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Hydrodynamic Tracking of the Massive Spring 1998
Red Tide in Hong Kong
Joseph H. W. Lee1and Bo Qu2
Abstract: In subtropical coastal waters around Hong Kong, algal blooms and red tides have been frequently observed over the past two
decades. In particular, in March–April 1998, a massive red tide invaded the northeastern and southern coastal waters of Hong Kong. The
devastating red tide resulted in the worst fish kill in Hong Kong’s history, the most significant impacts being at the Lo Tik Wan and Sok
Kwu Wan fish culture zones on Lamma Island. This work reports the first scientific investigation of the cause of this massive red tide. A
calibrated three-dimensional 共3D兲hydrodynamic model for the Pearl River Estuary, Delft3D, is applied to study the advective transport of
red tides. Based on the tidal boundary conditions and the measured wind data for a typical spring season, the 3D flow field is computed
and extensive surface drogue tracking performed for releases in different parts of the coastal waters and for different tidal and wind
conditions. The results show that a bloom initiated in Mirs Bay 共Nan Au orTap Mun兲in the northeastern water would likely be transported
to the southern coastal waters under the combined action of tidal current and wind. The computed bloom tracking patterns are generally
supported by observations and are consistent with the temporal and spatial patterns of individual fish kill events in the 1998 red tide. We
conclude that the major cause of the bloom being transported into the southern waters and East Lamma Channel 共and causing the massive
fish kill兲is the generally strong wind in March–April 1998 and the change in wind direction in early April under almost diurnal tidal
conditions. Further, it is most probable that the red tide originated in Mirs Bay rather than from outside Hong Kong. The findings provide
a firm basis for environmental and fisheries management.
DOI: 10.1061/共ASCE兲0733-9372共2004兲130:5共535兲
CE Database subject headings: Hong Kong; Coastal management; Fisheries; Disasters; Hydrodynamics; Hydraulic models; Water
quality; Eutrophication; Tracking.
Introduction
Hong Kong is situated at the mouth of the Pearl River Estuary in
Southern China 共Fig. 1兲. In subtropical coastal waters around
Hong Kong and South China, algal blooms and red tides 共due to
the rapid growth of microscopic phytoplankton兲are often ob-
served. Under the right environmental conditions 共favorable tem-
perature, solar radiation, nutrient concentration, predation pres-
sure, wind speed, and tidal flushing兲these blooms can occur and
subside over rather short time scales—on the order of days to a
few weeks. Algal blooms can lead to discoloration of the marine
water, which may lead to beach closures, severe dissolved oxygen
depletion, fish kills, and shellfish poisoning. Over the past two
decades, massive fish kills due to oxygen depletion have been
observed in some of the marine fish culture zones in Hong Kong
共Lee et al. 1991兲; a few toxic algal blooms have also been re-
ported. In particular, in April 1998, a devastating red tide 共due to
the dinoflagellate Karenia digitatum兲resulted in the worst fish kill
in Hong Kong’s history—it destroyed over 80% 共3,400 t兲of cul-
tured fish stock, with estimated loss of more than HK$312 million
共Dickman 1998; Yang et al. 2000兲. It appears that the dinoflagel-
late species produced copious amounts of a sticky mucus which
coated the fish gills, leading to suffocation and mortality within
hours after the fish farms were hit by the red tide 共Dickman
1998兲. Other explanations are also possible, such as the produc-
tion of fish toxins 共Anderson 1998兲.
The 1998 red tide was truly an unusual event compared with
all past blooms in Hong Kong waters. It was the most serious red
tide in Hong Kong’s history. It is recorded that 30 red tide inci-
dents appeared in the first six months of 1998 with the most
serious events during the period 19 March to 17 April 共Anderson
1998兲. Whereas the general ecological response of phytoplankton
to environmental conditions has been extensively studied, the
causality and dynamics of algal blooms are extremely compli-
cated and not well understood. In particular, for the massive red
tide of 1998, the press reports and water quality measurements
suggest a migration of a red tide initiated in mid-March in the
northeastern waters of Hong Kong, in Mirs Bay 共where red tides
in Hong Kong are usually first sighted in any given year兲, which
drifted to the southern coastal waters with tidal currents 关Fig.
2共a兲兴. There is also speculation that the red tide may have initiated
from outside Hong Kong, in Daya Bay along the South China
coast. Alternatively, the observations may also reflect merely a
change of environmental conditions in the various bloom loca-
tions during March–April 1998, with in situ growth occurring at
different times along the coast. Asystematic study of the probable
cause of this massive red tide is clearly desirable; a general un-
derstanding of the hydrodynamic transport of algal blooms would
be most useful for environmental and fisheries management.
1Professor, Dept. of Civil Engineering, Univ. of Hong Kong,
Pokfulam Rd., Hong Kong, China.
2Postdoctoral Research Fellow, Dept. of Civil Engineering, Univ. of
Hong Kong, Pokfulam Rd., Hong Kong, China.
Note. Associate Editor: A. Bruce DeVantier. Discussion open until
October 1, 2004. Separate discussions must be submitted for individual
papers. To extend the closing date by one month, a written request must
be filed with the ASCE Managing Editor. The manuscript for this paper
was submitted for review and possible publication on February 20, 2002;
approved on June 5, 2003. This paper is part of the Journal of Environ-
mental Engineering, Vol. 130, No. 5, May 1, 2004. ©ASCE, ISSN 0733-
9372/2004/5-535–550/$18.00.
JOURNAL OF ENVIRONMENTAL ENGINEERING © ASCE / MAY 2004 / 535
This paper reports a detailed study of the role of tidal hydro-
dynamics in the 1998 red tide. Particular emphasis is placed on
the intense red tide observed in southern waters and associated
fish kills in the fish farms located off the East Lamma Channel—
namely, the Lo Tik Wan and Sok Kwu Wan fish culture zones,
which suffered unprecedented complete losses. First, the three-
dimensional 共3D兲hydrodynamic model Delft3D is fully tested
against analytical solutions of long wave propagation in rectan-
gular and radial channels of varying bathymetry. The numerical
model 共previously calibrated with extensive field data for the
Pearl River Estuary兲is then employed to study the tidal circula-
tion during the average dry and wet seasons 共Hong Kong has a
Fig. 1. Pearl River Estuary model for algal bloom tracking
Fig. 2. 共a兲Reported red tide movement during March 18–April 14 1998 共from newspaper兲.共b兲Close-up view of Hong Kong Island and Lamma
Island.
536 / JOURNAL OF ENVIRONMENTAL ENGINEERING © ASCE / MAY 2004
distinct dry season with little rain from November to March, and
a wet season from June to September frequented by typhoons and
monsoons; the other months are transition periods兲. Extensive nu-
merical drogue tracking experiments are then carried out using a
refined grid for the northeastern waters of Hong Kong. The
drogue tracks are thoroughly studied for releases in different lo-
cations in the northeastern waters, and for the full range of pos-
sible scenarios 共release times, tidal range, wind conditions兲. The
results for both the typical March–April months and the particu-
lar conditions prevailing in spring 1998 are compared. Represen-
tative tracks are presented to illustrate the general nature of hy-
drodynamic transport of algal blooms in Hong Kong. The most
probable cause of the spring 1998 bloom is discussed in relation
to the hydrodynamic circulation and drogue transport patterns.
Hydrodynamic Modeling of Hong Kong’s Coastal
Waters
Governing Equations
The three-dimensional hydrodynamic model Delft3D is employed
for this study. Delft3D solves the Reynolds-averaged turbulent
flow equations for an incompressible fluid using a hydrostatic
pressure assumption. The resulting horizontal momentum and
continuity equations 共for a Cartesian coordinate system兲for baro-
clinic flow are as follows 共the shallow water equations兲:
u
t⫹uu
x⫹v
u
y⫹
d⫹
u
⫺fv
⫽⫺ 1
Px⫹Fx⫹1
共d⫹兲2
冉
V
u
冊
(1)
v
t⫹uv
x⫹v
v
y⫹
d⫹
v
⫹fu
⫽⫺ 1
Py⫹Fy⫹1
共d⫹兲2
冉
V
v
冊
(2)
t⫹
关共d⫹兲U兴
x⫹
关共d⫹兲V兴
y⫽S(3)
where (u,v)⫽horizontal velocities in the (x,y) directions, re-
spectively; ⫽free surface elevation above mean sea level;
d⫽mean depth; f⫽Coriolis parameter; P⫽pressure force term,
and Srefers to the source/sink term to simulate discharges and
withdrawal. The depth-averaged velocities are
U⫽
冕
⫺1
0ud⬘,V⫽
冕
⫺1
0
vd⬘
In the vertical direction, the coordinate 共dimensionless depth兲is
used
⫽z⫺
⫹d⫽z⫺
H(4)
with H⫽total water depth. At the bottom ⫽⫺1, and at the sur-
face ⫽0. The coordinate system is boundary fitted in the ver-
tical plane. In the coordinate system, the horizontal length scale
is assumed to be much larger than the water depth.
The vertical velocity in the coordinate system is computed
from the continuity equation
⫽⫺
t⫺
关共d⫹兲u兴
x⫺
关共d⫹兲v兴
y(5)
The vertical velocity win the x-y-zCartesian coordinate system
can be expressed in terms of the horizontal velocities, water
depths, water levels, and vertical coordinate according to
w⫽⫹u
冉
H
x⫹
x
冊
⫹v
冉
H
y⫹
y
冊
⫹
冉
H
t⫹
t
冊
(6)
The hydrostatic pressure is given by
P⫽Patm⫹gH
冕
0
共x,y,⬘,t兲d⬘(7)
where ⫽density of water computed as a function of salinity 共Sin
ppt兲and temperature 共Tin °C兲via an equation of state. The hori-
zontal pressure gradients are obtained by using Leibnitz’s rule
1
Px⫽g
x⫹gd⫹
0
冕
0
冉
x⫹
x
冊
d⬘(8a)
1
Py⫽g
y⫹gd⫹
0
冕
0
冉
y⫹
y
冊
d⬘(8b)
where 0⫽1,023 kg/m3⫽reference water density applicable to
Hong Kong waters. The forces Fxand Fyin the momentum equa-
tions 共1兲and 共2兲represent the horizontal Reynold’s stresses
Fx⫽H
冉
2u
x2⫹
2u
y2
冊
,Fy⫽H
冉
2v
x2⫹
2v
y2
冊
(9)
where H⫽horizontal eddy viscosity coefficient which is much
larger than the vertical eddy viscosity. The horizontal viscosity
coefficient His defined by H⫽2D⫹3D⫹mol and the vertical
eddy diffusivity coefficient v⫽3D⫹mol . Here the 2D part 2D
is associated with the contribution of horizontal motions and forc-
ings that cannot be resolved 共sub-grid-scale turbulence兲by the
horizontal grid; this coefficient is obtained by calibration. The 3D
part 3D is referred to as the 3D turbulence and is computed
following the standard two-equation turbulence model 共see
below兲.mol is the molecular viscosity.
Transport of Conservative Constituents
The transport of salt and heat is modeled by a conservative trans-
port equation
关共d⫹兲C兴
t⫹
关共d⫹兲uC兴
x⫹
关共d⫹兲vC兴
y⫹
共C兲
⫽共d⫹兲
冉
x
冋
Dh
C
x
册
⫹
y
冋
Dh
C
y
册
冊
⫹1
d⫹
冋
Dv
C
册
⫹Sc(10)
where Dh⫽horizontal diffusivity; and Sc⫽source/sink term.
Turbulence Closure
A standard two-equation turbulence model is used for turbulence
closure 共Launder and Spalding 1974; Rodi 1980兲. The transport
equation for the turbulence kinetic energy kand the rate of dissi-
pation of k() are nonlinearly coupled via the production and
dissipation terms and the eddy diffusivity Dv. The transport
equations for kand are given by
k
t⫹uk
x⫹v
k
y⫹
d⫹
k
⫽1
共d⫹兲2
冉
Dv
k
冊
⫹Pk⫹Bk⫺(11a)
JOURNAL OF ENVIRONMENTAL ENGINEERING © ASCE / MAY 2004 / 537
t⫹u
x⫹v
y⫹
d⫹
⫽1
共d⫹兲2
冉
Dv
冊
⫹P⑀⫹B⑀⫺c2⑀
2
k(11b)
The production terms Pk,Pand buoyancy source terms Bk,B
are defined as
Pk⫽vV1
共d⫹兲2
冋
冉
u
冊
2
⫹
冉
v
冊
2
册
(12a)
P⫽c1
kPk(12b)
Bk⫽
vV
g
0
1
d⫹
(12c)
B⫽c1
k共1⫺c3⑀兲Bk(12d)
where the empirical model calibration constants are adopted as
c1⫽1.44, c2⫽1.92, and c3⫽1.0 for stable stratification and
c3⫽0.0 for unstable stratification.
The vertical eddy viscosity vV共referred to earlier as 3D)is
determined by
vV⫽c
k2
(13)
with the empirical constant c⫽0.09. The horizontal eddy diffu-
sivity DHand vertical eddy diffusivity DVare assumed the same
as the corresponding viscosities.
Boundary Conditions
In practical applications such as the Pearl River Estuary model
共Fig. 1兲, the model uses orthogonal curvilinear coordinates 共,兲.
Application of orthogonal curvilinear coordinates yields a bound-
ary fitting in the horizontal plane. The free slip formulation is
adopted. The boundary conditions for the free surface, the seabed,
and the open boundary are as follows.
Vertical Boundary Condition
In the coordinate system, the free surface and bottom corre-
spond to a plane. The vertical boundary conditions for the ver-
tical velocity are given by
共⫺1兲⫽0 and 共0兲⫽0 (14)
Bed Boundary Condition
At the seabed, the boundary conditions for the momentum equa-
tion are
V
H
u
冏
⫽⫺1
⫽
bx
(15a)
V
H
v
冏
⫽⫺1
⫽
by
(15b)
where b⫽bottom shear stress; and bx and by⫽xand ycompo-
nents computed from the velocities in the first layer above the bed
via a standard quadratic law.
The turbulence quantities are prescribed via a local equilib-
rium assumption, with
k⫽⫺1⫽u*b
2
冑
c
,
兩
⫽⫺1⫽u*b
3
z0(16a)
where u*b⫽
冑
b/;⫽the von Ka
´rma
´n constant⫽0.41; and
z0⫽roughness height obtained by calibration. The logarithmic ve-
locity profile is assumed in the bottom boundary layer
u共z兲⫽u*b
ln
冉
z⫹z0
z0
冊
(16b)
The parameter z0can be linked to the actual geometric roughness
as a fraction of the RMS value of the subgrid bottom fluctuations.
For rough walls, z0⫽ks/30, where ks⫽Nikuradse roughness
length scale and is determined experimentally.
Surface Boundary Condition
At the free surface, the boundary conditions for the momentum
equations are
V
H
u
冏
⫽0
⫽
s
cos (17a)
V
H
v
冏
⫽0
⫽
s
sin (17b)
where ⫽angle between the wind stress vector and the local di-
rection of the grid line y⫽const. The magnitude of the wind shear
stress is determined by a quadratic expression
兩
s
兩
⫽aCd共U10兲U10
2(18a)
where a⫽density of air; Cd⫽wind drag coefficient; and
U10⫽wind speed 10 m above the free surface. In the present
study, the measured wind speed recorded by the Hong Kong Ob-
servatory at Waglan Island, at Z⫽55.8 m above mean sea level
共MSL兲, is adopted. This wind speed is corrected to U10 using an
empirical relation that has proved reliable by analysis of historical
data 共Chin and Leong 1978兲
U/U10⫽0.233⫹0.656 log10共Z⫺4.75兲(18b)
where Z⫽elevation above MSL. The wind drag coefficient Cdis
assumed to vary linearly with wind speed from 0.00063 to
0.00723 in the range of U10⫽0 –100 m/s 共Delft Hydraulics 1997兲.
In the presence of wind, the turbulent kinetic energy and its
dissipation rate are specified as
k
兩
⫽0⫽u*s
2
c,
兩
⫽0⫽u*s
3
zs(19)
where zs⫽roughness length obtained by calibration.
Open Boundary
Fig. 1 shows the Pearl Estuary model grid. Along open bound-
aries, water levels are specified by a time history of water levels
using a number of tidal constituents derived from long-term tidal
data 共east, south, and west boundaries兲. A linear vertical concen-
tration profile is specified at the open boundaries for an inflow
condition.
Numerical Solution
A staggered grid is used for the discretization of the horizontal as
well as the vertical gradients; the water level 共pressure兲and con-
centration 共salinity兲points are defined in the center of a cell,
whereas the velocity components are defined on the cell faces.
The horizontal diffusion terms are centrally differenced while an
538 / JOURNAL OF ENVIRONMENTAL ENGINEERING © ASCE / MAY 2004
upwind scheme is used for the advection terms. For the time
integration of the horizontal diffusion term, the Crank-Nicholson
method is applied; source terms are integrated explicitly. The so-
lution of the horizontal momentum and continuity equation pro-
ceeds via a cyclic implicit procedure using the alternating direc-
tion implicit scheme 共Stelling 1984兲. In the vertical direction, the
fluxes are discretized with a central scheme; the time integration
is fully implicit. Further numerical details can be found in Stelling
共1984兲and Delft Hydraulics 共1997兲.
The Delft3d model used in this study has been thoroughly
tested against analytic solutions of long wave propagation 共Ap-
pendix I兲. For cases in which the analytical model with linearized
bottom friction is applicable 共Lynch and Gray 1978兲, the com-
puted elevations and velocities are in very good agreement with
the analytical solutions.
Numerical Model Results of Pearl Estuary Model
Pearl Estuary Grid
Fig. 1 shows the Pearl River Estuary model set up for studying
the tidal circulation and water quality of Hong Kong’s coastal
waters. A 206⫻141 boundary-fitted orthogonal grid is used, with
ten uniformly distributed vertical layers; the grid in the northeast-
ern waters is specially refined to study algal bloom transport pat-
terns. Tidal forcing is applied along the eastern, western, and
southern boundaries; nine tidal constituents 共derived from an ex-
tended harmonic analysis of long term tidal data兲are used to
generate a time history of predicted water levels at the open
boundaries; they are O1, P1, K1, N2, M2, S2, K2, M4, and MS4.
The mean sea level conditions are set at the different boundary
stations from a low of 1.18 m in the southwest of the boundary
station to 1.31 m in the northeast of the boundary station 共for the
dry season兲. The measured salinities for both the dry and wet
seasons are used in the open boundaries. For the dry season, a
vertically uniform salinity of 34 ppt is specified at the ocean
boundaries 共east, south, west兲for inflow, except in the northwest
boundary station surface layer near the Pearl River Estuary, where
S⫽30 ppt is prescribed. Seasonal mean freshwater flows from the
nine outlets of the Pearl River are prescribed at the inflow bound-
aries 共the locations of five major discharge outlets are indicated in
Fig. 1 and the detailed discharges are listed in Table 1兲.
The horizontal eddy viscosity and diffusivity 共2D component兲
are all set to 1 m2/s. A Manning coefficient of n⫽0.020 is used
for shallow water; in deeper water 共greater than 25 m兲,n
⫽0.026 is used. These values for viscosity/diffusivity and bottom
friction were obtained by calibration and validation against exten-
sive tidal level, velocity, and salinity measurements 共Delft Hy-
draulics 1997, 1998兲. The model is run from an initial state ob-
tained by running the model from a cold start; typically the
transients are dissipated within 1–2 tidal cycles.
Tidal Circulation in Hong Kong Waters
The hydrography of Hong Kong’s coastal waters is mainly influ-
enced by three factors: tidal currents, monsoon-affected ocean
currents, and Pearl River discharges. In the dry season, the salin-
ity is approximately vertically homogenous and ranges from
about 34 ppt at the open boundary to 15–20 ppt at the mouth of
the Pearl Estuary near Shenzhen 关Fig. 3共a兲兴. There is no signifi-
cant difference between surface and bottom salinity in winter
共Fig. 3兲. In the wet season, however, tidal currents and the Pearl
River discharge create significant vertical and horizontal salinity
gradients. Compared to the dry season, there is much more sig-
nificant salinity stratification in the western part of the Pearl Es-
tuary 共Fig. 4兲. Surface and bottom salinity differentials of up to
7–10 ppt are commonly observed in the northwest areas of Hong
Kong. The eastern waters are relatively sheltered from the Pearl
River; these waters are more oceanic with typical salinity of
32–34 ppt.
In general, tides in Hong Kong are mixed and mainly semidi-
urnal. The range of spring tide and neap tide is from 1.0 to 2.1 m.
Tidal currents are determined by the interaction of ocean tides
with the local bathymetry. In the dry season, the currents in Hong
Kong waters are mainly from SE to NW through Victoria Harbor
and northwest up the Pearl River during flood 关Fig. 5共a兲兴 and
from Pearl River Estuary to southeast water during ebb 关Fig.
5共b兲兴. The tidal flow in the East Lamma Channel 关Figs. 5共a and
b兲, close-up view兴is mainly from the southeast to northwest di-
rection during flood and in the opposite direction during ebb.
Tidal currents south of Lamma Island generally flow from the
northeast to the southwest direction. Fig. 6 shows the detailed
flow field at midflood and beginning of ebb in Mirs Bay. It can be
seen that the flow in the northern part of Mirs Bay is mainly
characterized by an anticlockwise circulation. In the south of the
bay, the circulation is more likely in a clockwise direction. Both
types of circulation patterns are present in flood and ebb.
In the wet season, the flow pattern 共not shown兲is heavily
influenced by the Pearl River and is much more complicated than
the dry season flow, with significant vertical stratification.
Salinity-driven circulation is evident. The flow is mainly from
west to east. The residual currents are mainly from NW to SE in
Victoria Harbor and western areas, although currents in both di-
rections can also be found through northwestern waters and east
of the Lamma Channel. In southern waters, the flows are mainly
from W/SW to E/NE.
This study mainly focuses on the effect of the tidal circulation
and wind on the 1998 red tide that occurred toward the end of the
dry season.
Algal Bloom Tracking
Red Tide Tracking Model
The aim is to study the transport of an algal bloom initiated in the
northeast Hong Kong waters 共as frequently observed兲. In particu-
lar, the relation between tidal circulation and the reported se-
quence of events from March 18 to mid-April 1998 关Fig. 2共a兲and
Table 2兴is studied thoroughly. Initial extensive computations
using the original 共coarser兲Pearl Estuary grid led to the adoption
of a much more refined grid for the northeastern waters 共including
Table 1. Dry Season Pearl River Discharges from Nine River Outlets
River outlet Discharge
共m3/s兲
Humen 795
Jiaomen 700
Hongqili 225
Hengmen 441
Muodaomen 1,145
Jitimen 205
Hutiaomen 240
Aimen 365
Deep Bay 2.5
JOURNAL OF ENVIRONMENTAL ENGINEERING © ASCE / MAY 2004 / 539
Mirs Bay, Tolo Harbor, and Port Shelter兲shown in Fig. 1; the
computations are performed using two, four, eight, and ten layers.
In the area of interest 共northeast and southern waters兲, the grid
size varies from 70 m to 1.75 km; in the ocean waters next to the
western open boundary, a coarse grid up to 6 km is used. A time
step of ⌬t⫽1 or 2 min is adopted, with a Courant number
(⫽⌬t
冑
gh/⌬x) in the range of 0.24–1.8. The tidal circulation is
computed for the typical dry and wet seasons and extensive
drogue tracking experiments are performed. The massive red tide
of 1998 is then examined using the actual wind data from Febru-
ary to April 1998. The daily-averaged wind data at Waglan Island
共Hong Kong Observatory 1998, 1999兲are used.
Fig. 3. Computed salinity in dry season: 共a兲Surface and 共b兲bottom salinity
Fig. 4. Computed salinity in wet season: 共a兲Surface and 共b兲bottom salinity
540 / JOURNAL OF ENVIRONMENTAL ENGINEERING © ASCE / MAY 2004
The drogue tracking simply follows the path of a floating ob-
ject transported by the surface current 共i.e., the current in the
upper layer兲. In the drogue tracking computations, the drogue is
released after 5 days flow simulation, when the flow has reached
a dynamic steady state 共for the typical dry and wet seasons兲.In
view of the extensive drogue tracking simulations that need to be
made on the entire Pearl Estuary grid, the number of vertical
layers has been suitably reduced. Computations have been made
with a two-layer model 共0.5:0.5 vertical distribution兲and a four-
layer model 共with 0.1:0.2:0.3:0.4 vertical distribution兲, and the
results compared with those from an eight-layer model 共Appendix
II兲. Based on the results a two-layer model is considered inad-
equate; while a four-layer model gives accurate results and retains
reasonable computational economy for the large amount of
drogue tracking.
An intensive study in drogue tracking for March–April 1998 is
undertaken using a four-layer Pearl Estuary grid, with a Courant
number of around 0.8. As a drogue track of interest would depend
on the release location as well as the exact time of release, it
would be futile to enumerate the drogue tracks released in all
locations within northeastern waters during the months of Febru-
ary, March, andApril of 1998—or the general dry season months.
We thus proceed heuristically. Generally, a drogue is released
from the surface layer at the middle of a grid—for release posi-
tions throughout Mirs Bay, Tolo Harbor, and Daya Bay, see Fig.
7. Numerical experiments show that the drogue path for such a
release can almost describe the general path of movement of a
bloom initiated anywhere within the same grid, or within the
same region. In general, numerous particles released from differ-
ent positions within one grid would have similar drogue track
paths within Mirs Bay and even down to the southeast of Hong
Kong Island 共see later discussion, Fig. 11兲; these drogue tracks
start to diverge only after they arrive at the southeast of Hong
Kong Island. This is generally true in regions where the velocity
Fig. 5. Computed surface velocity in dry season during: 共a兲Flood tide and 共b兲ebb tide
JOURNAL OF ENVIRONMENTAL ENGINEERING © ASCE / MAY 2004 / 541
has a definite direction or weak velocity gradients; however, in
regions of significant velocity gradients, particles released from
different positions within the same grid may drift along different
paths. Through such drogue tracking experiments for a large num-
ber of releases at different tidal stages, a good idea of the general
trend of the red tide movement can be gained. The possibility that
a red tide could be transported to the southern waters and East
Lamma Channel can also be reliably assessed.
For a four-layer calculation on a 450 MHz PC, it generally
takes 30 h to run a one-month flow simulation and drogue track-
ing.
Massive Red Tide of Spring 1998
According to newspaper reports based on scattered observations
of the fishermen, the 1998 red tide appeared first in the northeast
Mirs Bay. It was sighted in the Kat O area on March 18, 1998 by
the Hong Kong Agriculture and Fisheries Department; the red tide
then appeared to be transported south toward and into Port Shel-
ter, and further westward to Lamma Island, where the most severe
fish kill occurred 关Fig. 2共a兲兴. There is also speculation that the red
tide may have originated from Daya Bay and been transported to
the southeast of Mirs Bay and then northward to the Kat O area.
These reports are not based on actual data or measurements. The
generally overcast sky conditions prevailing in March and April
in Hong Kong also make it difficult to extract the movement of
this massive red tide from satellite photos using remote sensing
techniques; so far, no successful attempt has been reported.
In addition to the informal reports and sightings, cell counts of
dominant algal bloom species were also measured on water
samples collected in fish farms or on beaches by the Agriculture,
Fisheries, and Conservation Department of the Hong Kong Gov-
ernment. Table 2 summarizes all the measurements of the harmful
algal bloom 共HAB兲species Karenia digitatum recorded during
the 1998 red tide. It can be seen that the measurements are gen-
erally consistent with the news reports. The HAB was first mea-
sured in Kat O on March 18; it was subsequently detected at the
Leung Shuen Wan fish culture zone 共FCZ兲at the mouth of Port
Shelter on March 23, apparently being transported to inner Port
Fig. 6. Computed surface velocity in Mirs Bay for typical dry season
during: 共a兲Flood and 共b兲ebb
Table 2. Measured Algal Cell Counts of the Harmful Algal Bloom Species Karenia digitatum during the Spring 1998 Hong Kong Red Tide
Time Location Cells/mL
March 18, 1998 O Pui Tong 共Kat O兲共FK兲3,480
March 23, 1998 Leung Shuen Wan 共southeast of Port Shelter兲共FK兲820
April 3, 1998 Kai Lung Wan 共inner Port Shelter兲共FK兲2,220
April 8, 1998 Lo Tik Wan 共East Lamma Channel兲1,760
April 9, 1998 Tung Lung Chau 共FK兲73,700
April 9, 1998 Ma Wan 14,380
April 10, 1998 Cheung Sha Wan 共Lantau Island兲共FK兲82,300
April 10, 1998 Tap Mun 4,440
April 11, 1998 Lo Tik Wan 共FK兲225,500
April 11, 1998 Yung Shue Au 共Tolo Harbour兲5,200
April 12, 1998 Lo Tik Wan 共East Lamma Channel兲共FK兲12,620
April 12, 1998 Repulse Bay 共South of Hong Kong Island兲34,300
April 12, 1998 Yim Tin Tsai 共Tolo Habour兲38,200
April 13, 1998 Chung Hom Kok 共South of Hong Kong Island兲17,950
April 13, 1998 Middle Bay 共South of Hong Kong Island兲19,075
April 13, 1998 Repulse Bay 28,900
April 13, 1998 Shek O 共Southeast of Hong Kong Island兲35,850
April 13, 1998 South Bay 共South of Hong Kong Island兲10,560
April 14, 1998 Cheung Chau 共Tung Wan兲7,875
April 14, 1998 Chueng Chau 共Kwun Yam Wan兲11,510
April 14, 1998 South Bay 29,150
April 14, 1998 Shum Wan 共Tolo Harbour兲19,900
April 15, 1998 Kwun Yam Wan; Shek O; Repulse Bay 690; 370;260
April 15, 1998 Lo Tik Wan; Sok Kwu Wan 1; 480;520
Note: Data from Hong Kong Agriculture, Fisheries and Conservation Department. FK⫽fish kill.
542 / JOURNAL OF ENVIRONMENTAL ENGINEERING © ASCE / MAY 2004
Shelter 共Kai Lung Wan FCZ兲by April 3. By April 8–9, high
concentrations of the HAB species were detected at Tung Lung,
Ma Wan, and Lo Tik Wan 共East Lamma Channel兲. Concentrations
as high as 225,500/mL were recorded on April 11 at Lo Tik Wan
FCZ 共where all the fish stock was destroyed within a couple of
days兲. Around April 12–13, high concentrations of the order of
10,000/mL were also measured at several important beaches fre-
quented by tourists on the south of Hong Kong Island 共Repulse
Bay, Chung Hom Kok, Middle Bay, Shek O兲. The red tide also
appeared to be transported to Cheung Chau 共west of Lamma Is-
land兲by April 14. The data suggest that the HAB also appeared in
Tolo Harbor 共Yung Shue Au on April 11, Yim Tin Tsai on April
12, Shum Wan on April 14兲at around the same time as or after the
devastating red tide hit Lo Tik Wan during April 11–12.
During this period, red tide outbreaks of other nonharmful
species also occurred, e.g., Porocentrum minimum in Yung Shue
Au and Yim Tin Tsai during March 25–31 and also in early April;
however, these red tides were not associated with fish mortalities
and have not been included in Table 2.
In order to unravel what really happened in spring 1998,
drogue tracking is performed for a release from different locations
in Mirs Bay and at different stages of the tidal cycle and different
wind conditions. This tracking is performed both for the typical
dry season and for spring 1998.
Drogue Tracking for the Dry Season in General
First, the algal bloom tracking is performed using the synthetic
tidal boundary conditions for March and April 1998 but with a
mean wind for the dry season. In general, for the dry season the
average measured wind direction in Hong Kong is 45° 共northeast
direction兲and wind speed is U10⫽5 m/s 共Delft Hydraulics 1997,
1998兲; these typical 共constant兲values are used. Adrogue/bloom is
released from different locations within Mirs Bay, Tolo Harbor,
and Daya Bay; extensive drogue tracking experiments are per-
formed for a release at different tidal conditions: March 11
共spring tide兲, March 16, March 20 共neap tide兲, and March 27
共spring tide兲, and early April. Based on a detailed study, the fol-
lowing points can be made and are illustrated in Fig. 7, which
shows the drogue tracks for the representative releases. It is found
that a drogue released in the northern part 共even Kat O兲of Mirs
Bay or in Tolo Harbor in the dry season would not likely travel
down south. Typically, the drogue follows a counterclockwise
关Figs. 7共a–c, h, and m兲兴 or clockwise path 关Fig. 7共g兲兴, and ends
up in the Kat O area, or is further transported from Kat O down to
Tolo Harbor 关Figs. 7共b, c, f, and k兲兴.A bloom in the Kat O region
may originate from Yian Tian 关Fig. 7共a兲兴, Xiao Mei Sha 关Fig.
7共b兲兴, or northeast of Mirs Bay 关Figs. 7共c and g兲兴 6–9 days earlier.
It is also possible for a bloom initiated in Nan Au, northeast Mirs
Bay, or the Tap Mun area to be transported directly into Tolo
Harbor 关Figs. 7共d, j, and l兲兴. A bloom located slightly east of Kat
O关Fig. 7共i兲兴 or along the north shore near Xiao Mei Sha 关Fig.
7共f兲兴 may be transported toward Starling Inlet. By the nature of
the counterclockwise circulation in Mirs Bay 共Fig. 6兲, a drogue
released around the Tap Mun area may move in two directions: it
can move northward toward Tolo Channel if released slightly
north of Tap Mun or southward down in the Tai Long Wan direc-
tion if released slightly south of Tap Mun 关Fig. 7共l兲兴. A bloom
from northeast Mirs Bay would also follow the counterclockwise
circulation toward Xiao Mei Sha, Yian Tian, and the northwest
coast of Mirs Bay 关Figs. 7共m, o, and p兲兴.
In general, it is extremely unlikely that a bloom initiated in the
northern part of Mirs Bay, the Kat O area, or Tolo Harbor would
be transported down to the East Lamma Channel in the typical
dry season. Fig. 7 shows clearly that a bloom from the Nan Au or
Tap Mun area can be transported along a NE/SWpath to Tai Long
Wan 关Fig. 7共j兲兴, or southeast of Lamma Island 关Figs. 7共n–p兲兴.
Typically, blooms transported southward along this path would
drift toward Victoria Harbor and less likely drift to East Lamma
Channel. The time required from Mirs Bay to East Lamma Chan-
nel is listed in Table 3.
Fig. 7. Surface drogue tracking for a release in different parts of Mirs Bay and at different tidal stages in typical dry season 共arrow indicates
drogue release point; output interval⫽3 days兲
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On the other hand, a bloom from Daya Bay would always be
transported in the southeast direction toward the southeast of
Lamma Island 关Figs. 7共e and q兲兴. It takes 6–12 days for a bloom
from Daya Bay reach southeast of Lamma Channel. The presence
of a strong wind can reduce the travel time of a surface drogue
dramatically.
Drogue Tracking in Spring 1998
Fig. 8 shows the measured wind speed and direction at Waglan
Island during March and April 1998; the wind speed corrected to
10 m above MSL, U10 , is also shown. It can be seen that the wind
is quite strong at the beginning of March and on March 22–23
and also relatively strong at the beginning of April. The wind
direction is mostly NE during March, but changed direction on
April 1, 4, and 6–7 to northwest/northerly; the wind direction
then changed in a clockwise manner to the SE direction during
April 7–12. The tidal elevation and velocity in the East Lamma
Channel from mid-March to mid-April are shown in Fig. 9; the
almost diurnal tide during April 3–6 can be noted.
For the actual wind conditions in March–April 1998, similar
extensive numerical drogue tracking as previously described is
performed for releases from different tidal periods in both March
and April. Figs. 10共A and B兲show a summary of representative
tracks. As in the dry season, a drogue released fromYian Tian and
Xiao Mei Sha follows a counterclockwise path 关Figs. 10共A—a
and b兲兴 or from Northeast Mirs Bay along a clockwise path 关Fig.
10共A—c兲兴 toward the Kat O area. This suggests that the observed
red tide at Kat O on March 18 共Table 2兲may well have initiated
in Yian Tian, Xiao Mei Sha, or Northeast Mirs Bay around March
10. A bloom initiated northeast of Mirs Bay or Nan Au can also
be transported into Tolo Harbor 关Figs. 10共A—d and f兲兴. The
bloom could drift from the Kat O area to Tap Mun, or pass Tai
Long Wan to southwest of Port Shelter, or move further down
even to Victoria Harbor 关Fig. 10共A—h兲兴. A red tide initiated in
Northeast Mirs Bay, Nan Au, or Tap Mun could have been trans-
ported to Tai Long Wan 关Figs. 10共A—e–g兲兴. This is consistent
with a reported red tide of unknown species in Tai Long Wan on
March 17 共not in Table 2兲. In particular, it appears the red tide in
Leung Shuen Wan on March 23 共Table 2兲may be caused by
blooms initiating from northeast of Mirs Bay around March 16
关Fig. 10共A—g兲兴. Compared to the typical dry season, the stronger
wind conditions in March–April 1998 increase the chance of
bloom transport toward Lamma Channel. Fig. 10共A—i兲shows
that a bloom could have been initiated at Nan Au on March 16
and been transported to Sok Kwu Wan in East Lamma Channel
on March 24 共due to the strong wind during March 22–23 and the
almost diurnal tide period兲. However, it is very unlikely that red
tide would be transported from north or northeast of Mirs Bay or
Tolo Harbor down to east Lamma Channel in March 1998.
The drogue tracks show clearly that blooms initiated in Nan
Au and Tap Mun in late March or early April can be transported
to East Lamma Island/southern waters several days later. The
bloom could possibly travel along the path from Nan Au to Tap
Mun and then down to the south beaches of Hong Kong Island or
East Lamma Channel 关Figs. 10共A—j, l, m, and o兲, Figs. 10共B—a
and b兲兴. This suggests that the red tide observed in the southern
beaches of Hong Kong Island 关Repulse Bay, Chung Hom Kok,
Middle Bay, Shek O; see Fig. 2共b兲and Table 2兴on April 12–14
mostly likely originated from the Nan Au area 关Figs. 10共B—b, g,
and h兲兴 or the Tap Mun area 关Fig. 10共B—f兲兴 5–10 days earlier. It
is also possible for a bloom from the Nan Au area to pass Tung
Lung into Victoria Harbor and be transported to the Ma Wan area
on April 9 关Fig. 10共A—p兲and Table 2兴. Most importantly, the red
tide at Lo Tik Wan on April 9–12 most likely originated from the
Nan Au area 关Figs. 10共B—a and c兲兴. We note that a bloom could
drift down even from the Kat O area, passing through south of
Port Shelter to southeast of Lamma Island in this special period
关Fig. 10共B—e兲兴.
Fig. 8. Daily prevailing wind at Waglan Island in March and April
1998 Fig. 9. Tidal elevation and current at East Lamma Channel during
3/16/98–4/15/98
Table 3. Travel Time from Key Locations in Mirs Bay in Typical Dry Season
From Yian Tian KatO Nan Au Nan Au Ko Lau Wan 共or Tap Mun兲Nan Au
To Kat O Tolo Channel Tolo Channel Ko Lau Wan East of Lamma Channel East of Lamma Channel
Days 5–6 3–9 3–12 2–3 3–8 5–10
544 / JOURNAL OF ENVIRONMENTAL ENGINEERING © ASCE / MAY 2004
It is also interesting to see the difference between drogue
tracks in March/early April and those in mid-April 1998. From
March to early April, the blooms would likely move from the Nan
Au area westward toward Tap Mun and then southward toward
East Lamma Channel 关Figs. 10共A—i, j, m, and o兲; Figs. 10共B—a
and b兲兴. When the wind direction changes from NE to SE during
April 9–12, a bloom can travel directly from Nan Au or northeast
of Mirs Bay toward East Lamma Channel without passing the Tap
Mun area 关Figs. 10共B—g–i兲兴. The path of algal bloom during
April 9–12 is more clearly shown in Fig. 13 below 共gray path兲.
As in the dry season, it is very unlikely for a bloom initiated in
Daya Bay 共not shown兲to enter the East Lamma Channel 共drogue
moves in southwest direction toward southeast of Lamma Island
within 3–12 days兲.
Fig. 11 illustrates the difference in possible algal bloom paths
between 1998 and the dry season in general for a group of
Fig. 10. Hydrodynamic transport for a bloom initiated in different parts of Mirs Bay in spring 1998 共A and B兲. Output interval⫽3 days for
共A—a-h兲; 1 day for 共A—i-p兲and 共B—a-j兲.
JOURNAL OF ENVIRONMENTAL ENGINEERING © ASCE / MAY 2004 / 545
drogues released in Mirs Bay. It is clear that blooms initiated in
northeast Mirs Bay or the Tap Mun area have a much greater
tendency to be transported to East Lamma Channel and southern
waters. In spring 1998 blooms from northeast Mirs Bay can be
transported south and then westward toward East Lamma Chan-
nel 关Fig. 11共a1兲兴, while for the typical dry season these blooms
would more likely be transported to the north part of Mirs Bay or
Tolo Harbor. Based on all of the above results we conclude that
there are three possible sources for the observed HAB in East
Lamma Channel in spring 1998: 共1兲Nan Au; 共2兲Tap Mun area;
and 共3兲northeast of Mirs Bay.
Role of Hydrodynamic Transport
Based on a study of numerous drogue tracks and hypothesis test-
ing, the unusually strong wind in March 1998 and early April and
the change in wind direction from NE to SE during early April
共Fig. 8兲appear to play a major role in the massive red tide ob-
served in the southern waters of Hong Kong in April 1998. In
particular, the change in wind direction in early April resulted in
the creation of a clockwise gyre in Mirs Bay—which in turn
greatly facilitated the transport of blooms toward Lamma Island
and southern beaches. The change of wind direction from NE to
SE during April 9–12 also enhances the transport of the red tide
into the East Lamma Island around April 11.
Fig. 12 shows the typical surface velocity field for the north-
eastern waters and approach to Hong Kong and Lamma Islands
for both ebb and flood tides during April 7–12, 1998. It is seen
that, contrary to the characteristic counterclockwise circulation in
Mirs Bay 共Fig. 6兲, a clockwise gyre can be found in Mirs Bay.
This results in a distinct high velocity belt extending diagonally
from the Nan Au area to Port Shelter and southeast of Lamma
Island 关Figs. 12共a2 and b2兲and Fig. 13兴. Within this belt, the
velocity is much larger than in the surroundings; the southward
velocity is also considerably stronger than that for the dry season
in general. In Figs. 12共c1 and c2兲the computed surface current in
Fig. 11. Comparison of paths of groups of drogues for 1998 and
typical dry season
Fig. 12. Typical surface velocity field for April 1998 during period of southeast winds 共April 7–12兲;共right兲comparison with typical dry season
546 / JOURNAL OF ENVIRONMENTAL ENGINEERING © ASCE / MAY 2004
the middle of Mirs Bay 共Location A兲and the mouth of Port Shel-
ter 共Location B兲in spring 1998 共dashed line兲is compared with
that for the dry season in general 共solid line兲. It can be seen that
during spring 1998 the southward 共negative兲velocity is signifi-
cantly higher than in the dry season—this no doubt contributed to
the transport of any red tide that was initiated in Mirs Bay.
A close examination of the circulation in April revealed the
following. A consistent clockwise circulation was formed in the
northeast of Mirs Bay starting from April 5, 1800 hrs 共the starting
time of the ebb tide兲. The formation of this distinct clockwise
gyre appears to be related to the clockwise change in wind direc-
tion from northerly winds on April 4 共360 N兲, April 5 共50 NE兲,
and April 7 共360 N兲, to SE winds during April 7–9; this change in
wind direction occurred under almost diurnal tidal conditions.
The longer flooding and ebbing periods provided the chance to
maintain the clockwise circulation. If the wind direction is
changed to 45 NE from April 6 to 12, the clockwise circulation in
north Mirs Bay is still maintained. However, if the wind is
changed to 45 NE from April 4 and maintained in this direction,
the circulation in Mirs Bay is no different from that found in the
typical dry season 共Fig. 6兲, with a characteristic counterclockwise
gyre. Likewise, if the actual measured wind direction in 1998 is
shifted backward in time by one week 共when the tide is semidi-
urnal兲, no clockwise circulation is formed.
Fig. 13 shows the computed surface current field in the north-
eastern and southern waters for both flood and ebb tides. Based
on the drogue tracking patterns, the path where an initiated bloom
could possibly be transported to the East Lamma Channel is in-
dicated by the gray strip. It seems highly unlikely that the fish
farms in the East Lamma area would be affected by a bloom
originating outside this ‘‘strip of influence.’’ Computed velocities
in the East Lamma Channel show that phytoplankton at the sur-
face can be transported in the NW direction along the channel
during a flood tide for an extended period of almost 10 h. Com-
pared to the normal dry season, the surface current near Lamma
Island has increased current speed toward the NW direction 共more
negative velocities兲up the East Lamma Channel 共Fig. 9兲.
It is apparent that any blooms initiated in the northeast of Mirs
Bay during this period would very likely be transported by this
clockwise gyre to the Nan Au area and then into the high velocity
belt 共‘‘gray strip’’兲to the southeast of Lamma Island 共Fig. 13兲.
The persistent SE wind during the four-day period from April 9
also would then drive the bloom to the East Lamma Channel. This
is illustrated by the close-up view of float tracks released within
the gray strip 共Fig. 14兲. Compared to the typical dry season situ-
ation 关Fig. 14共b兲兴, the bloom within the gray strip would more
likely enter the East Lamma Channel under 1998 real wind con-
ditions 关Fig. 14共a兲兴. During a diurnal flood tide, it is highly prob-
able for a bloom inside the gray strip to enter the East Lamma
Channel 共Lo Tik Wan area兲关Fig. 14共c兲兴. However, under a se-
midiurnal spring tide, the bloom would stay for less time inside
the East Lamma Channel 关Fig. 14共d兲兴 and would more likely be
transported to the southeast of Hong Kong Island or to the south
beaches of Hong Kong Island rather than to Lo Tik Wan. This is
consistent with the red tide outbreaks observed in Repulse Bay,
South Bay, and Shek O in mid-April 共Fig. 2 and Table 2兲.
Fig. 13. Computed flood and ebb surface currents near Lamma Island during the period of 4/9/98 –4/12/98 共path of algal bloom track indicated
by gray strip兲
Fig. 14. Drogue tracks in Lamma Island area for releases from high
velocity belt in 1998 关output interval is 1 day for 共a兲and 共b兲; 6 h for
共c兲and 共d兲兴
JOURNAL OF ENVIRONMENTAL ENGINEERING © ASCE / MAY 2004 / 547
The algal bloom tracking behavior in the wet season 共not
shown兲is distinctly different. In contrast to the dry season where
a bloom initiated in Mirs Bay tends to move from the northeast to
southwest direction, the bloom would tend to move from the
northwest to the southeast direction, away from Hong Kong.
Conclusions
A calibrated 3D hydrodynamic model 共Delft3D兲has been applied
to study the hydrodynamic transport of red tides in Hong Kong
via extensive numerical drogue tracking experiments. The novel
hydrodynamic tracking of algal blooms has led to valuable in-
sights into algal bloom transport, and unraveled the cause of the
massive 1998 red tide and fish kill observed in Hong Kong’s
southern waters. It is found that, for a typical dry season, a red
tide initiated in the northeastern waters of Hong Kong 共north Mirs
Bay, Tolo Harbor兲or Daya Bay would not normally be trans-
ported into the East Lamma Channel. On the other hand, the
spring 1998 red tide is very much related to the hydrodynamic
transport. First, the red tide in Kat O in mid-March 1998 may
have originated from the Yiantian or Xiao Mei Sha area, or been
transported from Nan Au by the typical counterclockwise circu-
lation in Mirs Bay. Second, the red tides recorded in Tolo Harbor
in March–April 共some of which were not toxic兲could have origi-
nated from Nan Au or Kat O, or the Tap Mun area. Third, the
massive red tide observed in southern waters and East Lamma
Channel from April 9 to 16 may have originated in Nan Au,
northeast Mirs Bay, or the Tap Mun area. The change in wind
direction under diurnal tide conditions in early April gave rise to
a consistent clockwise gyre in Mirs Bay, which greatly enhanced
Fig. 15. Comparison of model prediction and analytical solution for long wave propagation in rectangular channel: 共1兲Constant depth and 共2兲
quadratic bottom bathymetry
Fig. 16. Comparison of model prediction and analytical solution for long wave propagation in annular channel with quadratic bathymetry: 共a兲
Model grid for annular channel and 共b兲predicted and analytic free surface elevation and velocity
548 / JOURNAL OF ENVIRONMENTAL ENGINEERING © ASCE / MAY 2004
the transport of blooms in these areas into the southern coastal
waters and into the East Lamma Channel bordering the Lo Tik
Wan and Sok Kwu Wan fish culture zones. However, it is unlikely
that the red tide in spring 1998 originated from Daya Bay as
speculated by the press.
It is our belief that the advective transport process is, to first
order, the most important. The useful insights gained herein can
aid greatly in disaster mitigation. For example, the general trans-
port pattern under different tidal and wind conditions reported
here can serve as a useful supplement to a real time red tide
warning system. At least, the present findings would contribute
substantially toward the interpretation of future red tide observa-
tions. It is recognized that algal bloom dynamics and other im-
portant factors such as turbulent diffusion, algal growth and sink-
ing, and vertical migration have been neglected; these need to be
addressed in more refined modeling in the future. It is also likely
that the high frequency of red tides observed in 1998 is related to
the water temperature. 1998 was the warmest year in Hong Kong
since records began in 1884; the annual mean air temperature was
24°C 共compared to a normal 23°C兲. In January 1998 the water
temperature rose sharply from 20 to nearly 24°C; recent eutrophi-
cation modeling of Tolo Harbor 共Arega and Lee 2002兲has shown
that this resulted in more algal growth and nutrient depletion
compared to other years.
Acknowledgments
This study was supported by a Hong Kong Research Grants
Council Group Research Project 共RGC/CA/HKU 2/98C兲. The as-
sistance of Dr. Anthony Lee of the Hong Kong Environmental
Protection Department in the Delft3D 共Pearl Estuary兲model is
gratefully acknowledged. The writers are indebted to Dr. Patsy
Wong of the Hong Kong Agriculture, Fisheries and Conservation
Department for providing the data of Table 2 and many helpful
discussions. The comments of Dr. Don Anderson and the anony-
mous reviewers on an earlier version of the paper are much
appreciated.
Appendix I. Validation of
Delft3D
Model
The hydrodynamic model adopted for this application, Delft3D,
has been tested for its accuracy; this gives an idea of the Courant
number at which accurate simulations should be performed. In
addition to the analytical tests reported herein, the Pearl River
Estuary model has separately been validated against extensive
tidal, salinity, and velocity data. Three test cases of long wave
propagation are reported below. The open boundary is subjected
to a single harmonic tidal forcing with period T⫽12 h, and the
Courant number is set as 0.24. For each case, a linearized bottom
friction coefficient is used in the analytical solution and the cor-
responding Manning coefficient in the Delft3D hydrodynamic
model 共which uses a quadratic friction law兲can be obtained by
equating the rate of work done over a tidal cycle. The analytical
solutions for the respective cases can be found in, e.g., Ippen
共1966兲and Lynch and Gray 共1978兲.
Rectangular Channel with Constant Depth
The rectangular channel has a length L⫽5,000 m, width Y
⫽500 m, and mean depth H0⫽10 m. 0⫽0.5 m is the amplitude
of the tidal forcing at the open boundary. The linear bottom fric-
tion coefficient is 0.0001; the corresponding Manning coefficient
can be shown to be 0.0225. The computed standing wave is com-
pared with the analytical solution in Fig. 15 共Case 1兲.
Rectangular Channel with Quadratic Bathymetry
For this case, the channel depth varies quadratically from9mat
the closed end to 24.95 m at the open end, with an initial bottom
slope of 1/7,500. An average Manning coefficient of 0.0323 is
used, corresponding to a linear bottom friction coefficient of
0.0001. The model predictions of tidal elevation 共at high tide兲and
velocity 共at midtide兲are compared with the analytical solution in
Fig. 15 共Case 2兲. It is seen that for both cases the prediction is in
excellent agreement with the analytical solution.
Annular Channel with Quadratic Bathymetry
The third test case is the radial flow in an annular section with
outer radius r2⫽50,000 m and inner radius r1⫽20,000 m. ⌬r
⫽5,000 m along a ray direction 关Fig. 16共a兲兴. The depth varies
quadratically as H(r)⫽H0关3r/2(r2⫺r1)兴2⫽H0(slope⫻r)2with
Fig. 17. Example comparison of numerical results for a grid with
different layers: 共a兲Computed velocity profile near Lamma Island
and 共b兲computed time history of surface velocity in south of Mirs
Bay
Fig. 18. Comparison of computed drogue tracks for grids with
different numbers of vertical layers 共same release from 4/10/98
LW, 1400 hrs; output interval⫽1 day兲
JOURNAL OF ENVIRONMENTAL ENGINEERING © ASCE / MAY 2004 / 549
H0⫽3m,r苸(r1,r2). The bottom slope parameter 共from inner to
outer radial direction兲is 0.00005. Hence the depth varies from 3
m at the closed end to 18.75 m at the open end. Atidal forcing of
0.1 m amplitude is applied at the outer boundary. A Manning
coefficient of 0.0357 is used, corresponding to a linear bottom
friction coefficient of 0.0001. The comparison between the nu-
merical prediction and the analytical solution is shown in Fig.
16共b兲; good agreement is again obtained. It should be noted that
the above serves to validate the accuracy of the numerical solu-
tion of the shallow water equations, excluding the two-equation
turbulence model; the adequacy of the turbulence model for the
vertical structure is supported by validation against salinity data.
Appendix II. Selection of Number of Model Layers
The vertical variation of horizontal velocity computed by using
different vertical layers is compared at key locations 关e.g., Fig.
17共a兲兴. The time variation of surface current for three vertical
model resolutions is also compared for many locations; Fig. 17共b兲
shows the time history of the surface current south of Mirs Bay
inside the gray strip. The results show that the four-layer compu-
tation gives results very close to those of the eight-layer predic-
tion, with the correct phase and occasional minor difference in
peak velocity. On the other hand, based on this result and other
analytical drogue tracking tests 共in exactly known flow fields兲, the
two-layer model will likely result in unacceptable errors. As far as
algal bloom tracking is concerned, it is judged that the four-layer
model is both efficient and of sufficient accuracy. Fig. 18 shows a
drogue tracking comparison between eight- and four-layer model
results. In general, the drogue paths are similar, although the
travel time may differ by up to 1–2 days for typical tracking
periods of two weeks.
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