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A Hindcast Model of the Mid-Atlantic Ocean Region: a comparison with
observation currents
1. Introduction
This paper provides a comparison of a three-dimensional model simulation to
four observation datasets in the Mid-Atlantic Bight (MAB). The observations were
done mainly in the continental shelf regions, from near Cape Hatteras to southwestern
portion of Georges Bank (Figure 1). Each observation dataset has its own specific
time period from a few months to a few years. A detail description is in section 2.
These observations provide an excellent test of the model’s ability to reproduce the
seasonal as well as sub-tidal variations in ocean currents.
An outline of the paper is as follows. In section 2, we described the observation
datasets from four field studies. Section 3 presents the model setup. The comparison
of the numerical simulation with observations is described in section 4. Section 5 is a
discussion and summary.
2. Observation data
2.1 MMS moorings
The Minerals Management Service (MMS) funded a mooring array near Cape
Hatteras (Figure 1) from March 1992 through February 1994. 15 deployments of the
moorings were located along three cross-shelf lines (A, B, and C) and one along-shelf
line at the shelf edge (D). The offshore most moorings C4, B4, and A5 were situated
both upstream and downstream from the Gulf Stream separation point from the
continental shelf. Table 1 shows each depth for measurement at all mooing stations. A
technical report (Berger et al. 1995) summarized the conclusion of the field project.
The velocity data is used to validate the simulation results in the study.
2.2 CMO-Coastal Mixing and Optics Mooring
The Coastal Mixing and Optics project was funded by the Office of Naval
Research. The experiment was designed to examine the mixing of ocean water on a
continental shelf and the effects of mixing on water column optical properties. The
site of the CMO experiment was the "Mud Patch" of the Mid-Atlantic Bight (MAB)
continental shelf, the southwestern portion of Georges Bank (GB). The site is located
about 110 km south of Martha's Vineyard, Cape Cod, Massachusetts, U.S.A. in
approximately 70 m of water. The field experiment was conducted between
September 26, 1996 and June 9, 1997. The acoustic Doppler current profiler (ADCP)
measurements are used to compare with the model simulation.
2.3 COBY
A bottom mounted ADCP of 600-kHz was deployed at 32 m of depth at the
station of station 5 on the COBY transect. The instrument measured two-period
currents, first from Jan 28 through Jul 25, 2006 and the second from Oct 8, 2006
through Jun 23, 2007.
2.4 OMP-NC Ocean Margins Program
The Department of Energy designed and implemented a field study called the
Ocean Margins Program (OMP) to examine carbon cycling in the continental margin
of the western North Atlantic Ocean. The OMP mooring array was located on the
shelf and upper slope between the Chesapeake Bay and Cape Hatteras (Figure 1). A
total of 26 moorings were deployed during the first deployment, between 5 February
and 16 May 1996, while 23 moorings were deployed during the second deployment
from 23 June through 14 October 1996. This field program resulted in the most
extensive, multidisciplinary set of water column and seabed observations ever
obtained over an ocean margin. The observed currents are used to compare with the
model simulation.
3. Numerical model description
The three-dimensional model used in the study is based on the Princeton Ocean
Model (POM; Mellor, 2002). The model solves a hydrostatic, primitive Navier Stokes
equation on a horizontal orthogonal curvilinear Arakawa “C” grid and a vertical
terrain-following sigma coordinate. The ocean is assumed to be incompressible, and
Boussinesq approximation is used. We carried out a nested-grid simulation from the
northern portion of the South Atlantic Bight to the south and the Gulf of Maine to the
north, with x  y  5 km and 25 vertical sigma levels (Figure 1 lower panel). The
simulation is named ‘fine grid’ simulation hereafter. The nested domain is embedded
inside a larger-scale parent-grid domain of half the horizontal resolution x  y  10
km but the same 25 sigma levels. The large domain mainly covers the entire
northwestern Atlantic Ocean (98W~55W, 6N~50N, Figure 1 lower panel). The large
domain simulation is named ‘coarse grid’ simulation hereafter.
The coarse grid simulation is integrated from the end of 1992 through 2008 and
includes daily discharges from 17 major rivers and estuaries along the U.S. and
Canadian (the St. Lawrence River) eastern coast. The model is forced by six-hourly
Cross-Calibrated, Multi-Platform (CCMP) ocean surface wind velocity and also by
M2 tide. Real-time sea surface temperature and sea surface height anomalies from
satellite are assimilated into the model. The monthly temperature-salinity (T/S)
climatology is used to specify initial and open boundary conditions. The fine grid
simulation has completed the integration from the end of 1992 to the end of 1999.
4. Model-data comparisons
The comparison aims at validating the model simulation. The current data are
used for comparisons. Unless otherwise stated, all variables have been daily averaged
to remove the tidal oscillations prior to any analysis.
4.1 MMS moorings and fine grid simulation
The comparison is carried out between MMS mooring currents and fine gird
model from January 1993 through February 1994. Figure 2 compares mean and
ellipses of currents at depth 2 (referred to table 1) for fine-grid model with those
computed from observations at the 15 MMS moorings. Mean currents are shown as
arrows at each station. From observations, the mean currents are northeastward at the
southern stations of Cape Hatteras, and southward at the northern stations except at
A5. The mean currents are increasing offshore along the three cross-shore lines. The
amplitudes of the current ellipses reflect the current standard deviations. In the shelf
region, the standard deviations are larger than the mean, whereas the mean currents
are stronger in the further offshore region. This is caused by the influence of persistent
northeastward Gulf Stream. The current ellipses are mainly aligned with the local
isobath in both observations and model simulation. The model reproduced the general
circulation pattern similar to the observed, though the model ellipses are larger than
the observations.
To compare the seasonal velocity variations, an empirical orthogonal function
(EOF) analysis for MMS mooring currents and model currents are carried out.
Fifteen-day low pass of the currents at depth 2 (Table 1) of 9 mooring stations after
removal of stations with missing data were used to do the analysis. The first EOF
mode accounts for 58% of the total velocity variance for the observations and 70% for
the model, and the second mode accounts for 23% of the variance for the observations
and 12% for the model (Figure 3 and 4). The EOF 1 from both observations and the
model describes seasonal current variations in the shelf of the Cape Hatteras. The
currents mainly flow southward in winter and spring, and northward in summer and
fall. And the EOF 2 shows the currents have an along-shore convergence at the Cape
Hatteras. The EOF modes are in good agreement between observations and the model.
Table 1 indicates the complex correlation for depth-averaged MMS currents and
simulation currents. In general, the correlation coefficient is relatively high close to
the shore and low near the shelf break. The maximum coefficient is about 0.7 at
station A1. The rotation angle indicates that the modeled current is rotated
counterclockwise from MMS current. The minimum angle is about 30 at C1.
Figure 5 compares the mean (left panel) and standard deviation (right panel) of
depth-averaged principal-axis currents of the MMS moorings and the model. The
fine-grid simulation produced the mean currents close to the observations at the
inshore stations (e.g. A1, A2, C1, B2, D2, etc.), however, the currents in the offshore
station are over predicted (e.g. A4, A5, and C4). The simulation produced higher
standard deviation than the observed at all stations. The bias of model currents is
small (<0.1 m s-1) at inshore stations and increasing offshore (Figure 6). The
maximum bias is at B4, about -0.5 m s-1.
Figure 7 shows the correlation coefficient of depth-averaged principal axis
currents at all MMS mooring stations. Of the 15 stations, 6 stations give correlations
of > 0.5. The maximum coefficient is larger than 0.8 at C3, while the minimum is less
than 0.1 at A3. The skill assessment evaluates quantitative agreement between model
results and observations. According to Wilmott (1981), the skill is defined as
Skill  1 
m  o2
m 
o  o o
(1)

2
where m is the model variable, and o is the observed variable, and the time mean
denotes as < >.
The value of skill is in the range of 0~1, from a large discrepancy to
a perfect agreement between model and observations. In the study, the depth-averaged
currents along principal axis are used to evaluate the model skill. The simulated
currents exhibited comparatively high skill (>0.4) at many stations, while low skill (<
0.4) at stations near the shelf break (Figure 7).
Also according to Oke et al. (2002), there is a relationship between the root of
mean squared error, RMSE 
deviation
error,
cross-correlation
1
CC  S m S o
1
m 
m  o 2 , mean bias,
SDE  S m  S o 
error
m o  o
m 
i
m

2

CCE  2Sm So (1  CC)
 . The relation is
BIAS  m  o , the standard
o
i
.
 o

2
The
,
and
the
cross-correlation
RMSE 2  BIAS 2  SDE 2  CCE 2
(2).
Figure 8 shows the each item in Equation (2) at MMS mooring stations. The RMSE is
relatively low (less than 0.05 m-2 s-2) at most of the stations. The large RMSE (>
0.05m-2 s-2) is mainly attributed to the southeastward bias at stations A4, B3, B4, and
C4. At stations C2 and C3, all three error subcomponents contribute to the RMSE.
4.2 CMO mooring and fine grid simulation
Figure 9 compares the depth-averaged fine-grid model currents with CMO data.
The complex correlation produces the coefficient about 0.6 and the angle about 14
degrees between the two (Table 2). The bias for current speeds is -0.03 m s-1 and the
absolute error is 0.1 m s-1. The mean currents from model and CMO are in good
agreement, while the modeled current ellipse is smaller than the CMO one. Also, the
CMO current ellipse is more aligned with the local isobath. The model yields a skill
of 0.52.
4.3 COBY data and coarse grid simulation
Figure 10 compares the depth-averaged coarse-grid model currents with COBY
data. A good agreement between model and observations is present. The model yields
a skill of 0.83. The complex correlation coefficient is about 0.7 and the angle is -6
degrees (Table 2). The bias and absolute error are about 0.01 m s-1 and 0.09 m s-1,
respectively. The speed value of modeled mean current is about 0.003 m s-1, and the
observed is 0.01 m s-1. The modeled current ellipse is more aligned with the shoreline.
4.4 OMP moorings and coarse grid simulation
The mean and ellipses of depth-averaged currents from the fine-grid model and
the OMP moorings are compared in Figure 11. North of Cape Hatteras, the modeled
mean currents mainly flow southward, while the mean currents tend to flow
northeastward at the southernmost stations. The magnitude of currents is increasing
offshore. The maximum mean current (> 0.2 m/s) appears at station 26. The modeled
ellipses are mainly aligned along local isobath, in general agreement with the OMP
observations. Table 2 shows the complex correlation coefficients and rotation angles.
The maximum correlation is about 0.5 at stations 7 and 11, and the minimum angle is
about -50 at stations 12 and 14.
Figure 12 compares the time mean and standard deviation of the depth-averaged
currents along the principal axis. The simulation produces higher mean values at
stations near shelf edge, except for station 26, where the OMP observation is higher.
The simulation also produces higher standard deviation in offshore stations except for
station 26. The bias of the simulation is small (< 0.1 m/s), at stations in the shelf, but
large (>0.1 m/s) at stations close to the shelf break. The model skill assessment from
Equation 1 yields relative high skills (> 0.5) at stations in the shelf, and relative low
skills (<0.5) at the shelf break stations. For example, the maximum skill (>0.6) is
obtained at stations 3 and 4.
Figure 14 evaluates the contributions of BIAS, SDE and CCE to RMSE at OMP
mooring stations. The RMSE is relatively low (less than 0.2 m-2 s-2) at most of the
stations. The largest RMSE (> 0.35m-2 s-2) is at station 26. The CCE mainly attributes
to RMSE. The contribution of SDE is negligible.
5. Discussion
The comparison between the model and observations shows the model
reproduces the seasonal as well as sub-tidal variability of currents fairly well in the
MAB. For all stations, the model skill is relative high (>0.5) in the shelf regions, but
getting low at the shelf break. In general, the correlation coefficient shows similar
trend that it is relative high (>0.5) in the shelf but decreasing at the shelf break.
In the shelf region north of Cape Hatteras, the EOF mode 1 of MMS and model
indicate a clear seasonal cycle of current anomalies. It is southward in winter and
spring and northward in summer and fall.
References:
Berger, T. J., P. Hamilton, R. J. Wayland, J. O. Blanton, W. C. Boicourt, J. H.
Churchill, and D. R. Watts, (1995), A physical oceanographic field program offshore
North Carolina, Minerals Management Service Tech. Rep., OCS Study MMS 94-0047,
U.S. Department of the Interior, New Orleans, LA, 345 pp.
Wilmott, C.J. (1981), On the validation of models, Physical Geography, 2, 184-194.
Table 1: MMS moorings: station and depth
Station
A1
A2
A3
A4
A5
B1
B2
B3
B4
C1
C2
C3
C4
D2
D1
Depth 1
5
5
5
100
60
5
5
5
100
5
5
5
100
5
5
Depth 2
16
20
30
300
300
14
20
30
300
14
20
30
300
30
30
30
55
800
800
30
55
800
30
55
800
55
55
Depth 4
1200
1200
1200
1200
Depth 5
1900
1900
1900
1900
Depth 3
Depth 6
2900
Tabel 2. Complex correlation coefficients of depth-averaged MMS, OMP, CMO, and
COBY currents with depth –averaged fine-grid simulation currents. The rotation angle
indicates that the modeled current is rotated counterclockwise from the observed
current.
Θ
Station
R
Θ
Station
R
(deg)
Θ
Station
R
(deg)
(deg)
MMS A1
0.7
-10
OMP 1
0.1
33
OMP 18
0.3
-54
A2
0.3
-29
2
0.3
-88
19
0.2
-48
A3
0.01
-40
3
0.4
11
20
0.2
164
A4
0.6
-13
4
0.4
11
22
0.2
92
A5
0.5
-36
5
0.2
-44
23
0.3
-14
B1
0.4
-20
7
0.5
9
24
0.03
99
B2
0.4
4
8
0.4
-22
25
0.2
65
B3
0.6
-20
9
0.1
-151
26
0.4
-23
B4
0.4
-114
11
0.5
-123
27
0.2
-136
C1
0.4
3
12
0.4
-5
COBY
0.7
-5.8
C2
0.4
4
13
0.3
16
CMO
0.6
14
C3
0.6
7
14
0.3
-5
C4
0.3
-20
15
0.3
12
D1
0.01
15
16
0.1
68
D2
0.03
-172
17
0.3
171