Available online at www.sciencedirect.com

Journal of Hydro-environment Research 3 (2010) 224e231www.elsevier.com/locate/jher

A dedicated tidal stream atlas of the stratified tidal flows near StonecuttersBridge, Hong Kong, based on 3D numerical simulations with HLES

R. Morelissen a,*, A.C. Bijlsma a, M.J. Tapley b

a Deltares, Delft Hydraulics, P.O. Box 177, 2600 MH Delft, The Netherlandsb AECOM, 8/F, Tower 2, Grand Central Plaza, 138 Shatin Rural Committee Road, Shatin, New Territories, Hong Kong

Received 2 June 2009; revised 9 October 2009; accepted 9 October 2009

Abstract

Construction works at the Stonecutters Bridge crossing the Rambler Channel in Hong Kong involve bridge deck lift operations withdynamically positioned barges. Nautical simulations for marine safety assessment and the programming of the bridge deck lift operations requirereliable predictions of the local currents. To that purpose, we designed a detailed hydrodynamic Delft3D-FLOW model for simulating 3Dstratified tidal flow and larger-scale eddy-dynamics using Horizontal Large Eddy Simulation (HLES). This model was nested in the 3Dhydrodynamic model of the Pearl River estuary and the Hong Kong waters, which has been extensively calibrated and validated in other studiesin the Hong Kong area. The results of the detailed model show good agreement with dedicated field measurements for both the dry and wetseasons. Based on tidal analysis of the model results, predictions for the water levels and currents could be made that include the complex flowpatterns and (tidally driven) eddies and recirculations. For easy prediction of the flow conditions in the future, a digital tidal stream atlas (Delft-STREAM) was set up that is capable of predicting these flow fields. This tool provided a valuable contribution to the programming and executionof the marine works of Stonecutters Bridge. The new development in this study is the inclusion of complex 3D flow patterns into a digital tidalstream atlas, capable of predicting detailed flow fields for construction planning purposes.� 2009 International Association for Hydro-environment Engineering and Research, Asia Pacific Division. Published by Elsevier B.V. All rightsreserved.

Keywords: 3D hydrodynamic modelling; Project application; Large-scale eddies; Digital tidal stream atlas; Delft3D-FLOW; Hong Kong

1. Introduction

The flow regime in the area near the Stonecutters Bridge(Rambler Channel) in Hong Kong is very complex, both inhorizontal and in vertical direction. This depends on themonsoon seasons. The dry season flow condition is character-ized by a negligible stratification in the Hong Kong area, but inthe wet season the large Pearl River fresh outfall plume is forcedon an easterly track by the SW monsoon and enters the HongKong channels resulting in a stratified flow through RamblerChannel. This results in large current velocities at the surface. Inaddition, the currents show complex eddy and recirculationpatterns and associated large velocity gradients in the area in

* Corresponding author.

E-mail address: robin.morelissen@deltares.nl (R. Morelissen).

1570-6443/$ - see front matter � 2009 International Association for Hydro-environment Engin

doi:10.1016/j.jher.2009.10.007

both seasons. The Stonecutters Bridge (SCB) in Hong Kong isa new cable-stayed bridge from Kowloon to Tsing Yi Island,crossing the entrance to Rambler Channel, the access for ship-ping to the busy Kwai Tsing Container Port. The construction ofthe main span deck involves lifting steel deck segments fromdynamically positioned barges in the channel (see Fig. 1a,b).

To be able to plan construction phases (e.g. bridge decklifting operations from dynamically positioned barges) andallow for other navigation to continue safely in the 3 yearconstruction period in this busy port area, accurate flowmodelling and predictions were needed. This was done bysetting up a detailed Delft3D-FLOW model, including allrelevant processes, such as tide, seasonal variation in waterlevels and currents, horizontal large eddy simulation, salinitymodelling, etc. Based on simulations with this model, a digitaltidal atlas was set up to allow for detailed flow field

eering and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved.

Fig. 1. (a) Construction of Stonecutters Bridge, Hong Kong; (b) Deck lift

operation during construction of the Stonecutters Bridge, Hong Kong.

225R. Morelissen et al. / Journal of Hydro-environment Research 3 (2010) 224e231

predictions in the SCB region, which could be used indepen-dently from the model for construction planning purposes.

This paper describes the development of the 3D hydrody-namic model and tidal atlas. Firstly, the flow regime in theHong Kong area is described in Section 2. Section 3 presentsthe hydrodynamic modelling. The validation of the modelagainst field measurements is discussed in Section 4 and thetidal atlas is presented in Sections 5 and 6. Finally theconclusions are presented in Section 7.

2. Flow regime in the Hong Kong areaand near Stonecutters Bridge

2.1. Flow regime in the Hong Kong area

The complex flow regime of Hong Kong is caused by themixed tide, the erratic geometry containing many larger andsmaller islands, and by the seasonal variations in the wind andthe Pearl River discharge.

Two characteristic seasons and associated flow conditions canbe distinguished for the Hong Kong waters (Postma et al., 1999):

� the dry winter season, extending from December toFebruary, and

� the wet summer season from June to September.

The periods in between are called intermediate seasons.The dry season flow condition is characterized by a high

salinity and negligible stratification in the Hong Kong area.The NE monsoon with average wind of 5 m/s from NE, theNEeSW oriented coastal current and mean sea level gradientdirect the Pearl River outfall plume in a south-westerlydirection. The average Pearl River discharge of the dry seasonis about 4100 m3/s.

In the wet season, the large Pearl River outfall plume (withan average wet season discharge of about 19,400 m3/s) isforced on a more easterly track by the SW monsoon with anaverage wind of 5 m/s from SW, and a reversed coastal currentand mean sea level gradient. The fresh water plume enters theHong Kong channels and the flow through Rambler Channelbecomes stratified, resulting in larger surface currentvelocities.

2.2. Local current regime

The local currents in the SCB area are tidally dominated.The largest part of the flow passes this region through thedeeper area west of Tsing Yi island, but a significant part alsoflows through Rambler Channel. In the dry season, surfacevelocities reach values in the order of 0.6e0.7 m/s and thestratification of the flow is negligible. In the wet season,a significant stratification exists, with a salinity differencebetween the surface and the seabed of generally 12 ppt. Depth-averaged velocities in the wet season reach values in the orderof 0.7 m/s, but due to stratification, surface velocities canreach 1.2 m/s, which is significantly higher than in the dryseason.

The geometry in the vicinity of the SCB creates complexeddy and recirculation patterns, which may lead to strongvelocity gradients. Therefore, these patterns have a significantinfluence on navigation and the bridge deck lifting operations.

3. Hydrodynamic modelling

3.1. Procedure

The hydrodynamic model was developed for two reasons:1) to produce accurate flow fields for the nautical simulationsthat need to guarantee navigational safety during theconstruction of the bridge, and 2) to serve as input for thedigital tidal atlas.

In the setting up of the hydrodynamic modelling, the sameprocedures were used as in Bijlsma et al. (2004) regarding theconsiderations in every modelling step and in particular forsimulation of flow separation and the development of larger-scale eddies. Given the applications of the model, the requiredmodel accuracy was defined in advance at 0.25knots z 0.13 m/s in velocity and 30 min in time. Furthermore,the preparation of a tidal atlas requires simulations of at leastone month duration for proper tidal analyses. To resolve thelarger-scale eddies and to meet the above requirements, thefull 3D tidal dynamics in the SCB area need to be modelled on

226 R. Morelissen et al. / Journal of Hydro-environment Research 3 (2010) 224e231

a very fine grid for characteristic dry and wet seasonconditions.

Therefore, all of the Hong Kong waters, including the PearlRiver estuary and the adjacent sea area, needed to be included tobe able to model the horizontal and vertical salinity gradientsrelated to the Pearl River outfall plume. For this we used ourexisting and well validated Hong Kong and Pearl River estuarymodel, developed by Deltares jDelft Hydraulics in earlier studiesof the Hong Kong region (Ng et al., 1999; Postma et al., 1999). Inview of ongoing land reclamations the geometry of the model wasadjusted to the present situation, and boundary conditions wereimproved further to better meet the study objectives.

3.2. The Delft3D model

For the hydrodynamic modelling the Delft3D-FLOWmodel was used, see e.g. Lesser et al. (2004). This programhas been developed for modelling of unsteady water flow andtransport of dissolved matter in shallow seas, coastal areas,estuaries and rivers. Delft3D-FLOW solves the shallow waterequations for given initial and boundary conditions in two orthree dimensions. The continuity and the horizontalmomentum equations are solved by an implicit finite differ-ence method (ADI) on a staggered (spherical or orthogonalcurvilinear) grid. For the vertical grid, a s-coordinateapproach is used. In the continuity equation the mass balancefor each grid cell is considered. For this study, the Delft3D-FLOW model was used in 3D mode, to resolve the stratifiedflow during the wet season.

3.3. Modelling set up

A detailed model grid was nested in the existing overallHong Kong and Pearl River estuary model (Ng et al., 1999;Postma et al., 1999), see Fig. 2a,b. The curvilinear model grid

Fig. 2. (a) Overall model of Pearl River Estuary and Hong Kong Waters and indicat

Victoria Harbour, Rambler Channel and Stonecutters Bridge (purple line). (For inte

to the web version of this article.)

matches the alignment of the Stonecutters Bridge. The gridresolution varies from about 150 m on the edges of the modelto about 30 m around the Stonecutters Bridge area. The totalnumber of active grid cells is about 160,000 in 10 equidistantsigma layers over the vertical.

The tidal boundary conditions of the overall modelincluded initially 9 and after calibration 12 tidal constituents(i.e. O1, Q1, P1, K1, N2, M2, MU2, NU2, S2, K2, M4 andMS4) and a compensation to include the coastal currentsassociated with the dry or wet season conditions by tilting theoffshore model boundaries. The latter approach, introduced byUittenbogaard and Hulsen (1999), helped to provide efficientestimates of the coastal currents, see also Larson et al. (2005),while avoiding the application of larger-scale models, as forinstance used by Wong et al. (2003).

Both in the Hong Kong and Pearl River estuary model andin the detailed model the momentum transfer and mixing by3D turbulence subjected to density gradients is represented bythe k-3 turbulence model. This turbulence model does notinclude the vertical exchange of horizontal momentum byinternal waves. Adding a constant background eddy-viscosityof 0.5� 10�4 m2/s approximated this momentum transfer.

In the detailed model the k-3 turbulence model is combinedwith a numerical procedure called Horizontal Large EddySimulation (HLES) to simulate the formation and the evolu-tion of eddies with horizontal dimensions significantlyexceeding the water depth. The HLES method replaces thespecification of the horizontal eddy viscosity and horizontaleddy diffusivity, which would otherwise be calibrationparameters that depend on the flow and the grid size.

3.4. HLES

The HLES procedure is based on resolving the larger-scaleeddies (2D-turbulence) while using a grid-size dependent or

ion of project area (blue box); (b) Detailed model including Ma Wan Channel,

rpretation of the references to colour in this figure legend, the reader is referred

227R. Morelissen et al. / Journal of Hydro-environment Research 3 (2010) 224e231

subgrid-scale (SGS) model for the unresolved 2D-turbulence,for details see Uittenbogaard and van Vossen (2004). Theapplication of HLES combined with the k-3 turbulence modelto 3D stratified flow, was validated in Bijlsma et al. (2004) forapplication in hydrodynamic studies of the extension of thePort of Rotterdam. Following the requirements of a properapplication of HLES, three criteria were fulfilled: 1) theadvection Courant number CU ¼ jUjDtDl�1 � 1, with timestep Dt and grid size Dl in the direction of the horizontal flowvelocity vector U , 2) the Courant number for barotropicgravity waves CBT ¼ 2DtðgHðDx�2 þ Dy�2ÞÞ0:5 � 5:6, withgravitational acceleration g, total water depth H and gridsizesðDx;DyÞ, and 3) a sufficiently fine grid is applied toensure that the smallest eddy covers about 6 grid spaces. Withthe grid resolution of about 30 m this resulted in a time step of5 s. Furthermore, special attention is given to schematisationof geometric elements that might introduce flow separation inprototype and in the model. With help of a boundary-fittedmodel grid we avoided staircase boundaries with risk of arti-ficial wall friction and flow separation.

3.5. Dedicated field measurements

To be able to calibrate and validate the hydrodynamicmodel, field measurements were made available. These con-sisted of:

� Water level measurements at Container Terminal 8,roughly from January to September 2006;

� Dry season ADCP measurements along 4 RamblerChannel transects (January 2006) for a spring and neaptidal cycle (25 h measurements each);

� Wet season ADCP measurements along 4 RamblerChannel transects (July 2006) for a spring and neap tidalcycle (25 h measurements each);

� CTD (Conductivity, Temperature, Depth) measurementsduring the ADCP measurements.

Measured water levels and the tidal discharges over theADCP sections confirmed the mixed character of the tide. Forthe dry season measurements salinity and water temperaturevariability over the water column was very small (32.4e32.8 pptand 18.4e18.6 �C). In the wet season significant differences insalinity and temperature exist in space and time depending onthe spring-neap cycle and the diurnal/semi-diurnal character ofthe tide (24.0e33.6 ppt and 23.6e28.2 �C). These differencesconfirm the stratified hydrodynamic regime.

4. Discussion of model results

4.1. Initial dry season calibration and validation

The water level data were subject to tidal analysis.Combined with existing tidal data, the result was used forcalibration and validation of the tidal propagation in the modelon the basis of the reproduction of tidal constants. Based onthis, a number of additional tidal constituents were added to

the overall model boundary conditions (Q1, MU2 and NU2).This further increased accuracy for the modelled water levelsin the SCB area for the detailed application in the presentstudy.

Basically, the dry season ADCP measurements were usedto calibrate the currents and flow patterns in and around theSCB area. To increase the model accuracy regarding locationand size of measured eddies, a small number of modelparameters were calibrated within their range of uncertainty.These parameters existed of local bed level and friction, and ofthe schematisation of the harbour banks (e.g. rubble mouthslopes, piled decks, moored ships).

In the detailed model the high pass time filter of the SGSmodel of HLES was set at 30 min, being typically twice thetime scale of the passage of the larger eddies. Resultinghorizontal eddy viscosities yt ranged from negligibly small toabout 1 m2/s on the fine grid near SCB to about 10 m2/s in MaWan Channel where even stronger fluctuations in the flowoccur.

After careful set up of the model, the accuracy of the modelanswered to the prescribed accuracy levels for the dry seasoncondition, with only limited calibration effort.

4.2. Final wet season validation

The wet season ADCP measurements were received ata later stage in the study and were especially used for vali-dation of the model.

Comparison of the modelling results with the measuredflow data showed a very good agreement, both horizontallyand vertically over the water column. CTD measurementswere used to validate the degree of stratification.

Fig. 3 shows a snapshot of the horizontal, depth-averagedmodel results for the wet season simulation with eddy at lowwater slack during spring tide, in which the ADCP measure-ments are shown as red vectors. This figure shows good agree-ment of the flow patterns. Fig. 4 shows the vertical distribution ofthe velocity at 4 locations along the bridge alignment at anarbitrary time in the wet season. The red line shows the ADCPmeasurement and the blue line the model result at the same time.Also this result shows a very good agreement.

The observed eddies and recirculations have both a deter-ministic and random character. It is in principle impossible tocompute the exact shape and form of the eddies. However,since these eddies and recirculations are generated by the tidalcurrents, and therefore depend on the tidal conditions, theoccurrence of these larger eddies and recirculations can bemodelled accurately.

The model validation showed that the combination of tidalboundary conditions, average wet season Pearl Riverdischarge, treatment of local quays and banks and the use ofthe HLES method results in a very good representation of thecomplex currents in the Stonecutters Bridge area.

To assess the influence of variations in the Pearl Riverdischarge on the flow conditions near SCB a simulation wascarried out for an extreme condition existing of a 50% higherthan average wet season discharge (29,100 m3/s). According to

Fig. 3. (a) Horizontal velocity field in Rambler Channel entrance, simulated flow (blue vectors) and measured flow (red vectors), depth-averaged 12e07e2006

19:00 HKT; (b) Time series of simulated (blue) and measured (red) water levels. (For interpretation of the references to colour in this figure legend, the reader is

referred to the web version of this article.)

228 R. Morelissen et al. / Journal of Hydro-environment Research 3 (2010) 224e231

in-house data, this is about the highest observed monthlyaverage discharge. As a result, the depth-averaged currentvelocities in the SBC area were up to 10e20% higher, and inthe surface layer the increase could be as much as 30%.

5. Digital tidal stream atlas

5.1. Introduction

As described in Section 1, a detailed tidal atlas wasrequired to aid construction planning processes and to assessflow conditions for the remaining navigation in the SCB area.This digital tidal atlas is a computer program that is able topredict water levels and currents in a certain area based ontidal constants. These constants are derived by harmonicanalysis of modelling results over a period of one month.

The Hong Kong government maintained such a tidal atlas,but with less detail, for the entire Hong Kong area between 2003and 2006. Furthermore, tidal atlases were developed in previousstudies by Deltares j Delft Hydraulics for areas with significanteddy formation in and near harbours, such as Dunkerque.

The application of the tidal atlas in the present study requiredan extension in functionality compared to other tidal atlases, suchas the easy extraction of arbitrary predicted time series froma selected location. Therefore, a new tidal atlas was set up, calledDelft-STREAM, encompassing these new functionalities.

5.2. Tidal analysis

The observed tidal motion can be described in terms ofa series of simple harmonic constituents, each with its owncharacteristic frequency u (angular velocity). The amplitudes

Fig. 4. Current profiles perpendicular to the Stonecutters Bridge transect 12e07e2006 14:20 HKT.

229R. Morelissen et al. / Journal of Hydro-environment Research 3 (2010) 224e231

A and phases G of the constituents vary with the positionswhere the tide is observed. In this representation by means ofthe primary constituents, compound and higher harmonicconstituents may have to be added. This is the case in shallowwater areas, for example, where advection, large amplitude todepth ratio, and bottom friction give rise to non-linear inter-actions, and also when tide-dominated eddies and recircula-tions need to be represented.

The general formula for the astronomical tide is:

HðtÞ ¼ A0þXk

i¼1

Ai � Fi � cos�ui � tþ ðV0þ uÞi�Gi

�ð1Þ

in which:H(t)¼water level or current component at time t;

A0¼mean water level/current component over a certainperiod; k¼ number of relevant constituents; i¼ index ofa constituent; Ai¼ local tidal amplitude of a constituent;Fi¼ nodal amplitude factor; ui¼ angular velocity;(V0þu)i¼ astronomical argument; Gi¼ improved kappanumber (¼ local phase lag).

F and (V0þu) are time-dependent factors which, togetherwith u, can easily be calculated and are generally tabulated inthe various tidal year books. V0 is the phase correction factorwhich relates the local time frame of the observations to aninternationally agreed celestial time frame. V0 is frequencydependent. F and u are slowly varying amplitude and phasecorrections and are also frequency dependent. For mostfrequencies they have a cyclic period of 18.6 years. The tidalconstants A0, Ai and Gi are position-dependent: they representthe local character of the tide.

When for a specific location the tidal constants A0, Ai andGi are known, the above formula can be used to predict thelocal water level or current components at any time.Conversely, if at a location a series of tidal observations isknown, the above formula can be used in a least squaresanalysis to estimate the constants A0, Ai and Gi (DelftHydraulics, 2006).

5.3. Delft-Stream

The Delft-STREAM tidal atlas was initially developed forthe SCB study, but is applicable in many other regions. Thecomputational core of Delft-STREAM is based on the stan-dard tidal analysis and prediction software available withinDeltares j Delft Hydraulics.

The Delft-STREAM program was created in Matlab and isset up in such way that it allows for easy future extension offunctionalities. The version that was developed here includesfunctionalities such as the prediction of an entire flow field inthe SCB area, up to the model resolution with a maximum of30 m, prediction in different scenarios like dry or wet season,surface layer or depth-averaged, prediction of time series atarbitrary locations in the SCB area and exporting these,multiple post-processing options, etc.

This tidal atlas operates on the basis of a database con-taining the tidal constants for each model grid cell in thedetailed SCB model. In its current state it is capable of pre-dicting current velocities for 2000 locations instantaneously,forming a flow field at a certain point in time, or predictinga time series of water levels, current magnitude and directionfor a selected location, with a length up to months. Thesepredictions take generally less than a second to be performed,which makes it possible to step through time while makingpredictions of the flow field on-the-fly.

6. Stonecutters Bridge tidal atlas

For the current implementation of the Delft-STREAM tidalatlas for the SCB area, a tidal analysis was performed on theone month long modelling results for a total of 67 tidalconstituents. Furthermore, the current implementationincludes the ability to predict the 3D character (i.e. stratifi-cation) of the flow. To accomplish this, prediction of surfacelayer and depth-averaged flow was implemented, see Fig. 5,but in principle, arbitrary layers in the water column can beprepared to be used in the tidal atlas.

Fig. 5. Digital Stream Atlas, predicted (a) depth-averaged and (b) surface currents 12e07e2006 19:00 HKT.

230 R. Morelissen et al. / Journal of Hydro-environment Research 3 (2010) 224e231

To assess the accuracy of the predictions by the SCB tidalatlas, a validation of the predictions was carried out bycomparing the predictions to the model computations, whichwere in turn validated against measurements. A comparisonbetween model and tidal atlas is presented in Fig. 6, whichshows good agreement.

The study confirmed that the most important and largesteddies can be attributed to tidal forcing. This means that theserecirculations can be well described by defining the appro-priate tidal constituents. The predictions by the tidal atlasshow that the recirculations, such as the large flow recircula-tion in the Rambler Channel entrance, are reproduced well.

The tidal atlas is successfully used during the planning andthe execution of the marine works. Worst current conditions

Fig. 6. Comparison of prediction by tidal atlas with numerical model result.

were used in a study of the nautical impact of the deck liftingoperation on passing container vessels in the Hong Kong MarineDepartment Simulator, leading to restrictions in traffic enteringthe container port during lifting operations. The initial deck liftsproved that the dynamic positioning system for the barge is verysensitive to a number of factors, including the current. Initially,the deck lifts were arranged to only take place on a rising tide,but after accurate calibration of the dynamic positioning system,this requirement could be relaxed. For safety reasons all decklifts now take place in the early morning such that the segment issecured to the bridge before sunset.

7. Conclusions

To perform nautical simulations for marine safety assess-ment during the Stonecutters Bridge construction works andfor the programming of the deck lift operations, reliablepredictions of the flow conditions were needed in this area.

Based on extensive experience in the Hong Kong area and thewell calibrated and validated Delft3D model of Hong Kong andthe Pearl River estuary, it proved possible to accurately model3D flow conditions near Stonecutters Bridge at the RamblerChannel entrance, i.e. within the required accuracy of 0.25knots z 0.13 m/s in velocity and 30 min in time. The complexcurrents in that area include stratification during the wetmonsoon season and significant eddy patterns. The mostimportant and largest eddies are tidally driven, implying theycan be described when appropriate tidal constituents are defined.

The modelling results were subject to tidal analysis to allowend-users to make predictions of the flow fields, independentof the numerical model. To facilitate this, a tidal atlas (Delft-STREAM) was developed that uses the results of the tidalanalysis and is capable of predicting flow fields for an arbitrary

231R. Morelissen et al. / Journal of Hydro-environment Research 3 (2010) 224e231

moment in time. Delft-STREAM has shown to be capable ofreproducing the large flow recirculations and complex strati-fied flow conditions in the Stonecutters Bridge area.

Acknowledgement

The permission of the Maeda-Hitachi-Yokogawa-HsinChong Joint Venture to publish the work in this paper isgratefully acknowledged.

References

Bijlsma, A.C., Uittenbogaard, R.E., Blokland, T., 2004. Horizontal large eddy

simulation applied to stratified tidal flows. In: Jirka, G.H., Uijttewaal, W.S.

J. (Eds.), Shallow Flows. Taylor & Francis Group, London, pp. 559e565.

Delft Hydraulics, 2006. Delft3D-TIDE, Analysis and Prediction of Tides, User

Manual.

Larson, M., Bellanca, R., Jonsson, L., Chen, C., Shi, P., 2005. A model of the

3D circulation, salinity distribution, and transport pattern in the Pearl River

estuary, China. Journal of Coastal Research 21 (5), 896e908.

Lesser, G.R., Roelvink, J.A., Kester, J.A.T.M., vanStelling, G.S., 2004.

Development and validation of a three-dimensional morphological model.

Coastal Engineering 51, 883e915.

Ng, A.K.M., Roelfzema, A., Hulsen, L.J.M., 1999. 3-Dimensional water

quality and hydrodynamic modelling in Hong Kong: I. Concepts and

model set-up. In: Lee, J.H.W., Jayawardena, A.W., Wang, Z.Y. (Eds.),

Environmental Hydraulics. Balkema, Rotterdam, pp. 31e36.

Postma, L., Stelling, G.S., Boon, J., 1999. 3-Dimensional water quality and

hydrodynamic modelling in Hong Kong: III. Stratification and water

quality. In: Lee, J.H.W., Jayawardena, A.W., Wang, Z.Y. (Eds.), Environ-

mental Hydraulics. Balkema, Rotterdam, pp. 43e49.

Uittenbogaard, R.E., Hulsen, L.J.M., 1999. 3-Dimensional water quality and

hydrodynamic modelling in Hong Kong: II. Forcing residual currents. In:

Lee, J.H.W., Jayawardena, A.W., Wang, Z.Y. (Eds.), Environmental

Hydraulics. Balkema, Rotterdam, pp. 43e49.

Uittenbogaard, R.E., van Vossen, B., 2004. Subgrid-scale model for quasi-2D

turbulence in shallow water. In: Jirka, G.H., Uijttewaal, W.S.J. (Eds.),

Shallow Flows. Taylor & Francis Group, London, pp. 575e582.

Wong, L.A., Chen, J.C., Xue, H., Dong, L.X., Su, J.L., Heinke, G., 2003. A

model study of the circulation in the Pearl River Estuary (PRE) and its

adjacent coastal waters: 1. Simulations and comparison with observations.

Journal of Geophysical Research 108 (C5), 3156. doi:10.1029/

2002JC001451.