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The Seventh OMISAR Workshop on Ocean Models

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Numerical Modeling of Hydrodynamics and Suspended Sediment Transport in Malacca Strait

Q. Y. Zhang1 and E. S. Chan

Physical Oceanography Research Laboratory Tropical Marine Science Institute, National University of Singapore

14 Kent Ridge Road, Singapore 119223 1Email:[email protected]

Abstract

A three-dimensional coupled hydrodynamic/suspended sediment transport model for Malaccas coastal waters has been developed. The hydrodynamic circulation model is based on the Princeton Ocean Model (POM) and the suspended sediment transport model is developed under coordinate system. The model considers sediment resuspension, deposition and transport in the water column. The hydrodynamic/suspended sediment transport model has been applied to the Malacca and Singapore Straits. The model results show that the predicted tide elevations and currents are in good agreement with the data published in the Tide Table. The simulated suspended sediment concentration agrees reasonably with the seaWIFS satellite data at the same time and the model can reproduce the general pattern of the suspended sediment distribution in the Straits.

Keywords: modelling; sediment transport; tidal motion; Malacca Strait

1. INTRODUCTION

During the past few decades, the coastal regions in the Malacca Straits have been experiencing rapid changes. The Straits of Malacca and Singapore are situated between the East Coast of Sumatera Island and the West Coast of Peninsular Malaysia. The Straits form an international shipping route linking the Indian Ocean (via the Andaman Sea) with the South China Sea to the Pacific Ocean, which is among the busiest and most important waterways in the world. Increasing human activity and utilization of resources such as port development, land reclamation and construction of marinas and residential areas have led to a need for a careful evaluation and prediction of the hydrodynamic and sediment transport characteristics of the strait environment. In the past, numerical computations based on two-dimensional depth-averaged equations have been used to investigate suspended sediment transport in Singapore Strait (Choy, 1989). However, the model is depth-averaged and is only used in Singapore Strait. Hence, a three-dimensional (3D) hydrodynamic and sediment transport model is necessary for a realistic simulation of the flow and sediment concentration fields in Malacca and Singapore Straits waters.

In recent years, several 3D models for water flow and suspended sediment transport have been published. The layer-averaged 3D models for suspended load transport were devised for

estuarine and coastal areas (Lin and Falconer, 1996; Wai et al., 1996). Van Rijn (1986) and Guo and Jin (1999) established the combined models in which the sediment transport is calculated with a 3D approach and the flow with a depth-averaged approach in combination with the assumption of a vertical logarithmic velocity profile, which is valid only for gradually varying open channel flow. Gessler et al. (1999) and Wu et al. (2000) used the k turbulence model and coordinate transformation technique in the 3D simulations of the flow and sediment transport in meandering open channels. Later, Lou and Schwab (2000) developed a quasi-three-dimensional suspended sediment model for southern Lake Michigan, where the suspended sediment model was developed by introducing an asymptotic solution to a 2D vertical model for uniform flow and the POM (Princeton Ocean Model) circulation model and wind wave model results were used as hydrodynamic input.

In this paper, a complete 3D hydrodynamic/suspended sediment transport model with orthogonal coordinate in horizontal and coordinate transformation in vertical was developed to investigate circulation, sediment resuspension, deposition and transport in the water column of the Malacca and Singapore Straits.


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2. MODEL DESCRIPTIONS

The coupled hydrodynamic/suspended sediment modeling system is based on the well-tested and extensively used the Princeton Ocean Model (POM), developed by Blumberg and Mellor (1987). Detailed description of the original POM model can be found in the web site of POM (http://www.aos.princeton.edu/wwwpublic/htdocs.pom/). A brief description of the developed circulation and suspended sediment transport model is presented below.

Circulation Model

The POM is a 3D primitive-equation model that uses the sigma coordinate

]/)([ Dz = in the vertical direction to track free water surface and smoothly represent the bottom topography, the curvilinear orthogonal coordinate in the horizontal direction to fit irregular shoreline boundary. Here is the water elevation of sea surface above the undisturbed level, D is the total water depth and z is the distance from mean sea surface. The POM contains an embedded second moment turbulence closure submodel to provide vertical mixing coefficients. The model has a split time step. The external mode portion of the model is two-dimensional and uses a short time step and the internal mode is three-dimensional and uses a long time step. In the POM, complete thermodynamics have been implemented, and the stratification of salinity and temperature are considered.

The mass conservation equation for the internal model used in the POM can be written as:

0=

+

+

+

tyvD

xuD

(1) and the nonlinear momentum equations as:

xm F

uD

Kd

xD

DxgD

xgD

fvDu

yuvD

xDu

tuD

+

+

=

+

+

+

0

0

2

2

(2)

ym Fv

DK

dyD

DygD

ygD

fuDvyDv

xuvD

tvD

+

+

=++

+

+

0

0

2

2

(3)

Temperature and salinity transport equations are:

TH F

TDKT

yTvD

xTuD

tTD

+

=

+

+

+

(4)

SH FS

DKS

ySvD

xSuD

tSD +

=

+

+

+

(5)

Where u,v and = the mean velocity components in the x-, y- and - directions, respectively; 0 = the reference fluid density; = the fluid density which is the function of temperature and salinity; g = the gravitational acceleration; = the elevation of sea surface above the undisturbed level; D = +H, where H = the water depth defined by the bottom topography; t = the time; T = the temperature; S = the salinity; Fx, Fy, FT and FS = the horizontal diffusion terms of momentum, temperature and salinity; KM = the vertical turbulent diffusion coefficient of momentum modeled according to the second-order turbulence closure scheme of Blumberg and Mellor (1987); KH = the vertical turbulent diffusion coefficient of temperature and salinity; f = the Coriolis parameter.

The vertically integrated continuity and momentum equations for the prediction of the water elevation in the external model can be written as:

0=

+

+

tyVD

xUD (6)

)(00

10

2

bxsxxFddx

Dx

DgDx

gD

fVDuy

UVDxDU

tUD

++

=+

+

+

(7)

)(00

10

2

bysyyFddy

Dy

DgDx

gD

fUDy

DVx

UVDt

VD

++

=+

+

+

(8)

where U and V = the vertically integrated

velocities; xF and yF = the horizontal

turbulence diffusion terms; sx and sy = the atmospheric wind stress components in x- and y- directions; bx and by = the bottom stress components in x- and y- directions.

The atmospheric wind stress at the surface is

given as:

2

102

1010 yxxsasx WWWC += and2

102

1010 yxysasy WWWC +=

(9)

where sC = the drag coefficient at the air-sea interface; xW10 and yW10 = the wind speed components in the x and y directions (10 m



above mean sea level); a = the mass density of air.

The bottom shear stress is a quadratic

function of the near bottom velocity and can be written in the following form:

22bbbbbx vuuC += and

22bbbbby vuvC += (10)

in which bC = the drag coefficient in the ocean bottom boundary layer; = the water density; bu and bv = the near bottom velocity components in x and y directions.

The governing equations (1) to (8) are solved subject to initial and boundary conditions. The initial velocities are set to be zero and the initial water elevation, temperature and salinity are equal to the mean sea level, temperature and salinity in the study domain. A slip condition is assumed at land boundaries. The water elevations and background temperature and salinity are prescribed at the open boundaries.

Suspended Sediment Transport Model

The distribution of the sediment concentration in water column is governed by the convection-diffusion equation (Lin and Falconer, 1996; Lou and Schwab, 2000; Wu et al., 2000):

+

+

=

+

+

+

zc

zyc

yxc

x

zc

wwyc

vxc

utc

c

z

c

y

c

x

s

)( (11)

where t = the time; x, y, z = the Cartesian coordinates; u, v, w = the flow velocity

components in x, y , z directions; yx , and z = the turbulent diffusion coefficients in x, y , z directions; c = the sediment concentration; ws = the particle settling velocity in the vertical direction (z); c = the turbulent Schmidt number relating the turbulent diffusion of the sediment to the diffusion of the momentum. A value of c = 1 was used in this model.

In the three-dimensional coordinate system (x, y, ), the equation (11) can be easily transformed to:

cs Fc

Dc

Dw

vcDy

ucDxt

cD +

=

+

+

+

)()()(

(12)

where = the vertical turbulent diffusion

coefficient in direction; cF = the horizontal diffusion term of suspended sediments; D = the water depth.

The following boundary conditions were imposed to solve the equation (12): At the free surface, the vertical sediment flux is zero and hence the condition applied is

0=+

cDwc

s (13)

At the near bottom,

)( bb DEDc

=

(14)

where Eb = a coefficient describing the

entrainment of bed sediment into suspension due

to turbulence at bz =' ; Db = the deposition flux from water column into bed sediment at bz =' ;

b = the reference height above the bed (max(0.01D, kn); kn = physical bottom roughness (Nikuradse roughness height). An upwind advection equation ( 0// =+ ncVtc n , where V is velocity, n is a unit outward normal to open boundary) is used on the open boundary points.

In the suspended sediment transport model, the near-bed entrainment coefficient at a reference level, Eb, and sediment settling velocity, ws, for noncohesive sediments are computed (van Rijn, 1993; Guo, 2002):

*bsb cwE = (15)

3.0*

5.150

* 015.0 DTdc

bb

= (16)

+=

2/3*

3*

50

23

24 D

Dd

w s (17)

where D* = particle size parameter

3/1

250*

= gdD s

(18)

and T = non-dimensional excess bed shear stress

2*

2*

2*

cr

cr

uuu

T

= (19)



In these relations, d50 = the median diameter of the bed material; s = the material density; = the water density; g = the gravitational acceleration; is the kinematic viscosity; cru* = the critical bed shear velocity for sediment motion given by Shields diagram, *u = the effective bed shear velocity related to the grain and its apparent roughness.

When the bed shear velocity ( *u ) is less than the critical value ( cru* ), then the sediments in the water column deposit to the bed according to the formula:

bsb cwD = (20)

where Db = the noncohesive sediment depositional flux; bc = the near-bed suspended sediment concentration.

3. MODEL APPLICATION TO THE MALACCA AND SINGAPORE STRAITS Study Area

The developed 3D hydrodynamic/sediment transport model has been

applied to the coastal waters of Malacca and Singapore Straits. The horizontal model domain considered here covers an area of 370 km by 300 km, lying in a rectangle approximately defined by the latitudes 0059 N to 3041 N and longitudes 10101 E to 104019 E. The physical boundary of the domain is highly irregular together with the presence of the island groups within the domain. The water depth ranges from about 1 m to 110 m (Fig. 1). The hydrographic conditions of the Straits are dominated by the diurnal tides and by the northeast and southwest monsoons. General climate patterns have remained somewhat consistent over the years, although some limited variations have occurred (Chua et al., 1997). In the numerical simulation, the area is discretized by 397 325 points (0.5 minutes by 0.5 minutes) in the horizontal plane and 4 equal layers over the depth. x = 0.925 km, y = 0.92 km, Et = 0.8 s, It = 24 s.

Fig.1. Study area and depth contour of Malacca and Singapore

Straits (in meters)



Model Results

Simulation of tidal elevation and currents for 5-8 July, 1997

The flow due to tides is simulated. The model calibration is carried out based on the southwest monsoon tidal situation between 0400 hours, 5th July, 1997, to 0300 hours, 8th July, 1997. The tidal elevations and current velocities in the domain are predicted. The time history records of the tidal elevations and the current velocities in the Malacca Strait are currently not available. The time history records of the tidal elevations and the current velocities at selected stations in Singapore Strait after 24 hours physical time are compared with data published in Tide Table. As for the simulated tidal elevations, it can be observed from Fig. 2 that the simulated and published free surface water elevations show good agreement at station Bukom: the magnitude, as well as the phase of the free surface water elevation, are well simulated. The correlation coefficient between simulated tidal elevations and Tide Table data is 0.988. The comparison of the simulated and published tide-induced currents with regard to both magnitude and direction at the selected station, Gusong Beacon, is shown in Fig. 3. A comparison of the computed velocities and published data shows that the magnitude and the phase of the simulated currents are favorably matched at the selected station. The correlation coefficient between simulated tidal velocities and Tide Table data is 0.987 and the mean absolute difference is about 0.5 knots.

00.5

11.5

22.5

33.5

4

0 5 10 15 20 25 30 35 40 45

time (hrs)

elev

atio

n (m

)

Computed

Tide table

Figure 2 Comparison of computed tidal elevations with those published in Tide Table at station Bukom (01013.5N, 103046.7E) (04:00/06/07/1997 to 03:00/08/07/1997)

-4

-3

-2

-1

0

1

2

3

4

0 10 20 30 40

time (hrs)

velo

city

(kno

ts)

ComputedTide table

Figure 3 Comparison of computed tidal velocities with those published in Tide Table at station Gusong Beacon (+ for 670, - for 2470) (01011.1N, 103047.6E) (04:00/06/07/1997 to 03:00/08/07/1997) Simulation of flow and suspended sediment concentration for 12-18 April, 2001

In the Malacca and Singapore Straits there are few observations of the flow and suspended sediment concentration. But water color can be obtained from satellite remote sensing which can be used to validate the model results. The remote sensing data on the water leaving radiance used here are the seaWIFS satellite data from the National Aeronautics and Space Administration (NASA). The spatial resolution is 0.5 minutes. In the following images (Figs. 5(b) and 6(b)), bright areas represent high reflectance and thus, high suspended load concentrations and the strong absorption (dark area) may indicate low suspended load concentrations in the Straits.

There are 26 images available covering parts of the Malacca and Singapore Straits in 2001. Unfortunately, only seven images were comparatively cloud free to reflect the patterns of the suspended load in the water. From these images, some eminent characteristics can be identified. In the present model application, the verification simulation runs for suspended sediment transport were carried out from 12 to 18 April, 2001, because there are four clearer images during this time period. To get convergent results, the simulation runs start from 01 hour, 28th March, 2001. The simulated typical current patterns for the selected tide phases (13:00/14/04/2001 and 13:00/16/04/2001) at the free surface and near bottom are shown in Fig. 4 and the corresponding suspended load concentration patterns of the near-surface water are compared with the satellite images in Figs. 5 and 6.

A comparison of Fig. 4 with Figs. 5(a) and 6(a) shows that the simulated suspended sediment concentration at free water surface is closely related to circulation pattern at that time. In general, the flow is similar in direction for free water surface and near bottom, with the largest velocity in the surface and a great reduction in velocity at the near bottom. The



smaller flow velocities and lower suspended load sediment concentration can be found in the near shore area, compared to the offshore areas. The concentrations at the connection between the Malacca Strait and Singapore Strait and around islands: Rupat and Bengkalis are much higher than those in other areas because the Malacca Strait becomes narrow and shallow and the flow velocities are greatly increased in these areas. It is also observed that the predicted distribution of suspended sediment concentration (Figs. 5(a) and 6(a)) is generally in good agreement with the satellite images (Figs. 5(b) and 6(b)). There is a belt of high suspended sediment concentration along the centerline of the Malacca Strait just as in the satellite images. The low concentration can be seen in the nearshore area in both images. Comparing the model results with the corresponding satellite images some other similarities can be found. At present, it is not easy to get the absolute value of the suspended sediment concentration directly fro m remote sensing. The further calibration work on remote sensing data and model results will be done in future.

Overall, the comparison between the computed values and satellite images proves that the model simulation is successful. The results can at least reproduce the general pattern of the suspended sediment distribution in the Malacca and Singapore Straits.

4. CONCLUSIONS

A 3D hydrodynamic and sediment transport model with sigma coordinate system, which can well track free water surface and bed deformation, has been developed to simulate the hydrodynamic and sediment transport characteristics of Malacca and Singapore Straits. The model calibration and verification show that the simulated free surface water elevations and currents are favorably matched with the published data in Tide Table at the selected stations. The simulated suspended sediment concentration is closely related to circulation pattern at that time. The predicted distribution of suspended sediment concentration is generally in good agreement with the satellite images. Overall, the developed model can reproduce the general pattern of the suspended sediment distribution in the Straits.

One of the main problems in the modelling study is the difficulty in obtaining sufficient field data for calibration and verification. Future work could be carried out to focus on recalibration of simulated currents and

suspended sediment concentration as more field data become available and investigation of the effects of wave-current interactions on sediment transport in the model. Finally, the 3D hydrodynamic and sediment transport model could be expected to predict some typical and long-term scenarios, which occur in the Malacca and Singapore Straits.

REFERENCES

Blumberg, A. F. and Mellor, G. (1987). A description of a three-dimensional coastal ocean circulation model. Three-dimensional coastal ocean models, N. S. Heaps, ed., American Geophysical Union, Washington, D. C., pp. 1-16.

Choy, Y. Y. (1989). Mathematical modeling of sediment transport under tidal flows. M. Eng. Thesis, National University of Singapore.

Chua, T. E., Ross, S. A. and Yu, H. (1997). Malacca Straits environmental profile. GEF/UNDP/IMO Regional Programme for the Prevention and Management of Marine Pollution in the East Asian Seas.

Gessler, D., Hall, B., Spasojevic, M., Holly, F., Pourtaheri, H. and Raphelt, N. (1999). Application of 3D Mobile Bed, Hydrodynamic Model. Journal of Hydraulic Engineering (ASCE), Vol. 125, No. 7, pp. 737-749.

Guo, J. (2002). Logarithmic matching and its applications in computational hydraulics and sediment transport. Journal of Hydraulic Research, Vol. 40, No. 5 (accepted).

Guo, Q. C. and Jin, Y. C. (1999). Modeling sediment transport using depth-averaged and moment equations. Journal of Hydraulic Engineering (ASCE), Vol. 125, No. 12, pp. 1262-1269.

Lin, B. L. and Falconer, R. A. (1996). Numerical modeling of three-dimensional suspended sediment for estuarine and coastal waters. Journal of Hydraulic Research, Vol. 34, No. 4, pp. 435-456.

Lou, J. and Schwab, D. J. (2000). A model of sediment resuspension and transport dynamics in southern lake Michigan. Journal of Geophysical Research, Vol. 105, No. C3. pp. 6591-6610.

Van Rijn, L. C. (1986). Mathematical modeling of suspended sediment in nonuniform flows. Journal of Hydraulic Engineering (ASCE), Vol. 112, No. 6, pp. 433-455.

Van Rijn, L. C. (1993). Principles of Sediment Transport in Rivers, Estuarines and Coastal Seas, Amsterdam: Aqua Publications I11, The Netherlands.



Wai, W. H.O., Lu, Q. M. and Li, Y. S. (1996). Multi-layer modeling of three-dimensional transport processes. Journal of Hydraulic Research, Vol. 34, No. 5, pp. 677-691.

Wu, W. M., Rodi, W. and Wenka, T. (2000). 3D numerical modelling of flow and sediment transport in open channels. Journal of Hydraulic Engineering (ASCE), Vol. 126, No. 1, pp. 4-15.


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