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In Press, GRL, 2012
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Why does the Loop Current tend to shed more eddies in summer and winter?
Y.-L. Chang and L.-Y. Oey*
Princeton University (*Corresponding Author: lyo@princeton.edu)
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Abstract
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The observed seasonal preferences of Loop Current eddy shedding, more in summer and
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winter and less in fall and spring, are shown for the first time to be due to a curious combination
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of forcing by the seasonal winds in the Caribbean Sea and the Gulf of Mexico. The conditions
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are favorable for the Loop to shed eddies in summer and winter when strong trade winds in the
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Caribbean produce large Yucatan transport and Loop's intrusion, and concurrently when weak
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easterlies in the Gulf offer little impediment to eddy shedding. The conditions are less favorable
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in fall and spring as the trade winds and Yucatan transport weaken, and the strengthening of the
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Gulf's easterlies impedes shedding.
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1. Introduction
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Early studies of the Loop Current in the Gulf of Mexico in the 1960's~1980's suggest that
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it may vary seasonally. The northward penetration of the Loop Current was bimodal: maximum
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penetrations occur, on average, in winter (Dec~Jan) and summer (Jun~Jul) [Leipper, 1970;
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Behringer et al. 1977; Molinari et al. 1978; Sturges and Evans, 1983]. Molinari et al. [1978]
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concluded that the seasonal intrusion of the Loop Current varied with the geostrophic transport
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through the Yucatan Channel. Sturges and Evans [1983] suggested that the Loop Current varied
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in response to wind. These pioneering authors also recognized that there were substantial
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deviations from the seasonal cycle, and intrusions and eddy-sheddings can occur in virtually any
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month of the year. That the Loop Current can intrude into the Gulf and eddies can separate from
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it without the need for a seasonal forcing such as the inflow transport was first demonstrated
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numerically by Hurlburt and Thompson [1980], and since then confirmed by numerous studies
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using more elaborate models.
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The idea of a seasonal Loop Current is nevertheless very attractive; the system is more
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predictable, and understanding the underlying mechanisms can lead to improved predictions of
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the strong currents and heat content associated with the Loop, which have practical significance.
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In this work, the old problem of a seasonal Loop Current is revisited taking advantage of the
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order-of-magnitude increase in data coverage from satellite, advent in models and forcing data,
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and improved theoretical understanding of Loop Current dynamics.
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2. Observed Loop Current Shedding Events
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The dates of Loop Current eddy separation from 1974 to 1992 are from Vukovich [1988],
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Sturges [1994] and Sturges and Leben [2000] using a combination of satellite-SST images as
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well as in situ and ship measurements to identify eddy separations. From 1993 to 2010, satellite
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altimetry data from AVISO [http://www.aviso. oceanobs.com/] is used. For shedding period
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shorter than 2 months (one in 1993, the other one in 2002), the two consecutive events are taken
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as the same event, and the first shedding is recorded. There are 47 eddy shedding events from
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1974 to 2010. Fig.1a sorts the number of shedding events by months (a seasonal histogram or
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SeH) and indicates that eddy shedding has a bimodal (biannual) seasonal signal: maximum in
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summer (Jul~Sep) and winter (Mar), and minimum in late fall (Nov~Dec) and late spring
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(May~Jun). The maximum difference in eddy count (Mde) is 7 between the period of most and
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least eddies. Approximately 40% of the eddies are shed during summer, but only one eddy is
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shed in the late fall (Nov~Dec). However, most of the seasonal signal is for the record after
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1993 (bars in fig.1a); summer eddy sheddings then account for 45% of the total, and no eddies
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were shed in Nov~Dec. This difference suggests a shift in the Loop Current's behaviors between
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the two periods - a point we will comment on later. The seasonal preference of eddy-shedding
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strongly suggests that the system is forced. Such a possibility was anticipated by Chang and Oey
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[2010; see also Oey et al. 2003; henceforth CO2010 and OLS2003 respectively] whose process
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experiments show the effects of wind on Loop Current eddy-shedding.
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Another way of displaying the eddy-shedding data is to plot the eddy-shedding histogram
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(ESH; fig.1b). The ESH has peaks (e.g. 6, 9 months etc), but most importantly it shows wide-
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ranging shedding periods P from 4~19 months: the eddy-shedding process appears to be chaotic.
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However, the "broad-spectrum" ESH can be a consequence of the seasonal shedding preferences
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of eddy-shedding. The argument is straightforward as summarized in fig.1c. For example,
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suppose the forcing is such that the Loop sheds eddies in August and September, the ESH then
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shows values at 1, and 11-13 months. By including only 4 observed, preferred shedding months:
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March, July, September and October (3,7,9,10 in fig.1c), a broad-spectrum ESH with periods
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from 1-20 months can exist. The solution is not unique, but this is not central to our argument.
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The point here is that an orderly, seasonally forced Loop Current that sheds eddies only in
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certain months is consistent with the existence of a broad spectrum of shedding periods; in other
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words, a chaotic system is not necessary for the existence of the broad spectrum. In addition to
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possible contribution from some natural shedding periods which depend on internal physics [e.g.
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Hurlburt and Thompson, 1980; OLS2003], peaks in the ESH may then be thought of as the
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result of some interannual variations of the forcing that perturb the shedding month from one
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year to the next, or even no shedding at all until the following year. That the Loop Current and
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eddy-shedding system may be non-chaotic was first suggested by Lugo-Fernandez [2007] .
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The contrary is not necessarily true. In other words, a chaotic Loop Current with a broad-
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spectrum ESH which may contain some prominent peaks (fig.1b) does not in general lead to
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seasonal preferences of eddy-shedding (fig.1a). With steady forcing a modeled Loop Current
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can display a natural period [e.g. CO2010]; on the other hand, experiments can be designed to
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produce a chaotic system with a broad-spectrum ESH [OLS2003]. Assuming such a system
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exists in the observed world, that the corresponding ESH has a broad spectrum with prominent
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peaks around some natural periods, what then can be deduced about its SeH? Given P, the
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month Msh when shedding occurs is:
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Msh = Msh0 + 12.(n˗1)/FP,
n = 1, 2, .., FP,
(1)
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where FP = 12/gcd(12,P) is the number of peaks in the SeH for that P, gcd = greatest common
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divisor, P = 1, 2, 3, ..., 19, 20 months, and Msh0 = the month of the first shedding; fig.1d shows
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the case for Msh0 = 1. It is readily shown that, despite the presence of biannual and/or annual
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peaks in the shedding periods (that may therefore favor a seasonal SeH), the existence in the
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observed ESH (fig.1b) of a P = PFull = 5, 7, or 11, etc for which gcd(12, PFull) = 1, can yield a
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non-seasonal SeH [details in Auxiliary Materials].
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The simple calculations above demonstrate the importance of order in the shedding
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events. It appears that nature has selected an order that, in the case of the Loop Current, is
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largely non-random. In other words, the shedding process is largely controlled by some form of
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external forcing, such as the winds. Model experiments support this assertion.
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3. Processes that Control the Seasonal Shedding of the Loop Current Eddies
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The importance of wind forcing on eddy-shedding has previously been noted [OLS2003,
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CO2010]. We now demonstrate that the existence of a bimodal SeH (fig.1a) is caused by a
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curious complementary effect (on the Loop Current) of the zonal component of the seasonal
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winds in the Caribbean Sea and the Gulf of Mexico.
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Seasonal Winds: Winds in the Caribbean Sea vary depending on the movement and intensity of
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the North Atlantic Subtropical High and, in winter, on the North American High also (Auxiliary
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Materials figs.A.2-3). In the Gulf of Mexico, winds are additionally modified by the North
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American monsoon in summer, the high pressure over the northeastern US in fall, and the low
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pressure over the western US in spring. The combined effect is that the seasonal winds are 180o
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out of phase in the two regions: the Caribbean easterly is strong in winter and summer and weak
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in spring and fall while the Gulf's easterly wind is stronger in fall and spring and weak in
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summer and winter (fig.2a).
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Numerical Experiments: This out-of-phase relation between the seasonal winds in the Caribbean
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Sea and the Gulf of Mexico is central to the understanding of why the Loop Current tends to
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shed more eddies in some months than others. Within the Gulf, easterly wind forces an eastward
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return flow across the middle of the basin which counters the westward-growing Loop Current
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by Yucatan inflow and Rossby-wave dynamics and delays eddy-shedding [Chang and Oey,
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2010]. We may expect then that the easterly peaks in the Gulf of Mexico in Oct~Nov and, to a
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lesser degree, in Apr~May, would delay eddy-shedding, which would be consistent with the
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observed SeH (fig.1a) that less eddies are shed in those months. However, explanations based on
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the Gulf's forcing alone are incomplete; the dynamics of the Caribbean Sea are necessary.
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The NW Atlantic Ocean model (5o-50oN and 98oW-55oW; see fig.A.4 in the auxiliary
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materials which also contains model descriptions) that we have previously tested [e.g. OLS2003;
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CO2010 ] for studying Loop Current dynamics is set up to run various experiments to isolate
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processes. The "Basic" experiment is forced by the CCMP wind stresses (0.25°x0.25°, 6-hourly
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satellite+NCEP blended dataset ) from 1988-2009. The "NoWind" experiment has no wind. In
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the "Atl" experiment, the wind is applied to the east of 82oW only, and the experiment
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"GOM+NWCar,"
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"GOM+NWCarNoCurl" also has winds applied west of 82oW but they are zonal only and are
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spatially constant averaged over the Gulf of Mexico and the NW Caribbean Sea (fig.2a). This
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last experiment has the essentials of the out-of-phase relation between the seasonal winds in the
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Caribbean Sea and the Gulf of Mexico. Each experiment was conducted for 22 years (1988-
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2009). To ensure robustness of our results, the Exp.Basic, Atl and GOM+NWCarNoCurl were
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repeated for additional 22 years with different initial fields and with a reduced Smagorinsky's
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constant (0.05 instead of 0.1) for the horizontal viscosity.
has
wind
applied
to
the
west
of
82oW
only.
Finally,
the
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The Exp.NoWind yields P ≈ 7~10 months around a peak ≈ 8 months [e.g. OLS2003;
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CO2010]. Its SeH is basically full (no seasonal preference with small standard deviation (sd) =
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0.5 and an Mde of only 1; not shown) as may be anticipated from the discussions (fig.1c,d) of the
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previous section. Exp.Atl also gives a full SeH, also with small sd = 0.4 and Mde =1 (fig.3a,
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grey). Remote winds in the eastern Caribbean Sea and the North Atlantic Ocean are therefore
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unlikely to force a seasonal shedding. The Exp.Basic (fig.3a, solid) has sd = 1.8 and Mde = 6; it
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shows eddy-shedding preferences in winter (Feb~Mar) and summer (Jul~Aug), with less
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shedding in late spring (May, 4 less) and early fall (Oct~Nov, 6 less), in general agreements with
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observations. This suggests that the seasonal eddy-shedding is wind-forced. This deduction is
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confirmed by the SeH from Exp. GOM+NWCar (fig.3b; sd = 1, Mde=4), which shows similar
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winter (Mar) and summer (Aug) shedding preferences. Experiments GOM+NWCar and Exp.Atl
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show that it is the regional wind in the Cayman Sea (i.e. NW Caribbean Sea) and the Gulf of
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Mexico that influences the seasonal eddy-shedding of the Loop Current. Finally, when the wind
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stress curl is removed, Exp. GOM+NWCarNoCurl (fig.3c; sd = 1.3, Mde = 5) shows that the
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zonal component of the wind alone can explain the seasonal preferences with more sheddings in
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winter (Mar) and summer (Jul~Sep). While there are some differences in the preferred months
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of shedding amongst the three experiments, we do not consider them to be significant.
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Why can wind force a seasonal preference in the shedding of Loop Current eddies?
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transport (TrYuc) also varies biannually: stronger in summer and winter and weaker in spring and
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fall [Molinari et al. 1978; Rousset and Beal, 2010]. Simulated TrYuc and Caribbean wind stress
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(τo, and wind stress curl ∇×τo) are significantly correlated with wind leading by 0~3 months.
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Correlation maps show that winds in the Cayman Sea are effective in driving transport
Yucatan
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fluctuations (fig.2d,e): westward wind stress (τox<0) and negative ∇×τo drive stronger TrYuc. The
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TrYuc is positively correlated with τox in the eastern Gulf: TrYuc decreases as westward wind in
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the Gulf becomes stronger [CO2010].
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The seasonal preferences of eddy-shedding can now be explained. It is well-known that
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the Loop Current tends to shed eddies more readily when it extends northward into the Gulf, and
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that once the Loop is in the extended state and ready to shed, the process is relatively fast [a few
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weeks; e.g. Hurlburt and Thompson, 1980]. The fundamental variable for the Loop's intrusion is
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TrYuc. In summer and winter, TrYuc increases as the negative wind stress and wind stress curl in
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the Caribbean Sea increase (see wind plots in Fig.A.3 in the auxiliary materials); the easterly
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peaks (Jul and Jan) in the Caribbean correspond well to the peaks in TrYuc especially for summer
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(fig.2a,b). The larger TrYuc leads to stronger inflow velocity vo and cyclonic vorticity ζo on the
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western (~50 km) portion of the Yucatan Channel, and a more extended Loop Current [OLS2003;
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Oey, 2004]. The ζo/f (f = Coriolis parameter) is an excellent predictor of the Loop Current's
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northern boundary with high R2 = 0.83 for their linear regression (fig.2c). While this linear
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relation agrees well with the Reid's formula [Reid, 1972; OLS2003], we treat it to be merely an
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empirical one. The Loop Current therefore tends to be extended in summer and winter. As TrYuc
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decreases (Sep and Mar) when the Caribbean (westward) windstress weakens (Jul~Sep, and
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Jan~Mar), the Loop retracts as ζo also weakens. The mass influx (Qi) feeding the Loop also
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decreases, providing a favorable condition for the westward Rossby wave speed of the extended
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Loop (Ci ~ -βRd2, where Rd = Rossby radius based on the depth of the matured Loop) to
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overcome Qi, hence also a favorable condition for eddies to separate [Nof, 2005].
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weakening of the wind (and transport) are abrupt especially in summer (fig.2a,b). Moreover,
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because the Gulf of Mexico's easterlies are weak during those periods (fig.2a), the eastward
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momentum flux that impedes eddy-shedding [CO2010] is also weak. This combination of strong
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Caribbean easterly, abrupt weakening, and weak easterly in the Gulf of Mexico favors a larger
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proportion of eddies being shed from Jul~Aug and Feb~Mar (fig.3). In fall and spring, TrYuc and
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the Caribbean easterly remain weak but at the same time westward wind in the Gulf of Mexico
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intensifies (Oct and May; fig.2a). The Loop Current's expansion and eddy-shedding are now
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impeded by the eastward momentum flux that intensifies along the mid-latitudes within the Gulf.
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These factors lead to a reduced number of eddies being shed in fall and spring (fig.3). These
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processes are summarized schematically in fig.4. In the auxiliary materials, the dynamics are
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further examined using a simple reduced-gravity model (Exp.RG). The Exp.RG confirms that
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easterly wind in the NW Caribbean Sea drives a seasonal shedding. The Gulf's easterly wind
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accentuates the seasonality by delaying eddy-shedding in fall and spring: it increases the
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summer-fall (or winter-spring) difference in the number of eddies shed. We also compared the
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RG experiments with the 3D Exp.Basic (and Exp.GOMCarNocurl) using the ensemble averaging
The
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idea of the Loop Current Cycle described in Chang and Oey [2011]. In the 3D experiments, we
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found that on average eddy-shedding follows shortly (~1 month) after the maximum Yucatan
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transport, but that in Exp.RGCarib there is an additional time-lag of 1~2 months. The RG
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response is similar to the EOF modes 1+2 of the 3D experiments while interestingly the EOF
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mode 3 accelerates the shedding in the 3D experiments and closely resembles the Campeche
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Bank instability mode [Oey, 2008]. Therefore, dynamical instability takes part in the eddy-
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shedding process, but it does not control the seasonal timing.
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4. Summary and Conclusions
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The Loop Current is observed to shed more eddies in summer and winter. Numerical
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experiments also yield seasonal preferences with more sheddings in winter and summer, and less
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in fall and spring in agreement with observations. The seasonal preferences are forced by the
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seasonal winds in the Caribbean Sea and the Gulf of Mexico. The Loop sheds more eddies in
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summer and winter in response to intensified Yucatan transports driven by the stronger trade
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winds in the Caribbean, and concurrently when weak easterlies in the Gulf offer little
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impediment to eddy shedding.
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Caribbean's (Gulf's) easterlies weaken (strengthen). Since wind plays a central role, our results
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suggest the existence of an interannual variation of the eddy-shedding process. Indeed, fig.1a
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indicates that the biannual seasonal preferences are much less distinct for the first half of the data
The conditions are reversed in fall and spring when the
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period from 1974-1992. The second half (1993-2010) has more shorter (biannual) periods, and
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why that is so may be due to a basic change in the wind. This and other consequences will be
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examined in a future study.
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Acknowledgements
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We gratefully acknowledge the supports by the Bureau of Offshore Energy Management
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contract# M08PC20007 and the Portland State U. contract# 200MOO206.
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References
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Behringer, D.W., R.L. Molinari, and J.F. Festa, 1977: The Variability of Anticyclonic Current
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Patterns in the Gulf of Mexico. JGR, 82, 5469-5476.
208
Chang,Y.-L. and L.-Y. Oey, 2010: Why can wind delay the shedding of Loop Current eddies? J.
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Phys. Oceanogr, 40, 2481-2495.
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Chang,Y.-L. and L.-Y. Oey, 2011: Loop Current Cycle: coupled response of Loop Current and
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deep flows. J. Phys. Oceanogr, 41, 458-471.
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Hurlburt, H.E., and J.D. Thompson, 1980. A numerical study of Loop Current intrusions and
213
eddy shedding. J. Phys. Oceanogr., 10, 1611-1651.
214
Leipper, D.F., 1970: A sequence of current patterns in the Gulf of Mexico. JGR, 75, 637-657.
215
Lugo-Fernandez, A., 2007: Is the Loop Current a chaotic oscillator? JPO, 37, 1455-1469.
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Molinari, R.L., J.F. Festa & D. Behringer, 1978: The circulation in the Gulf of Mexico derived
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from estimated dynamic height fields. J. Phys. Oceanogr., 8, 987-996.
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Nof, D., 2005: The momentum imbalance paradox revisited. J. Phys. Oceanogr., 35, 1928-1939.
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Oey, L.-Y. 2004. Vorticity Flux in the Yucatan Channel and Loop Current Eddy shedding in
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the Gulf of Mexico. JGR, 109, C10004, doi:10.1029, 2004JC002400.
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Oey, L.-Y., 2008: Loop Current and Deep Eddies. J. Phys. Oceanogr. 38, 1426-1449.
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Oey, L.-Y., H. Lee and W. J. Schmitz, 2003: Effects of Winds and Caribbean Eddies on the
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Frequency of Loop Current Eddy Shedding, JGR, 108, 3324, doi:10.1029/2002JC001698.
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Reid, R.O., 1972. A simple dynamic model of the Loop Current. Contributions on the Phys
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Oceanogr of Gulf of Mexico, II, L.R.A. Capurro & J.L. Reid, Eds., Gulf Pub., 157–159.
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Rousset, C. and L.M. Beal, 2010: Observations of the Florida and Yucatan Currents from a
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Caribbean cruise ship. J. Phys. Oceanogr., 40, 1575-1581.
228
Sturges, W. 1994: The frequency of ring separations of Loop Current, JPO, 24, 1647-1651.
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Sturges, W., and R. Leben, 2000: Frequency of ring separations from the Loop Current in the
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Gulf of Mexico: A revised estimate, J. Phys. Oceanogr., 30, 1814– 1818.
231
Sturges,W. and J.C.Evans,1983:Variability of Loop Current in Gulf of Mexico, JMR,41,639-653.
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Vukovich, F.M., 1988: Loop Current boundary variations. JGR, 93, 15,585-15,591.
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(C)
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(D)
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Fig.1 (a) Seasonal Histogram (SeH; eddies vs. Calendar months) using 1974-2010 data (solid
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line; dash is 3-mo weighted (1/4-1/2-1/4) mean) and 1993-2010 data (bar); (b) Eddy-Shedding
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Histogram (eddies vs. periods P). (c) P's (shaded if shedding) vs. shed-months (8=Aug etc). (d)
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Shed-month vs. P's, shown for first shedding in Jan. For each P, summed shades = peaks in SeH.
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The "˅" means "or."
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Figure 2. Seasonal cycles (1988-2008) of (A) zonal wind stresses averaged over Gulf of Mexico
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and NW Caribbean Sea (negative westward), and (B) Yucatan transport anomaly from Exp.Basic
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with mean = 25.6 Sv shown. (C) Regression of Loop's northern boundary vs. ζ/f from Exp.Basic.
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Maps: correlations (wind leading 1 month; above the 95% significance, otherwise white)
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between Yucatan transport and (D) zonal wind stress and (E) wind stress curl; contours are 0.2
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and 0.4, black positive and white negative.
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Fig.3. Seasonal histograms (eddies vs. Calendar months, 3-month weighted (1/4-1/2-1/4) mean,
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and plotted over two cycles) for model experiments forced by CCMP wind: (a) Basic and Atl
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(grey) both 44 years, (b) GOM+NWCar (22 years) and (c) GOM+NWCarNoCurl (44 years).
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Fig.4. A schematic plot of seasonal eddy shedding according to the dynamics explained in text.
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Upper panels from left to right: extended Loop when Caribbean wind and Yucatan transport are
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strongest (Jul and Jan), wind and transport weaken (Sep and Mar; squiggly arrow represents
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Rossby wave), and wind in the Gulf is strongest (Oct and May; blue arrows indicate wind-forced
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upper-layer circulation). Lower panel: base line represents the zero wind when the Loop Current
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sheds eddies at or near its natural period. The solid up arrow "↑" indicates increased shedding
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and dashed down arrow "↓" decreased shedding. The easterly wind is stronger away (up or down)
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from the base line: solid for Caribbean wind and dotted line for the Gulf. The time lag is
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approximate indicating a range rather than a fixed value.
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Auxiliary Materials
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Why does the Loop Current tend to shed more eddies in summer and winter?
Y.-L. Chang and L.-Y. Oey*
Princeton University
*Corresponding Author: lyo@princeton.edu
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The SeH of a Broad-Spectrum ESH with Prominent Biannual and/or Annual Periods:
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We calculate the seasonal histogram (SeH) that results from each of the possible eddy-
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shedding periods P = 1, 2, 3, ..., 19, 20 months. For example, the seasonal histogram for P = 2
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has FP = 6 peaks at calendar month Msh = 1 (Jan), 3, 5, 7, 9 and 11, assuming that the initial
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month of shedding Msh0 = 1. Equation (1) in text gives the general case:
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Msh = Msh0 + 12.(n˗1)/FP,
n = 1, 2, .., FP,
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where FP = 12/gcd(12,P), gcd = greatest common divisor, P = 1, 2, 3, ..., 19, 20 months, and
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Msh0 = the month of the first shedding. We demonstrate, in two steps, that the existence of even
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a minor (to be specified below) PFull (for which gcd(12, PFull) = 1) can, for a random system,1
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sufficiently modify the ESH that it becomes dissimilar from the observed SeH (fig.1a). Firstly,
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we take a pool of Nse (=50) shedding events 80% of which have P = 6 and 20% have P = PFull =
1
It is not obvious what the appropriate chaotic (rather than a random) analog for the Loop Current would be for
the simple experiments to be described here; we will instead rely on the results from the primitive-equation
numerical models discussed in the main text. In what follows, we will be somewhat sloppy in not making a
distinction between chaos and randomness, and the conclusions thus deduced are strictly valid only for the latter,
and are therefore likely to be only sufficient, i.e. they may not be necessary.
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7 (the observed number of events in fig.1b is 47, and the 6-7 month periods partition is 80:20).2
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The observed ESH is therefore idealized by just these two periods, the major one tends to
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produce a semiannual SeH while the minor one a full SeH. Shedding events are then randomly
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selected (and subsequently deactivated) from the pool, one at a time; for a given Msh0 this yields
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one SeH. The experiment is then repeated K times using K randomly selected Msh0, and an
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ensemble mean is calculated. For large K (10 or more), the resulting SeH has no seasonal pattern
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(fig.A.1a). Secondly, we use the observed pool of eddy-shedding events (fig.1b). If in addition
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to the observed P’s, the observed Msh0 and shedding order are also used, we trivially recover the
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observed SeH (fig.1a). However, in a chaotic system, while the P’s may be those observed in
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fig.1b, other Msh0 and order are equally valid. The resulting SeH is again devoid of any
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seasonality (fig.A.1b). The conclusion is unchanged when the Msh0 is fixed at the observed (=
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Apr of 1974) but the order of shedding is random. We see that PFull modifies the ESH that,
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despite the presence of biannual and annual peaks in the shedding periods, a non-seasonal SeH
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results in a random system.
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Seasonal Winds in the Caribbean Sea and the Gulf of Mexico:
2
The P = 6 is used since the observed ESH has a dominant semi-annual peak which may be the natural period of
the observed system, and which therefore can contribute to the observed SeH in a chaotic system.
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Winds in the Caribbean Sea are governed by the movement and intensity of the North
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Atlantic Subtropical High (NASH) and, in winter, by the North American High (NAmerH) also;
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excellent descriptions are given in Wang [2007].3 The NASH is strongest in the summer and
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extends toward the Caribbean where the easterly wind is also strong (see Figs.A.2 & A.3). In the
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fall, the NASH weakens and its center moves eastward, and the Caribbean easterly also weakens.
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In the winter, NASH’s isobars extend westward and connect with the NAmerH centered over the
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northwestern US, and the Caribbean easterly is again strong.
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American monsoon starts to develop, the NASH’s isobars retreat toward the east and the
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Caribbean easterly weakens. The seasonal wind from 0.25°x0.25°, 6-hourly CCMP data (Cross-
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Calibrated Multi-Platform; Atlas et al. 2009) averaged over the northwestern Caribbean Sea (i.e.
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the Cayman Sea) is shown in Fig.2 which shows clearly the biannual variation of the Caribbean
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easterly: strong in winter and summer and weak in spring and fall.
In the spring, as the North
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Apart from the influences of the NASH and NAmerH, the seasonal wind in the Gulf of
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Mexico are strongly modified by (i) North American monsoon in summer, (ii) the high pressure
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that develops over the northeastern US in fall, and (iii) the low pressure that develops over the
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western US in spring (Figs.A.2 & A.3). These factors result in weakened easterly in summer,
3
Wang [2007] discussed the possible coupling between the wind and SST gradient (south-north) in the Caribbean
Sea. This is an interesting topic that possibly can influence the sheddings of Loop Current eddies; it may deserve a
more detailed study in the future.
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strong east-northeasterly in fall, weakened easterly in winter, and strengthening easterly again in
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spring. As in the Caribbean Sea, there is therefore also a biannual variation in the zonal wind
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over the Gulf of Mexico, but the seasonal timing is (nearly) out of phase (fig.2).
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Descriptions of the Numerical Model:
The NW Atlantic Ocean model [5o-50oN and 98oW-55oW; see fig.A.4] that we have
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extensively tested [e.g. Oey et al. 2003; Chang and Oey, 2010] for studying Loop Current
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dynamics is set up to run various experiments to isolate processes. Orthogonal curvilinear grid is
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used in the horizontal with grid sizes   10 km (or less) in the Gulf of Mexico, expanding to  
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15 km in the central and eastern Caribbean Sea. The model has 25 vertical sigma levels and a
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fourth-order pressure-gradient scheme is used to ensure that the sigma-level pressure gradient
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errors are small [Berntsen and Oey, 2010]. The World Ocean Atlas data (“Climatological” data)
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from NODC [http://www.nodc.noaa.gov/OC5/WOA05/pr_woa05.html] was used for initial
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condition as well as boundary condition along the eastern open boundary at 55oW, where steady
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transports (with radiation and advection conditions etc) are specified for the Gulf Stream
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extension and the returning, subtropical gyre. Heat and salt fluxes are zero at the sea surface. A
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more complete description is given in Chang and Oey [2010]. Extensive tests of our model have
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previously been documented - please see http://www.aos.princeton.edu/WWWPUBLIC/
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PROFS/publications.html.
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Reduced-Gravity (RG) Model Experiments:
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The RG model is the same as that used previously in Chang and Oey [2010]. Its domain
336
is the same as the Northwest Atlantic Ocean domain shown in fig.A.4, except that the coastline is
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defined at the 200m-isobath, and the eastern boundary at 55oW is closed. A zonal wind stress
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(with curl) is then specified east of 80oW (i.e. in the Atlantic Ocean only) to drive a gyre that has
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a transport  22 Sv through the Yucatan Channel. Table A.1 gives various model parameters and
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their meanings. Weak dissipative processes are included as AH for numerical stability, and αN
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and Cb for dissipating eddies after they propagate into the western Gulf of Mexico. Three
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experiments are conducted: RG-GOM, RG-Carib and Rg-GOMCarib. Each was carried out for
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15 years but a quasi-steady state (when the model Loop Current sheds eddies at a regular period)
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was achieved in about 3 years. The last 12 years results are used for the analysis.
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The RG-GOM experiment applies a time-dependent zonal momentum flux as a body
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force (kinematic, unit m2 s-2) to model the x-momentum associated with the wind-forced returned
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flow along the mid-latitudes of the Gulf of Mexico. The momentum flux is applied over the
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western portion of the model Loop Current only (90oW < longitude < 86oW) [Chang and Oey
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2010] as a semi-annual sinusoidal function to idealize the observed bimodal seasonal wind stress,
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so that the eastward momentum flux is maximum in March and September (to mimic the strong
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westward wind), and minimum in December and June (fig.A.5a). The RG-Carib experiment
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specifies wind stress directly in the Northwestern Caribbean Sea (87oW < longitude < 80oW,
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15oN< latitude < 22oN). A semi-annual sinusoidal function is used to idealize the time-dependent
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variation of the observed zonal wind stress: maximum westward in December and June, and
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minimum in March and September (fig.A.5a). The RG-GOMCarib experiment combines the
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above two experiments: applying the momentum flux in the Gulf of Mexico and the wind stress
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in the Northwestern Caribbean Sea. Meridional forcing is set to zero in all the experiments.
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Figures A.5b-d plot contours (color) of monthly-mean upper-layer depth h along 90oW
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inside the Gulf, across which RG-model eddies pass after they separate from the Loop Current.
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The black curves show the actual number of shedding (i.e. SeH), 3-month averaged to reduce the
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ambiguity associated with the beginning and end of each calendar month.
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normalized by its maximum value shown on each panel. The SeH for Exp.RG-GOM is basically
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"full" with equal eddy-shedding likelihood in each month, the max-min difference in #eddies = 1,
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and the eddies are weak (fig.A.5b). The SeH for Exp.RG-Carib shows more eddies being shed in
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Dec~Jan and in Jun~Jul, the max-min difference in #eddies = 1.8, and the eddies are strong.
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When the Gulf's forcing is also turned on (Exp.RG-GOMCarib), the seasonal signal becomes
Each curve is
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more distinct, and the max-min difference in #eddies is increased to 3.5. In particular, the fall
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and spring minima are reduced to become nearly zero because of the effects of strong returned
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(eastward) momentum flux due to the wind in the Gulf of Mexico. These results are consistent
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with the 3D experiments discussed in text.
371
REFERENCES
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Atlas R., Hoffman R. N., Ardizzone J., Leidner S. M., Jusem J. C., 2009: Development of a new
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cross-calibrated, multi-platform (CCMP) ocean surface wind product. AMS 13th Conference on
374
Integrated Observing and Assimilation Systems for Atmosphere, Oceans, and Land Surface
375
(IOAS-AOLS).
376
Berntsen, J. and L.-Y. Oey, 2010: Estimation of the internal pressure gradient in σ-coordinate
377
ocean models: comparison of second-, fourth-, and sixth-order schemes. Ocean Dyn. 60, 317-
378
330. DOI 10.1007/s10236-009-0245-y.
379
Chang,Y.-L. and L.-Y. Oey, 2010: Why can wind delay the shedding of Loop Current eddies? J.
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Phys. Oceanogr, 40, 2481-2495.
381
Oey, L.-Y., H. Lee and W. J. Schmitz, 2003: Effects of Winds and Caribbean Eddies on the
382
Frequency of Loop Current Eddy Shedding, JGR, 108, 3324, doi:10.1029/2002JC001698, 2003.
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Wang, C., 2007: Variability of the Caribbean low-level jet and its relations to climate. Clim.
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Dyn., 29, 411-422.
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Table A.1: Reduced-gravity model parameters (domain in fig.A.4)
Parameters
Meanings
Values
g'
0.01 m s-2
g∆/o
H
mean ‘upper-layer’ depth
600 m
∆x, ∆y
variable x and y grid spacings
~10 km in the Gulf of Mexico
Hcoast
isobath where coastline is defined
200 m
AH
horizontal viscosity
100 m2 s-1
αN
Newtonian cooling coefficient
1.25×10-3 day-1
Cb
quadratic ‘bottom’ drag coefficient
10-4
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(A)
(B)
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Fig.A.1. The 100-run ensemble of monthly number of eddies (i.e. the seasonal histogram) using
393
(a) 6- and 7-month periods and (b) observed periods shown in fig.1b of the main text.
394
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(A) Jul
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(B) Oct
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Fig.A.2. NCEP Reanalysis mean geopotential heights for (a) Jul, (b) Oct, (c) Jan and (d) May,
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illustrating the movements and intensities of the North American Subtropical High (Azores or
400
Bermuda High; all seasons), the North American High (Jan - over NW US), the NE US high
401
(Oct), and the (weak) western US low (May). These pressure systems control the wind patterns
402
over the Caribbean Sea and the Gulf of Mexico as discussed in text.
403
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(C) Jan
405
(D) May
406
407
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Fig.A.2. (Continued).
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Fig.A.3. January, May, July and October monthly-mean wind climatologies calculated from the
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CCMP data from 1988-2010, showing the strong easterlies (hence also anticyclonic wind stress
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curls) in the western Caribbean Sea in winter and summer, and weaker values in spring and fall.
413
In contrast, in the Gulf of Mexico, winter and summer winds are comparatively stronger than in
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spring and fall.
415
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Fig.A.4. The northwest Atlantic Ocean model domain. Dotted contour shows the 200-m isobath.
Line at 82W separates the regions where wind is applied for experiments Atl (wind applied to the
east of the line) and GOM+NWCar and GOM+NWCarNoCurl (wind applied to the west of the
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line). Vectors are the mean CCMP (kinematic) wind stress from 1988 to 2009.
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421
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Fig.A.5 The reduced gravity experiment: (a) momentum flux in the Gulf of Mexico (solid) and
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wind stress in the northwestern Caribbean Sea (dash). (b) to (d) are the upper layer depth in
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colors and the monthly number of eddy shedding (black curve) of experiment RG-GOM (b), RG-
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Carib (c) and RG-GOMCarib (d).
427