A Numerical Study of the
Circulation and Drifter Trajectories of Cobscook Bay
Danya Xu, Huijie Xue, David A. Greenburg*
School of Marine Sciences, University of Maine,
Orono, ME 04469, USA
*Bedford Institute of Oceanography, Dartmouth, Nova Scotia
1006,Canada
Abstract
Cobscook Bay is situated in the easternmost part of Maine, US,
bordering Canada’s New Brunswick. Vigorous tidal
currents mix the water column rich of nutrients, which make this small bay very
productive. Rapid growth in salmon aquaculture has a great impact to the
ambient coastal environment. Since the intertidal flats occupy a large amount
of total bay surface area at low water, it
is necessary to include the wetting/drying process in numerical models when
simulating the circulation of Cobscook Bay. The 3D nonlinear finite element
ocean model Quoddy_dry is used in this study to examine the capacity of tides to flush
nutrients, pollutants and waste products from the inner reaches of Cobscook
Bay.
Driven by M2
tide and real-time winds, the modeled circulation agrees well with observation
data. Comparisons of time series from the model with in situ observations show
that the currents at the GoMOOS buoy J are almost back and forth following the
regular cycle of the semidiurnal tide.
Several passive drifter experiments are simulated using a Lagrangian
particle-tracking program, which agree very well with observed drifter
trajectories.
The fundamental mechanisms for exchanges between Cobscook Bay and the adjoining
Passamaquoddy Bay are strong flooding/ebbing tidal currents and to a less
degree the instantaneous local winds. Residence time is estimated for various
parts of Cobscook Bay. More experiments are being conducted to examine the
effects of multi-tidal constituents and baroclinicity.
1.Introduction
Cobscook
Bay is located at the easternmost part of Maine, on the border between the
United States and Canada, connected with Passamaquoddy Bay and offshore water
of Gulf of Maine at the mouth of the Bay of Fundy. Generally, Cobscook Bay and
Passamaquoddy Bay and adjacent water-land are called the Quoddy region.
Cobscook Bay has very complex
coastal line, many small islands lie around all water land and bays. It has
approximately 37 km2 of intertidal flats, compared to a total bay
surface area of about 74 km2 at low water (Larsen et al. 2004).
Because of the vigorous tidal current mixes the water column very well, the
exchange of nutrients with adjoining Passamaquoddy Bay and offshore water in
the Gulf of Maine occurs very frequently. Cobscook Bay was famous for its ocean
production and diversity of ecosystem. Since 1980s, salmon aquaculture has been
introduced in the Quoddy region, and aquaculture makes great contribution to
the local economy. But at the same time, the increasing density of salmon pens
leads to many environment problems: pollutants and wastes dispersion and
distribution, capacity of self clearness of the bay, seawater quality
decreasing, impact to benthos … All of these problems are closely
related to the circulation pattern and the residential time of the bay. This
report is going to summarize some preliminary results of a numerical study.
Brooks
(1992,1999,2005) is a pioneer of numerical study of the circulation and
residential time in Cobscook Bay. His Previous model work showed some special
features of the circulation pattern of Cobscook Bay. 3D numerical model POM and
ECOM-si were used to simulate the circulation driven by M2 tide and runoff from
Dennys River and Pennamaquan River. The models showed a bay wide averaged
flushing time of about 2 days, a pair of counter-rotating eddies that forms in
the central bay during each flooding tide. The model results are guidance but
the model resolution was relatively low, about 255m. So it did not resolve well
the narrow channels and consequently small-scale circulation features. At same
time, a significant shortcoming of these model studies is that there is no
wetting and drying process to simulate intertidal zone of Cobscook Bay.
Panchang et al
(1997) use a 2D model to study aquaculture waste transport at several sites
in Cobscook Bay, Even through this model resolution is 75m, higher than Brooks’ but they use the same topographic data, and the model grid
is rectangle, so the coastal line can not be well matched. There were no eddy
dipoles. In
panchang’s model, he considers the intertidal zone in
low water, but the inconsistent algorithm of drying/wetting process leading to
irregularities and rapid changes in some of the coastal area.
Recently, Dave
Greenberg et al (2005) test different finite element models Fundy,
QUODDY and QUODDY_dry
with same unstructured triangular mesh in Quoddy region, the model
represents well the complex shoreline and topography. The strong tidal currents
in Quoddy region are well simulated, but he focuses on Passamaquoddy Bay. The
resolution in Cobscook is comparable to that of Brooks. The agreement with the
tidal stations in Cobscook Bay is very poor with the model showing large
differences in both amplitude and phase with these observations. The model
resolution and the topography are inadequate for accurate modeling of this
subergion.
We hypotheses the
complexity of the coastal line and topography would induce many small-scale
circulation in Cobscook Bay. At the same time, intertial zone should be
included in circulation modeling. Multiple tidal constituents, wind force,
baroclinicity… all of these factors would greatly
affect the circulation pattern and Lagrangian trajectories in Cobscook Bay.
2. Method
2.1 Ocean
circulation model
Our
ocean model QUODDY_dry is an extension of QUODDY. QUODDY was developed by Lynch et al (1996)
and QUODDY is a 3D, fully nonlinear, free surface, finite element model
with turbulence closure scheme (Mellor and Yamada,1982), user can specify the
surface or lateral ocean boundaries. In QUODDY_dry, Greenberg et al
(2005) developed effective numerical technique to add and subtract intertidal
areas as the tide rises and falls. It has been used to test wetting/drying
process in idealized coast and Quoddy region successfully. The specific
intertidal algorithm and the model parameter details are described in Greenberg
et al. (2005).
Our study region
covered the entire Quoddy region. The work presented in this paper with same
model mesh with Greenberg’ except high resolution in
Cobscook Bay. The model
triangular mesh has more than 11,750 nodes and 19,557 elements. The
elements are unequal and the length of the element sides varies form 35 m to
3.88 km. Most of the smallest
elements are in Cobscook Bay and the area around Frye Island. At low water,
many tips of these regions will be exposed to land when sea surface dropped
below the mean level. The stability and consistent of the algorithm require
very high resolution in intertidal zone. Otherwise it is hard to keep mass
balance and energy balance in different tidal regime. The fine model mesh
resolves the coastal line very well. There are 21 vertical sigma layers follow
sinusoidal distribution, which has higher resolution near the surface and
bottom.
Model
topography range from 148m below the undisturbed surface to 5m above mean
sea level. In Cobscook Bay, most regions are very shallow, with water depth
less than 20 meters. Only in the main tidal channel, depths are greater than 20
meters.
2.2
Particle-tracking algorithm
The
Largangian Particle-tracking model Drog3ddt is developed
by Brain Blanton (1994). The original model only had the advection term, and particles
could move freely in all directions. Till now we don’t
have random walk term add to this tracer program. Users can set particles
transport only in horizontal plane without vertical movement to simulate
drifter dragged in fixed layer of water column.
2.3 Open
Boundary Condition
The M2 tide on the
open boundary was taken from a roughly calibrated model of the outer Bay of
Fundy (Greenberg, unpublished). These boundary amplitudes and the phases from
the outer Bay of Fundy model were adjusted to give a better fit to observation
data.
3. Results
3.1 Tidal
circulation
As the water depth
of Cobscook Bay is very shallow, only after 2-3 tidal cycles integration, the model
is almost stable. So the simulations were run for 3 days. The first two days
were as spin up. The 6th tidal cycle results were used to analysis.
A half-hour frame movie of the
depth averaged tidal current in Cobscook Bay over a full tidal cycle is present
here to show the change of the tidal current regime. At low water, at some tips
of the bay, when the sea level dropped below the mean water depth, these
regions (red lines) are intertidal zone. It can be seen that the dry area
gradually increases to its maximum at low tide and then shrinks until
disappeared at high tide. Once in ebbing time, the intertidal zone is gradually
built up, there is no current and sea surface elevation there cause these
regions are dry area. Only in flooding time, sea surface elevation and currents
reestablished in these regions. Most of the current in Cobscook Bay just do
back and forth movements follow the regular tidal cycle. The tidal current in
the central main channel is very strong, at mid flood or ebb, it could be greater
than 1.5 m/s. Most other bay region current is about few centimeters per
second. Current through Lubec Narrows attains a velocity of about 1.5m/s
northward during flood and the ebb surges flow southward as much as 2m/s. The strongest current is
near Mulholland Point, Campebello Island. This depth averaged current speed is
comparable with NOAA’ Coast Pilot (2005), according it
note, ebbing currents are stronger than the floods in Lobec Narrows with
velocity of about 8 knots (about 4m/s) during spring tides. Such great tidal
currents attracted many proposals make Lubec Narrows as one of the best sites
of tidal-power electricity generation plant of the world.
Because the ratio of
the width to the length of main water pathway of Cobscook Bay is too small, the
tidal current regimes show there is a little phase lag between the eastern and
the western ends of the bay when in transform period of flooding/ebbing or vice
versa. From the snapshot of
these periods, it shows clearly that the water in the east is still
falling/rising near the time of low/high water while the currents are reversing
in the west. So, in the central bay, water may convergence
when at early flooding or divergence at
early ebbing. At early flooding,
in the eastern part of the bay, water flow westward meet still out-flowing
current of west part of the bay at Birch and Gove points. An anticlockwise
rotating eddy occupied the Outer Bay. More interestingly, a pair of counter
rotating eddy dipoles are formed east of Leighton point and Denbow neck fill
the central bay, the clockwise rotated southern eddy supplies water to the
rising tide in South Bay, a part of water of the anticlockwise rotated northern
eddy flow into Pennamaquan and East Bay. On the contrary, at early
ebbing, divergence formed in the central bay and the eddy dipoles appears
again but this time the eddies rotated direction are reversed with their
counterparties in early flooding. The formation of these eddy dipoles is
because of the convergence or divergence of the water at central bay produced
by the current phase lag of east and west part of the bay. This interesting
phenomena and mechanism never been reported in the previous model studies. Brooks’ model (1999,2004) described a pair of counter-rotating
eddy dipoles form on each side of the main channel in the central part of the
bay as the flood intensifies. Obviously, these are not the eddy dipoles as we
described above. However, we also find the existence of the eddy dipoles Brooks
(1999,2004) inferred in our model and the formation mechanism is similar with
he claimed.
As for there is no
wetting/drying process in Brooks’ model, so his model
shows the eddy dipoles formed as the flood intensifies. But our model shows the
eddy dipoles formed as flood weaken and it could persist to early ebbing. Falls
island right impedes at the center of main tidal channel as a obstacle to
block water move in or out, that means a part of water have to turn back around
Leighton and Denbow necks instead pass the narrow neck of tidal channel flow
into west part of the bay when all arms of Cobscook Bay at high water. Only after mid
flood, intertidal zones close to coastal line are in high water, the “superfluous” water turn back and
form the
pair of eddy dipoles on each side of the main channel.
From tidal
averaged residual current, it shows obviously that most of residual
currents are very small, less than 5 centimeter per second. Currents around
Falls Island and in Lubec narrows are very strong. The depth-averaged residual
current in Lubec Narrows is about 40cm/s. Assume this channel is about 100m
wide and 5m deep, so over a tidal cycle about 0.009 km3 seawater
through Lubec Narrows leave Cobscook Bay and flow into Gulf of Maine. Compare
to the low water and intertidal volumes in Cobscook Bay of 0.56 km3
and 0.49 km3 (McGrail,1973) respectively, this volume is less than
1% total seawater enters the bay on each flood and leaves on each ebb. So
Passamaquoddy Bay is the main water exchanger with Cobscook Bay at Eastport
Channel. But the net outflow through Lubec Narrows may important to the
pollutants and wastes be flushed out of Cobscook Bay.
As the shape of
Cobscook Bay is approximately symmetry, so several pairs of counter rotating
eddies on each side of the main channel formed right at the entrance of narrow
neck. Several small scale eddies also formed in inner, outer bay and arms of
the bay. The diameter of these small eddies are less than 200 meters. These
small eddies never seen before from previous models, probably they are induced
by the complexity of the coastal line and topography. The existents of some of
these eddies already been proved by drifter observations. The mechanism of the
formation of these small eddies need more investigation.
3.2 Comparisons
of GoMOOS Buoy J & model output
GoMOOS buoy J is
located right at the entrance
to Cobscook Bay between Eastport and Seward Neck. It records every hour the
current direction and speed at 2 m. These continuous observations are suitable
for us to compare the time series with our model output. Bouy J also provides
hourly wind direction and speed to our model for real-time simulations. Fig 5 and Fig 6 are
the wind direction and speed from two periods of 5 days each, one in October
2003 and another in August 2004.
Fig
10 is the comparisons of time series of the hourly current direction
recorded by GoMOOS buoy J and our model output. The blue dots are the buoy J
and magenta is our model output. We can see buoy J currents are almost back and
forth following the regular cycle of the semidiurnal tide. Our model results
show a high degree of the consistence with data. Fig
11 is the comparisons of time series of the magnitude of the current
velocity. The difference between model and data is not too big (what is the
difference, both as the absolute value and as the percentage?) although the
modeled current speed is always smaller than data. Fig
12 and Fig
13 are the simulation for August 2004, same as the pervious one. We see
similar differences. However, there are some differences between model and data
(for example the asymmetry between the flooding and the ebbing phases) that is
because we only have M2 tide in our simulation. In reality, multi constitutions
of tidal waves may interact with each other and make the currents more
complicated.
3.3 Drifter
experiments
We simulated two
drifter experiments conducted summer 2003 and fall in 2004 in Cobscook Bay. Fig
14 , Fig
16 and fig15
are the students of Shead High School. They designed and built the drifters
used in the 2003 study and participated in field experiments. The drifters
moved in the surface layer, less than 2 meters deep. They rode on fishing boats
to follow the drifters and recorded the locations of drifters every 10-20
minutes with hand-held GPS.
Fig 16
show the trajectories of drifter experiment conducted on Oct.7th,
2003. Six drifters were initially deployed in a transection between Indian Island,
Eastport and Deer Island Point at 10:00AM. High water in Eastport was at 9:30AM. The ebb had already set up in this location when the drifters were
deployed. From the very beginning the drifters did not follow the ebbing tidal current
flow out but redistributed, then the drifters split into 2 groups and 2 of them
bypass Indian Island from north and the other 4 from south. 2 drifters were
retrieved from the Campobello shore. Fig 18
is our model results, it is clear to be seen that our model catch this split
pattern and predict the drifter trajectories tendency successfully. Our model
did not show the initial drifter redistribution (most likely due to the lack of
Lagrangian mixing), maybe we did not catch the local wind effect, maybe it is
because the students did not deployed the drifters exactly simultaneously then
contribute to the Lagrangian chaotic effect. One of the tracers is stuck on the
southwest corner of the Indian Island soon after release, and unlike drifters
in the field no tracers in the model were stuck on the shore of Campobello.
Again, there are many factors that can contribute to the small differences we
see here, e.g., multiple tidal constituents, spatial variability of the wind,
baroclinicity, and the Lagrangian chaotic behavior…
Fig19 is
another drifter experiment conducted on Aug. 05th, 2004. Five CAST barrel
drifters were initially deployed in the
waterway NW of Campobello Island at about 9:00AM. These kind of drifters carry
GPS itself, so they transmit information automatically every few seconds. So
the trajectories appear to be smoother. Low water in Eastport was at 9:13AM.
The deploy time is near the end of ebb, so from the very beginning all drifters
went out of the bay first, then circled back at the beginning of the flood and
then were carried into the inner bay. One of the drifters went north along the
border of the United States and Canada into the Western Passage. The other 4 in
the main channel moved into Cobscook Bay. Interestingly, these 4 drifters have
different destiny. One drifter GPS is invalid after 3 hours. The other three
stayed together untill they reached the entrance near Leighton Point and then
split from each other. One went north and reached Hershey Neck, one west
westward and reached Leighton point, the last one almost hit the Falls Island.
Fig 20
is model result, as the modeled tide led slightly such that flooding already
occurred in the model at 9:00 am. Hence there was not the round about right
after the release. From the trajectory of the one went into the Western
Passage, an anticlockwise eddy formed in the passage. This eddy is clearly
shown in the plot of residual currents shown in fig10. However, our Lagranian
model did not catch this eddy feature. At the same time, three instead of one
went into the Western Passage and one hit the corner of Moos Island. For the
two drifters carried into Cobscook Bay, our model also showed that they also stayed together and reached the same point
those drifters did. Overall, our model described the basic tendency of the
drifter trajectories.
4.
Discussion
Comparisons of time
series from the model with in situ observations show that the currents at the
GoMOOS buoy J are almost back and forth following the regular cycle of the
semidiurnal tide.
Fundamental mechanisms for exchanges between Cobscook Bay and the adjoining
Passamaquoddy Bay are strong flooding/ebbing tidal currents
Complexity of coastal line and topography produce several small-scale
eddies and eddy dipoles.
Model predicted
tracer trajectories are consistent with drifter data.
Here are some works
we are going to do in future: More experiments are being conducted to examine the effects of
multi-tidal constituents and baroclinicity. Residence time will be estimated for various parts
of Cobscook Bay.
Acknowledgements
We are grateful for
the helpful comments and suggestions of Randy Losier, Stephen
Cousins. Heidi Leighton
and Will Hopkins from the Cobscook Bay Resource Center provide us with the
drifter data. Students at Shead High School, they did fabulous job on design
and built the drifters and participated in field experiments in 2003.
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coastal Maine, Estuaries,20,(1),14-41. Under Construction! If you have questions please
contact Danya Xu
