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A dynamical analysis of the shedding of a Loop Current eddy in the Gulf of Mexico
F.-H. Xu,1 Yu-Lin Chang,1 L.-Y. Oey1,* and P. Hamilton2
1: Princeton University; 2: SAIC
*Corresponding Author: lyo@princeton.edu
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Abstract
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The shedding of Loop Current eddies in the Gulf of Mexico has long been considered to
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be driven by internal chaotic dynamics. Recent studies suggest, however, that eddy-shedding is
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both internally-driven and wind-forced. An example of such a case is analyzed here based on the
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shedding event in July of 2011 using the outputs of a time-dependent, primitive-equation
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numerical model (the Princeton Ocean Model). The model results are first validated using
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satellite and in situ observations. It is then shown that model initialized from a data-assimilated
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analysis on Jul/01, 2011 predicted eddy shedding near the end of July in agreement with
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altimetry data. From May through June, the Yucatan transport increased in response to the
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strengthening trade wind in the Caribbean Sea. The Loop Current grew and ultimately reached a
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sufficiently large size that β effects became important. Trade wind and Yucatan transport
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weakened in early July, and the Rossby wave speed (-βRo2) exceeded the Loop Current growth,
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providing a favorable condition for eddy shedding. Instability analysis shows that at incipient
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shedding, baroclinic instability growth rate increases north of the Campeche Bank, thereby
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accelerating the eddy shedding.
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1. Introduction
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The Loop Current (LC) is the dominant feature of the circulation in the eastern Gulf of
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Mexico (GOM) and the formation region of the Florida Current-Gulf Stream system. It is a
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component of the meridional overturning circulation, playing a key role in the global climate.
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The LC episodically sheds large warm-core eddies or rings (200-300km wide, 500-1000m deep)
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that generally propagate westward at 2~5 km day-1, with maximum swirl speed ≈1.8-2 ms-1 (see
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Oey et al. 2005 for a review). The LC and eddies affect every aspect of oceanography in the
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GOM, either directly or indirectly through the action of their smaller-scale subsidiaries.
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The LC eddy shedding was observed (e.g. Vukovich 1988; Sturges 1994; Sturges and
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Leben 2000) and simulated in several numerical models (Oey, 1996; Oey et al. 2003; Chang and
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Oey 2011; Chang and Oey 2012a; Le Hénaff et al. 2012). Chang and Oey (2011) describe the
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ideal case of the Loop Current Cycle: LC expansion, shedding, and retraction cycle. However,
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LC eddy often detaches and re-attaches to the LC several times before final separation (Oey et al.
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2003; Hénaff et al. 2012), suggesting a highly nonlinear and complex process.
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The shedding of Loop Current eddies can be understood as a competing imbalance
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between the mass influx through the Yucatan Channel, which grows the Loop, and westward
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Rossby wave which tends to ‘peel’ eddy from the Loop; this will be referred to as the Pichevin-
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Nof mechanism (Pichevin and Nof, 1997; Nof, 2005). The Loop Current grows larger and deeper
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with mass influx from the Yucatan Channel. When its Rossby radius Ro (based on the Loop’s
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upper-layer depth) reaches a certain size, the variation of the Coriolis parameter (f) becomes
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significant ( effects), and the westward Rossby wave velocity (-βRo2) exceeds the LC growth
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rate due to the mass influx. At this point, the Loop Current eddy begins to detach. The idea may
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be extended to the case when the mass influx (i.e. Yucatan transport) varies slowly in time
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(longer than 1~2 months), so that eddy-shedding may also depend on this variation. Oey et al.
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(2003) show that models forced by time-dependent wind produce strong Yucatan transport
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fluctuations, of order of a few Sv’s and larger, which in turn also influence the shedding periods.
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Chang and Oey (2012a) identify biannual preferences in summer and winter of the LC eddy
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shedding by analyzing long-term observational data and numerical model results. They found a
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strong dependence of eddy-shedding on Yucatan transport. The biannual variation in the trade
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wind forces a corresponding biannual transport through the Yucatan Channel; as a consequence,
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the Loop Current has a tendency to shed eddies as the wind weakens from summer to fall, and
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also from winter to spring.
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The Pichevin-Nof mechanism is fundamental for Loop Current eddy-shedding. Other
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factors such as baroclinic instability and upper-lower layer coupling do not determine eddy
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shedding, but they can modify it, by accelerating the timing when eddies are shed (see the
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companion submitted manuscript: “Chang and Oey, 2012b: Loop Current EOF modes”). Oey
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(2008) showed that north of Campeche Bank is a fertile ground for baroclinic instability which
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can generate deep cyclones below 1000m.
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accelerates the upper-layer LC eddy shedding. The upper and lower layer (shallower and deeper
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than 1000m) mass coupling in the eastern Gulf (east of 900W) can also accelerate eddy shedding
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(see Fig.5 of Chang and Oey, 2011, hereafter CO2011). They examined mass exchanges between
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the upper and lower layers, and also between the eastern and western Gulf of Mexico. At
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incipient shedding, the westward-extended Loop Current forces a deep return flow into the
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eastern Gulf where the upper layer then becomes divergent while the lower layer becomes
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convergent. The strong upwelling in the eastern Gulf again accelerates eddy-shedding.
The cyclone in turn produces upwelling that
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In late July, 2011, an eddy was observed to separate from the Loop Current, coincident
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with the weakening of the summer trade wind in that year. The scenario appears to match the
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idea discussed in Chang and Oey (2012a), and outlined above. In this paper, we attempt to
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support the idea based on a realistic case-study. We describe a free-running (i.e. non data-
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assimilated) model initialized on Jul/01 and forced by realistic wind that predicts eddy shedding
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near the observed shedding time. We analyze this case in detail in order to understand the
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underlying eddy-shedding dynamics. Section 2 describes the model and experiment setup.
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Section 3 presents the results, and here we also validate the model against observations. Section
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4 is discussion and section 5 concludes the paper.
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2. The Numerical Model
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The Princeton Regional Ocean Forecast System (PROFS) for the Gulf of Mexico is used
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for this study; this model is based on the Princeton Ocean Model (POM) and has been
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extensively tested for (i) process studies to understand the Loop Current and eddy-shedding
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dynamics (see, e.g. above quoted works by Oey et al. and Chang and Oey); (ii) comparison
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against observations (e.g. Wang et al. 2003; Fan et al. 2004; Oey et al. 2004; Lin et al. 2007);
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and (iii) hindcasts and forecasts (e.g. Oey et al. 2005; Yin and Oey, 2007). (For a more complete
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list of references please visit http://www.aos.princeton.edu/WWWPUBLIC/PROFS/publications).
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The present version of the model has MPI directives implemented into POM by Dr. Toni Jordi
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(http://www.imedea.uib-csic.es/users/toni/sbpom/) and achieves good (i.e. linear) scalability.
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Most of the original PROFS (and POM) features are retained. There are 25 terrain-following
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sigma levels with (logarithmically) finer resolutions near the surface and bottom, but a fourth-
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order pressure gradient scheme (Berntsen and Oey, 2010) is used to guarantee small pressure-
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gradient errors. An orthogonal curvilinear grid is used in the horizontal with x and y  2~5
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km in the Gulf of Mexico.
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modified by Craig and Banner (1994) to include input of turbulence energy due to breaking
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waves near the surface is used. A Grant and Madsen (1979) type bottom-drag scheme is used in
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the bottom boundary layer to empirically account for increased bottom roughness due to surface
The Mellor and Yamada’s (1982) turbulence closure scheme
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gravity waves; this is particularly effective over shallow shelves and under strong wind
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conditions. The Smagorinsky’s (1963) shear and grid-dependent horizontal viscosity is used with
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a nondimensional coefficient = 0.1; the corresponding horizontal diffusivity is made five times
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smaller.
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(http://gcmd.nasa.gov/records/GCMD_NAVOCEANO_MCSST.html) with an e-folding time
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constant of 1 day-1. However, tests (and previous experience – e.g. Yin and Oey, 2007) indicate
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that the effects of SST boundary conditions on Loop Current dynamics are minor.
The
sea
surface
temperature
(SST)
is
relaxed
to
AVHRR
MCSST
The model domain includes the north-west Atlantic Ocean west of 550W and from 50N
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World
Ocean
Atlas
data
(“climatology”)
from
NODC
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~550N.
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(http://www.nodc.noaa.gov/OC5/WOA05/pr_woa05.html) is used for boundary condition along
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the eastern open boundary at 550W. The topography was set up according to Etopo2 and edited
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on shelves using NOS digitized maps. An analysis field was obtained for 19 years from 1993-
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2011
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(http://www.aviso.oceanobs.com/) is assimilated into the model using a statistical surface-
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subsurface projection method (see Yin and Oey, 2007 for details and references). The model is
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forced by six-hourly winds (1993-2009: 0.25o×0.25o CCMP (cross-calibrated Multi-platform),
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and 2009-2011: NCEP 0.5o×0.5o GFS (Global Forecast System)), by M2, S2, K1 and O1 tides
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specified along the open boundary at 55oW, and by daily river discharges obtained from the U.S.
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Geological Survey at 51 locations along the U.S. coastline (34 rivers in the Gulf and 17 rivers in
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the eastern coast).
The
during
which
satellite
sea-surface
height
anomaly
(SSHA)
from
AVISO
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Results obtained from the above hindcast analysis run are used as initial conditions for
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two free-running experiments to study July/2011 Loop Current eddy-shedding dynamics: an
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experiment initialized from July/01/2011 hindcast field (Exp.Jul01) and another experiment
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initialized from May/15/2011 hindcast (Exp.May15). The rationale for these experiments will
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become clear shortly. For these free-running experiments, neither the AVISO SSHA, nor the
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MCSST data were used; other forcing are the same as in the hindcast analysis run.
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convenience, these experiments will be called “forecasts” even though strictly-speaking they
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really are not since wind (and other forcing) are used. Additional, sensitivity experiments were
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also conducted, as will be mentioned below. For each experiment, daily-averaged fields are used
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for analyses.
For
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3. Results
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The Exp.Jul01 predicts a LC eddy shedding during the last week of July in agreement
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with that observed in AVISO satellite sea surface height (SSH) data (Fig.1). The hindcast and
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AVISO both show on Jul/01 (Fig.1a) a northwestward-extended Loop Current, although AVISO
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zero-SSH contour is some 50km more extended. Ten days later (Jul/11), the forecast LC
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intrudes northwestward, and which compares well with AVISO. On Jul/21, both AVISO and
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model Loop developed a thin neck typical of the situation at incipient eddy shedding (Oey, 1996;
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Schmitz et al. 2005; Oey, 2008). The forecast shows that a large eddy was shed shortly thereafter
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on Jul/25 in agreement with AVISO.
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Model Skill Assessment Against Satellite Observations:
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To evaluate forecast skill, time series of the spatial correlation coefficient and root mean
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square errors between the model and AVISO SSH anomalies are calculated and compared
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against persistence for the open-ocean region of the GOM: north of 23oN and west of 84oW in
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water depths deeper than 500m (Fig.1b). The correlation  0.8 on Jul/01 – the initial hindcast
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value; it remains above 0.65 during the first 5 weeks of the forecast in agreement with Yin and
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Oey (2007) who concluded based on bred-vector analyses that the limit of Loop Current and
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eddy forecast horizon in the Gulf of Mexico is 4~6 weeks (see also Oey et al. 2005). At week#6,
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the correlation drops to approximately 0.5 but it remains above this value from weeks6~7 before
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degrading further to about 0.45 at the end of week#8. The RMS errors increased from 0.18 to
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0.23 over the first 8 weeks. In both measures, the model forecast beats persistence.
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Model Validation Against in situ Measurements:
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In addition to evaluating the model skill against AVISO, we have also conducted an
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extensive comparison of both model hindcasts and forecasts against direct current-meter (ADCP)
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measurements in the Loop Current collected for Bureau of Ocean Energy Management (BOEM)
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by Dr. Hamilton and co-investigators.
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separately. The study confirms the above model-AVISO comparison that during the 2011 July
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eddy-shedding event the Exp.Jul01shows considerable skills. We now examine more closely the
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model results with the objective of understanding the relevant dynamics and forcing that can
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explain the eddy-shedding event in July 2011. The hypothesis is that, according to Chang and
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Oey (2012), the trade wind and hence Yucatan transport are important to eddy-shedding over the
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seasonal time scale. To simulate the corresponding variation over several months prior to the
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July shedding, we analyze in details another free-running run (Exp.May15) initialized from the
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May/15 hindcast field. The free-running experiment then eveolves in accordance to wind and
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edd-forced model dynamics unhampered by spurious force balances that may result from a data-
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assimilated run.
Details of this comparison study will be reported
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Analysis of the Exp.May15:
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The Exp.May15 produces an eddy-shedding event on Jul/8, 2~3 weeks earlier than the
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observed (and Exp.Jul01) shedding date. The eddy-shedding date is some 7~8 weeks into the
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forecast horizon which is near the limit of modeled Loop Current predictability, and some
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discrepancies from observation are therefore to be expected (Yin and Oey, 2007). Overall,
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however, the Exp.May15 shows good skill (plots not shown), and the fact that the model predicts
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an eddy-shedding, albeit a little earlier, is of great interest, and suggests an underlying dynamics
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to be learnt.
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Eddy-Shedding and Its Conneciton to Caribbean Trade Wind & Yucatan Transport Variations:
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Figure 2 shows the SSH on June 10th from Exp.May15. This shows that both model and
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observed LC are well-extended at this time. As the LC is fed by inflow through the Yucatan
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Channel, it grows to a sufficiently large size (diameter  200~300km), and is sufficiently deep
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(upper-layer thickness h(t)  500m) that -effects become important (Nof, 2005). The westward
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Rossby wave velocity = Ci = - βRo2, where Ro = (g’h(t))1/2/f, then exceeds the inflow growth rate,
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and a portion of the Loop’s mass – i.e. a warm eddy – is “peeled” westward. The Ci is calculated
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at the star location (-89.40, 260) of Fig. 2, and its temporal variation is shown in Fig. 3 (bottom).
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The Ci increased from March to June, became maximum at the end of June, and then dropped
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rapidly in early July when eddy shedding occurred.
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The growth of the Loop Current is caused by continual influx of warm water into the
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Gulf of Mexico from the Caribbean Sea.
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increases with the trade wind strengthens from spring to summer, and it weakens from summer
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to fall concomitant with a corresponding weakening of the trade wind. During 2011, the trade
Chang and Oey (2012) showed that this influx
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wind stress (negative zonal component) in the Caribbean Sea strengthened from near-zero in
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mid-May to -10-4 m2 s-2 in late June, and it weakened to -0.3×10-4 m2 s-2 in mid-August (Fig. 3,
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top). The modeled Yucatan transport increased from mid-May to late June when it peaked, and it
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then weakened through August (Fig. 3, middle). This relation between the trade wind and the
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Yucatan transport agrees well with Chang and Oey’s (2012) conclusions.
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correlation coefficient between the daily zonal wind stress and Yucatan transport is -0.6 (above
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the 95% significance; -0.75 if 10day-running mean time series is used). The authors analyzed a
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long-term (20 years) model run forced by reanalysis wind stress dataset derived from satellite
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and buoy observations and model, and found that the Yucatan transport peaks (weakens) at
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approximately the same time (with a short lag ~ 1 month) as when the trade wind in the
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Caribbean Sea peaks (weakens). They concluded that the weakening of wind and Yucatan
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transport together with the matured development of the Loop Current (i.e. with large Ci) provide
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a favorable condition for the separation of the LC eddy. In the present case, the weakening of
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the trade wind and Yucatan transport occurred from the end of June through mid-August
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coincident with the near-maximum Ci (Fig.3), and an eddy is shed shortly thereafter (on Jul/08);
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the scenario agrees well with Chang and Oey’s (2012) analysis.
The zero-lag
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Upper & -Lower-Layer Coupling
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Now we examine the upper and lower layer coupling. As CO2011, we define a semi-
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enclosed volume in the eastern Gulf, bounded by 900W (west), Yucatan Channel (South), and the
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Straits of Florida (east). The transports through west, south, and east boundaries in the upper and
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lower (shallower and deep than 800m) layers were calculated (not shown). Note that the east
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boundary of the lower layer is closed due to the shallow sill of the Straits of Florida. The
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divergence/convergence of the upper and lower layer is calculated as transport out of the layer
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(Trout) subtracts transport into the layer (Trin). Therefore, the positive value indicates divergent,
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and the negative is convergent. The time series of 10-day running average of Trout-Trin of upper
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(solid) and lower (dash) layers are shown in Fig. 4. From the end of March to mid June (before
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Jun/18), the upper layer was mainly convergent and the lower layer was divergent, indicating the
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growth of the LC. This corresponds to the Loop reforming phase described in Fig. 5a of CO2011.
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The mean SSH in the eastern Gulf (grey line in Fig. 4) also shows the higher sea level before
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Jun/18, consistent with the convergent. After Jun/18, the sea level dropped, the lower layer is
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convergent, and upper layer is divergent, corresponding to the incipient shedding phase in Fig.
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5b of CO2011. An upward motion induced by the two layer coupling contributed to the shedding.
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Considering the eddy size = 250km and the Rossby wave vecolity C i=0.05 m s-1, the time
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required for the eddy to move over its own size is about 2 months. If Yucatan inflow and Rossby
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wave dynamics alone, the eddy shedding would occur in mid August instead of Jul/08. There
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must have other processes accelerating the eddy shedding.
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Baroclinic instability was calculated over two 30-day periods, May/16 - Jun/15 and Jun/01 -
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Jun/30 at depth 750m (Fig. 5). During the first period, a dominant instability (positive; shown in
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red; right panel) BC was seen north of the Campeche Bank around 24.80N, 88.30W where the LC
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flows over the deeper regions of the Gulf. The dominant instability was getting larger and
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spreading northwestward in the second period. These results are consistent with the 10-yr
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ensemble average of baroclinic instability in Oey (2008). The corresponding growth rate is about
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1/40 ~ 1/10 per day. Therefore, the instability accelerated the eddy shedding for about 10-40
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days after Jun/18. This is consistent with the model estimated shedding on Jul/08.
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The cyclonic vorticity ζ on the western (~50km) portion of the Yucatan Channel divided by f
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gives a good predictor of the LC northern boundary (Chang and Oey 2012). A high correlation,
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R2 = 0.83, was obtained (see Fig.2c of Chang and Oey 2012). This relation is in good agreement
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with the Reid’s formula (Reid 1972). The larger the ζ/f is, the more northward the LC extends.
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The Loop retracts as ζ weakens. The 10-day average time series of the ζ/f and northern boundary
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of the LC represented by latitude was shown in Fig.6 for the free model run May/15. From the
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end of the June to mid July, the ζ/f (red) decreases from 0.475 to 0.41, and meantime the
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northern boundary of the LC retracts from 26.80 N to 25.50 N, coincide with the eddy shedding.
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1.
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This paper studies an eddy shedding event of the Loop Current in Jul, 2011 using a mpi-version
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of the Princeton Ocean Model. A real-time forecast was conducted starting from Jul/01, 2011.
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The model predicted the eddy shedding on Jul/22/2011, consistent with the shedding time during
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Jul 22-29 from the satellites. To study the underlying dynamics of the eddy shedding, we
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conducted a free-model run starting from May/15 to eliminate the influence of data assimilation
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on the ocean state in late May and June for the Jul/01 case. The May/15 run created an eddy
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shedding on Jul/08. We found that the underlying dynamics of the eddy shedding are:
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1)
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fed by the Yucatan influx, and ultimately reached a large size where the Rossby wave velocity (-
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βRo2) was about -0.05 m s-1. Meantime, the easterly wind stress in the Caribbean Sea decreased
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and consequently the Yucatan inflow dropped. The Rossby wave speed exceeds the LC growth
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fed by Yucatan inflow. This provided a favorable condition for the eddy shedding;
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2)
Summary
The primary dynamics is the β effect as discussed by Nof (2005). The growing LC was
The baroclinic instability north of the Campeche Bank accelerated the eddy shedding;
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3)
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to the eddy shedding too.
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Reference:
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Anderson, D. L. T., and R. A. Corry, 1985: Seasonal transport variationsin the Florida Straits: A
model study. J. Phys. Oceanogr.,15, 773–786.
Berntsen, J. and L.-Y. Oey, 2010: Estimation of the internal pressure gradient in σ-coordinate
ocean models: comparison of second-, fourth-, and sixth-order schemes. Ocean Dyn. 60, 317-330.
Chang, Y.-L., and L.-Y. Oey, 2012:Why does the Loop Current tend to shed more eddies in
summer and winter? Geophys. Res. Lett., doi:10.1029/2011GL050773, in press.
Chang & Oey, 2011: Loop Current Cycle: Coupled Response of the Loop Current with Deep
Flows. J. Phys. Oceanogr., 41, 458-471.
Cooper, C., G. Z. Forristall, and T. M. Joyce, 1990: Velocity and hydrographic structure of two
Gulf of Mexico warm-core rings, J. Geophys.Res., 95, 1663– 1679.
Craig, P.D. and M.L. Banner. 1994: Modeling wave-enhanced turbulence in the ocean surface
layer. J. Phys. Oceanogr., 24, 2546-2559.
DiNezio, P.N., Gramer, L.J., Johns, W.E., Meinen, C.S., and Baringer, M.O., 2009: Observed
interannual variability of the Florida Current: wind forcing and the North Atlantic Oscillation, J.
Phys. Oceanogr. 39 (3), 721–736
Elliott, B.A., 1982: Anticyclonic rings in the Gulf of Mexico, Journal of Physical Oceanography,
12,1292-1309.
Forristall, G. Z., K. J. Schaudt, and C. K. Cooper, 1992: Evolution and kinematics of a loop
current eddy in the Gulf of Mexico during 1985, J. Geophys. Res., 97, 2173– 2184.
Le Hénaff, M., V. H. Kourafalou, Y. Morel, and A. Srinivasan (2012), Simulating the dynamics
and intensification of cyclonic Loop Current Frontal Eddies in the Gulf of Mexico, J. Geophys.
Res., 117, C02034, doi:10.1029/2011JC007279.
Nof, D., 2005: The momentum imbalance paradox revisited. J. Phys. Oceanogr., 35, 1928-1939.
Oey, L.-Y., Ezer, T., Forristall, G., Cooper, C., DiMarco, S., Fan, S., 2005: An exercise in
forecasting loop current and eddy frontal positions in the Gulf of Mexico. Geophysical Research
Letters, 32, L12611.
Pichevin, T., and D. Nof, 1997: The momentumimbalance paradox. Tellus, 49, 298–319.
Reid, R. O. (1972), A simple dynamic model of the Loop Current, in Contributions on the
Physical Oceanography of the Gulf of Mexico, Tex. A&M Univ. Oceanogr. Ser., vol. 2, edited
by L. R. A. Capurro and J. L. Reid, pp. 157–159, Gulf, Houston, Tex.
Yin and Oey, 2007: Bred-Ensemble Ocean Forecast of Loop Current and Eddies. Ocean
Modelling, 17, 300-326.
Oey, 2008: Loop Current and Deep Eddies. J. Phys. Oceanogr. 38, 1426-1449.
Oey, L.-Y., T. Ezer, G. Forristall, C. Cooper, S. DiMarco and S. Fan, 2005. An exersise in
forecasting loop current and eddy frontal positions in the Gulf of Mexico. Geophys. Res. Let., 32,
L12611, 10.1029/2005GL023253.
Sturges, W. (1994), The frequency of ring separations of Loop Current, J. Phys. Oceanogr., 24,
1647–1651, doi:10.1175/1520-0485(1994) 024<1647:TFORSF>2.0.CO;2.
Sturges, W., and R. Leben (2000), Frequency of ring separations from the Loop Current in the
Gulf of Mexico: A revised estimate, J. Phys. Oceanogr., 30, 1814–1819, doi:10.1175/15200485(2000)030<1814: FORSFT>2.0.CO;2.
The upwelling induced by the upper-lower layer coupling in the eastern Gulf contributed
Page | 12
298
299
300
Vukovich, F. M. (1988), Loop Current boundary variations, J. Geophys. Res., 93(C12), 15,585–
15,591, doi:10.1029/JC093iC12p15585.
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