands and passages (H am ner and Hauri, 1981; W olanski and Hamner, 1988; W olanski et al., 1988,1996; Deleersnijder et al., 1992). The above-m entioned processes occur over a w ide range of space and tim e scales, from a few m etres to hundreds of kilom etres and from a few seconds to several years. It is essential to sim ultaneously sim ulate all scales of motion, because small- and largescale processes experience significant interactions (W olanski et al., 2003c). Clearly, a m odel focusing on a single phenom enon w hile ignoring others m ay lead to misleading results. However, all scales of m otion cannot be reproduced by th e present-day structured uniform grid m odels of the Great Barrier Reef. Typically, th e cell size of these m odels is around 2000 m (King and Wolanski, 1996; Brinkman et al., 2001), i.e. larger than the characteristic sizes of a w hole class of biological and hydrodynam ic processes. For a uniform grid m odel to reproduce small-scale processes such as eddies and tidal jets, the com putational cost is likely to be crippling. This is w hy variable resolution is needed. This could be achieved by having recourse to nested grids (Spall and Holland, 1991 ; Fox and Maskell, 1995). However, th e regions w here enhanced resolution w ould be needed are so num erous in the Great Barrier th at this approach is unlikely to be feasible. This is w hy the parallel m odel developed herein is based on an unstructured, variable-resolution m esh that offers a very strong geom etrical flexibility (Pietrzak et al., 2005; W alters, 2005; Legrand et al., 2006). 2. Unstructured-m esh hydrodynamic m odel Using the sam e m athem atical fram ew ork as the previous structured grid m odels (W olanski et al., 1996; Brinkman et al., 2001), a depth-averaged barotropic m odel is im plem ented to com pute the m ean horizontal vector and the sea surface elevation. Unlike previous models, the equations are here discretized on a fully unstructured m esh of approxim ately 850,000 triangular elem ents depicted in Fig. 2. The m esh resolution ranges from 150 m along tiny islands to 10 km in open areas: high resolution is introduced only w here th e flow features require it. The local resolution is often quite finer than the grid cell of 2 km used in the simulations of Brinkman et al. (2001 ). Paradoxically, th e ability of the grid to represent th e reef scales leads one to question th e use of a depth-averaged barotropic model. W hen the grid size is larger than 1 km, the shallow w ater equations can be used to sim ulate the flow because at those length scales the shelf w ater is generally well mixed throughout the year and the flow is prim arily horizontal, as pointed by Brinkman et al. (2001 ) and W olanski (1994). At the reef scale, three-dim ensional features, like th e eddies in the wake of islands, can no longer be neglected. Both experim ental observations and num erical sim ulations reveal th at these eddies have a full three-dim ensional structure th at creates som e strong upw elling in their centre and even stronger dow nwelling along their edges (Wolanski, 1994; W hite and Deleersnijder, 2007). Moreover, if the elem ent size is of the order of the local w ater depth, non-hydrostatic effects can no longer be neglected and a hierarchical m odelling should be introduced. Such an approach is a very am bitious task th at w ould require num erous validations, com parisons and tailored param eterizations (W olanski et al., 1996). It m ust also be pointed out th at several authors claim th at tw o-dim ensional m odels produce very accurate and physically relevant horizontal currents even for the tidal circulation in island s w akes or headland eddies (Falconer et al., 1986; Pattiaratchi et al., 1986). This is because the depth is small and th e w ater colum n is well mixed. The present m odel m ay be considered a first step to w ards a m uch m ore sophisticated sim ulation tool in w hich the equations and num erical m ethods w ould locally depend on the m esh size. The m odel dom ain covers m ost of th e Great Barrier Reef from the Great Keppel Island in th e south to the Forbes Island in the north. This com putational dom ain is alm ost tw ice as large as th at of Brinkman et al. (2001 ). The continuity and horizontal m om entum equations read 3i, d(hu) d(hv) a t J a* ^ ay du du du, ai; b u b V------fV + s - dt dx dy 3 s 9x 9v 9v 9v f 9rç dt + ubtx + vbry +fu+gdï + Zx g lu l ay' 9ji - i ) ) ph C2HU -9y\ Í '..HÎXV) dy).) + i ph - - C2H Ä, w here r, u and v are th e sea surface elevation (positive upw ards) and the horizontal velocity com ponents. The actual w ater depth is H = h- -y, w here h is th e reference w ater depth below th e m ean sea level. The Coriolis param eter, th e gravitational acceleration, the horizontal eddy viscosity, th e m ean w ater density are respectively denoted f g, v and p. At the surface of the sea, the w ind stress is T (tx,tu). The bottom stress is param etrized as a quadratic expression, (g/c2h) u u, w here the Chezy coefficient is C = Hi1/6) /n, n being the M anning coefficient. The system of partial differential equation above has to be supplem ented w ith m athematically relevant initial and boundary conditions in order to define a w ell-posed boundary value problem. It is notew orthy that the influence of the initial conditions becom es negligible after som e time, due to exchanges w ith th e Coral Sea as well as frictional and viscous dissipations. (i)

3 ]. Lambrechts et al. / Estuariae, Coastal and Shelf Science 79 (2008) Rattray island Rattray island Fig. 2. Mesh of 850,843 triangles of sizes comprized between 150 m and 10 km. The number of elements and nodes are 850,843 and 500,142, respectively. A zero mass flux and a tangential m om entum flux proportional to th e m ean tangential velocity are im posed along the im perm eable boundaries incom ing characteristic variables (Reid and Bodine, 1968; Blayo and Debreu, 2005) and to supplem ent it by im posing a zero depthaveraged shear stress f u = 0, { dlls n (2) I V aits = 0, ^ ' L On w here the indices s and n are associated w ith th e direction tan gential and norm al to the boundary, respectively, us and un are the com ponents of the depth-averaged horizontal velocity along those directions. The unresolved boundary layer along the coasts is param etrized by an em pirical and purely phenom enological partial slip condition (Deleersnijder, 1996). Designing conditions to be im posed on the open part of the boundary is rather delicate. As m entioned by Blayo and Debreu (2005), a large num ber of alternative conditions can be used to introduce the tides and th e lowfrequency currents at an open boundary. A usual approach w ould be to specify th e elevation as a function of position and time. However, it was observed by Flather (1976) th at such an approach is unsatisfactory near the shelf edge. It seem s th at th e best option is to prescribe a relationship betw een elevation and velocity in term s of w here the function is derived from external data. For th e Great Barrier Reef, m easurem ents of the sea surface elevation at some locations in the Coral Sea can be used to force the tides and the m ean currents. By assum ing a zero norm al transport gradient on the boundary, the norm al velocity outside the dom ain of interest m ay be obtained by extrapolation from th at com puted inside the com putational domain. These conditions appear to be satisfactory, m ainly because they prevent num erical instabilities from developing. An approxim ate solution of th e partial differential equations under th e boundary conditions specified above is obtained by using the finite elem ent m ethod, as it can handle unstructured grids, contrary to th e finite difference m ethod. A linear piecewise

4 146 ]. Lambrechts et al. / Estuariae, Coastal and Shelf Science 79 (2008) discretization is used for both elevation and velocity fields. In order to avoid any spurious num erical modes, w e use a discontinuous velocity together w ith a continuous piecewise linear elevation. Such an approxim ation is know n as Pffc-Pi. Details about the m athem atical analysis and num erical validation of this elem ent for the shallow w ater equations are given by Hua and Thomasset (1984), H anert et al. (2004, 2005), Le Roux (2005). W ith this scheme, special care is needed for im plem enting th e boundary conditions. We w eakly im pose boundary conditions in term s of the characteristic variables of the first-order hyperbolic term s of the equations. Regarding th e tim e-m arching procedure, a third order explicit A dam s-bashforth integration schem e is selected. It is only conditionally stable but appears to be a quite good com prom ise betw een simplicity, efficiency and accuracy. In order to take advantage of parallel com puting, th e m esh is partitioned into subdom ains attributed to each of the processors of a parallel cluster. The m esh partitioning is designed to uniform ly distribute the com puting charge and m inim ise th e com m unications. The parallel speed-up is defined as the ratio of the com puting tim e for the m odel running on one processor to th e tim e needed to carry out a run on several processors. If the com m unication tim e is negligible and the com puting load is equally distributed, th e speed-up m ust be equal to th e num ber of processors. This ideal, theoretical value is alm ost obtained by th e present model, as illustrated in Fig Selection o f the physical and th e num erical parameters The first ingredient of the num erical calculations is the design of the unstructured grid. Firstly, it is critical to accurately represent the Australian coastline, the open boundaries and all relevant islands. Secondly, w e define the m esh resolution from the physical processes th at should be simulated. The m esh is obtained by means of th e gmsh software. The resolution of the m esh in Fig. 2 depends on tw o a priori criteria. The local m esh size has to be proportional to the square root of the w ater depth in order to obtain the sam e C ourant- Friedrichs-Lewy condition (CFL condition) for the gravity 40 time on 1 processor time on n processors waves over the w hole domain. In other words, th e elem ent size is adjusted in such a w ay th at th e external inertia-gravity waves travel over the sam e fraction of each elem ent for a given tim e interval (Henry and W alters, 1993; Foreman et al., 1995; Jarosz et al., 2005; W alters, 2005). The local m esh size depends on th e distance to islands and reefs in order to cluster m esh nodes in regions w here smallscale processes are likely to take place. The m esh is refined even m ore in th e vicinity of islands w here eddies and tidal jets can be expected. Both criteria are blended together so as to have a high resolution in the vicinity of reefs and islands and a resolution depending only on the bathym etry elsew here (Legrand et al., 2006). A m ore am bitious strategy w ould be to introduce adaptive meshes. The elem ent size could be dynamically adjusted using an a posteriori error estim ator from the num erical discontinuities in the solution at the elem ent interfaces (Bernard et al., 2007). A quasi-optim al m esh could then be derived for a w hole simulation. Even if it m ay appear attractive, w e think th at dynamically adapting the m esh during the tim e integration w ould not provide a significant im provem ent as m ost refinem ent regions can be easily predicted a priori. The second issue is to define the param eters to represent subgrid effects. To incorporate unresolved turbulent features and boundary layers along th e coastlines and islands, w e use a Smagorinsky s param e- trization (Smagorinsky, 1963). The value of the horizontal eddy kinem atic viscosity v depends on the local m esh size A and the flow structure. The param eter controlling th e friction on coast and islands, a is constant, 1.,2 L f d u \ 2 t / 9 v \ 2 7dU d v V ' = <014 ^ H ï «) +2y + f e +ïs) (4) a= 2.5 X 10 3 m /s. Finally, the value of th e M anning coefficient is taken from (King and Wolanski, 1996) n = 2.5 x 10~2 m _1^3s. The external forcings of the hydrodynam ics of th e Great Barrier Reef are the wind, th e adjacent Coral Sea circulation and the tides. W ind data are extracted from the NCEP reanalysis data provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA (Kalnay et al., 1996). The stress acting on th e sea due to th e w ind is m odelled by using th e param etrization proposed by (Sm ith and Banke, 1975) T = IO -3 (0.630 vw vw 2) vw, (5) C(vw) number of processors Fig. 3. Partition of the mesh into 25 sub-domains for parallel computing. The speed-up almost exactly follows the ideal line. w here vw is the surface w ind velocity in m /s and C(vw) is a scaling param eter expressed in kg m -2 s_1. To incorporate th e effect of the East Australian Current, the Coral Sea Coastal Current and th e tides coming from th e Coral Sea, w e have to specify the elevation 4sea(x.y.t) on th e open-sea part of the boundary. The m easurem ents of the elevations at several locations accurately provide th e tidal dynamics, but the global currents effect is largely covered by noise and long-term fluctuations. Therefore, w e prescribe the elevation at the open-sea boundary as follows: r (x,y, t) = rj(x,y) + r '(x,y, t) (6) w here rj'(x,y,t) is the tem poral variations of th e m easurem ent of the sea level in th e Coral Sea and rj(x,y) is a steady-state elevation im posed to obtain the East Australian Current and the Coral Sea Coastal Current in the com putational dom ain in a tim e-averaged sense. The tem poral variations of the tidal elevation on th e n orthw estern, eastern and south-eastern open boundaries are obtained

5 ]. Lambrechts et al. / Estuariae, Coastal and Shelf Science 79 (2008) S ea Surface Elevation (cm) 0.5 Fig. 4. On the left-hand side, mean sea surface elevation ))(x) obtained from the auxiliary steady-state problem and prescribed on the open-sea boundaries to enforce the lowfrequency currents. On the right-hand side, Lagrangian particles trajectories illustrating both the tidal motions and the large-scale currents. by a linear interpolation from 15 m easurem ent sites w here the National Australian Time Tables provide the elevation and phase shift of the 12 principal tidal constituents. As the am plitude of the tem poral variations is larger than th e variations of rj(x,y), it appears unw ise to have confidence is the constant part of the data. M oreover, large-scale features also are included in those data and render them incom patible w ith th e assum ption of a spatially established flow along th e boundary. In order to circum vent this incompatibility, w e use an auxiliary steady-state problem to identify the suitable form of the function?)(x,y). This auxiliary problem consists in using th e East Australian Current and the Coral Sea Coastal Current as the unique forcing in term s of velocity along the w hole boundary. Opposite flows are induced by prescribing th e longshore velocity at th e upper and low er parts of the open-sea boundary. In an interm ediate neutral area, w e define a zone of incom ing cross-shore current separating them. Dividing the boundary in such a w ay is justified from the observations (Brinkman et al., 2001). W hen a steady state is reached, the surface elevation on th e boundaries is considered as a good candidate to enforce both currents. Left-hand side panel in Fig. 4 shows contour lines of the m ean sea surface elevation rj(x) obtained from the auxiliary steady-state problem and used as prescribed m ean elevation at the open boundary. Due to th e Coriolis force, the elevation essentially varies in the longshore direction in the central part of the Great Barrier Reef w hile it is in the crossshore direction elsewhere. On the right-hand side, trajectories of Lagrangian particles are displayed in the box draw n on the lefthand side panel. Both tidal m otions and large-scale current effects can be easily identified. The separation of th e oceanic inflow into tw o branches occurs at a location in accordance w ith field data. As th e problem is non-linear and as the tidal m otions generate a larger am ount of dissipation, it is necessary to m ultiply the steady-state solution to get the adequate rj(x,y) by a scalar factor in order to obtain the correct m ean flow w hen the tim e average is perform ed. Typically, this factor ranges from 2 to 3. It m ust be pointed out th at this approach is a purely phenom enological w ay to close th e problem and to enforce large-scale flow features in the com putational domain. This approach is the least stringent w ay to enforce the global currents and seem s to be less invasive than the strategy proposed by Brinkman et al. (2001 ). 4. D iscussion Low-frequency, longshore currents are well predicted by the model, as show n in Fig. 4 w here the trajectories of Lagrangian particles illustrate both the tidal variations and th e long-term flow. More critical is the m odel s ability to represent a broad range of» t e l Fig. 5. Sticky water in the southern part of the Withsundays Islands Archipelago (20 21' S ' E).

6 148 ]. Lambrechts et al. / Estuariae, Coastal and Shelf Science 79 (2008) scales: let us ju st cite th e tide as a propagating wave over th e shelf described by W olanski and H am ner (1988), the eddies and tidal jets created by th e topography. The interaction of the tidal currents w ith m any islands and reefs acting together generates m acroturbulence w hich m akes the regions of high-reef density less perm eable to low -frequency currents at spring tides than at neaptides. This large-scale sticky w ater effect (W olanski and Spagnol, 2000; Spagnol et al., 2001) illustrates a feedback process w hereby the small-scale processes influence the large-scale flows, as discussed by W olanski et al. (2003a) for one specific area. Those secondary flows, illustrated in Fig. 5, are w idespread throughout the Great Barrier Reef both in coastal w aters as well as in the Great Barrier Reef matrix. This has im portant biological im plications because the connectivity betw een various areas will vary according to th e reef and island density. In order to estim ate th e accuracy of th e m odel in m odelling the tidal waves propagation, w e com pare the calculated sea surface elevation w ith observations at five sites w idespread on the continental shelf away from boundaries. Numerical results and observations are show n in Fig. 6. We see a good agreem ent betw een the predicted and observed elevations, both in term s of am plitude and phase shift. W e com pare th e predicted results w ith som e sm all-scale three-dim ensional calculations perform ed by W hite and Deleersnijder (2007) and W hite and W olanski (2008) around Rattray Island. In th eir calculations, W hite and D eleersnijder (2007) used a rectangular com putational dom ain of approxim ately 100 km 2 and obtained results th at com pare favourably w ith m easurem ents perform ed by W olanski et al. (1984). Fig. 7 show s the eddies past Rattray Island sim ulated by th e present tw o- dim ensional m odel and the aforem entioned three-dim ensional model. Though th e resolution of th e form er m odel is coarser, the eddies sim ulated by both m odels are quite similar, pointing to th e ability of th e tw o-dim ensional to represent sm all-scale flow features. Presumably, tidal jets are also w ell sim ulated. They occur w hen th e flow is accelerated through narrow reef passages. The resulting unstable je t produces a pair of eddies at the outflow (Fig. 8). These m ushroom shaped circulation patterns, w ell predicted w hen th e flow is accelerated betw een both islands, have been observed in the field by W olanski (1994). To avoid sm earing Pelican Island o V) Sudbury Cay Stanley Reef Karamea Bank Gannet C ay time (days) Fig. 6. Series of observed and predicted sea surface elevation at measurement sites spread over the GBR. Measured elevations are represented with dashed lines, while the predictions are given in a continuous line.

7 J. Lambrechts et al. / Estuariae, Coastal and Shelf Science 79 (2008) M esh i m «S ' ï a < SSpBWsÿ i te C ssásssíssffis? V.' *«'. J ;.N.n t '»':' t. ; ' *V»-. î, /*» v4 i rj > í î l : i Í : - i C.. '. - : - ' : :? i \ t & m sp Wíí/J'iíí s S ^ ^ l i? tí5'>íí?eâi2&%»>s2n* M M K S f l t e s l l C urrent m W jjb p p é Ê M Ë w m S mm Fig. 7. Close-up views of meshes, bathymetry and eddies at a given time from our global model and the three-dimensional small-scale calculations of White and Deleersnijder (2007) are presented on the left- and right-hand sides, respectively.

8 150 J. Lambrechts et al. / Estuariae, Coastal and Shelf Science 79 (2008) m/s 1 km ' í r / v - m odel of th e ocean system, w hich is funded by th e Communauté Française de Belgique, as Actions de Recherche Concertées, under contract ARC 04/ This w ork is a contribution to th e d e velopm ent of SLIM, the Second-generation Louvain-la-Neuve Iceocean Model. Emmanuel H anert thanks th e Nuffield Foundation for a newly appointed lecturer award. - ^ v i i i ' - ' \ ƒ W * ' References 'i'tlh, t r i i 1! i i - ; / i * i - / / i * * Fig. 8. Tidal jets and eddies due to the interaction of the flow with the topography near the open-sea boundary (14,:,17' S 145:08' E). out these flow features, th e diffusion induced by th e num erical schem e m ust be kept as sm all as possible. In our calculations, this num erical viscosity is alw ays sm aller th an th e param etrized physical viscosity. Even if small-scales features are well predicted by the model, we m ust em phasize th at the hierarchical adaptive grid does not correspond to a hierarchical m athem atical modelling. Basically, we still consider the sam e shallow w ater equations w hen the grid refinem ent implies th at the non-hydrostatic processes m ight not be negligible. A careful analysis of the subgrid closure modelling and param etrization is certainly the next step of our work. However, our sim ulations show th at th e com plex topography of the Great Barrier Reef introduces m ajor spatial and tem poral variability in the circulation of this region, as m entioned by King (1992), King and W olanski (1996), W olanski and Spagnol (2000) and Brinkman et al. (2001). Even th e flow around a single coral reef is also taking place over a broad range of scales (M onismith, 2007). The physics involved undergoes huge changes w hen going from the size of a coral colony (m m to cm) to th e w hole reef scale (100 m -1 km). Of particular interest is the boundary layer flow over the reefs, w hich is mainly influenced by the com plex and porous geom etry of the reefs. The resulting drag from reefs is m uch larger than the drag from m uddy or sandy seabeds (Roberts et al., 1975; Lugo Fernandez et al., 1998). Therefore, incorporating variable bottom friction coefficient and adapting the subgrid viscosity m odel could render the m odel m ore realistic as a predictive tool for ecological applications. But even if the present w ork has to be considered as a first attem pt tow ards a three-dim ensional high-resolution m odel of the w hole Great Barrier Reef, it now appears possible to broaden the range of scales sim ulated by a single model. A large num ber of small-scale features could be well represented and used to better understand the com plex flow dynam ics of th e Reef. 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