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Loop Current Growth and Shedding Using Models and Observations: Numerical Process Experiments and Satellite Altimetry Data

YU-LIN CHANG National Taiwan Normal University, Taipei, Taiwan, and Princeton University, Princeton, New Jersey

L.-Y. OEY Princeton University, Princeton, New Jersey, and National Central University, Jhongli, Taiwan

(Manuscript received 1 August 2012, in final form 10 October 2012)

ABSTRACT

Recent studies on ’s variability in the Gulf of suggest that the system may behave with some regularity forced by the biannually varying trade winds. The process is analyzed here using a reduced-gravity model and satellite data. The model shows that a biannual signal is produced by vorticity and transport fluctuations in the Yucatan Channel because of the piling up and retreat of warm water in the northwestern Caribbean forced by the biannually varying trade wind. The Loop grows and expands with increased northward velocity and cyclonic vorticity of the Yucatan Current, and eddies are shed when these are near minima. Satellite sea surface height (SSH) data from 1993 to 2010 are analyzed. These show, con- sistent with the reduced-gravity experiments and previous studies, a (statistically) significant asymmetric biannual variation of the growth and wane of Loop Current: strong from summer to fall and weaker from winter to spring; the asymmetry being due to the asymmetry that also exists in the long-term observed wind. The biannual signal is contained in the two leading EOF modes, which together explain 47% of the total variance, and which additionally describe the eddy shedding and westward propagation from summer to fall. The EOFs also show connectivity between Loop Current and Caribbean Sea’s variability by mass and vor- ticity fluxes through the Yucatan Channel.

1. Introduction of eddy shedding through model and observational analyses. The intrusion and retraction of the Loop Current The shedding of Loop Current eddies can be in- in the eastern and eddy shedding (i.e., terpreted as being a result of competing imbalance separation of warm rings from the Loop) constitute between the volume influx (Q) through the Yucatan one of the most fascinating geophysical fluid dynam- Channel,whichgrowstheLoop,andwestwardRossby ical phenomena in the (see Oey et al. 2005 for wave (velocity C ’2bR2, R 5 Rossby radius based a review). The resulting circulation is the source of i o o on the matured eddy), which tends to ‘‘peel’’ the eddy much of the variability in the Gulf of Mexico. Sea from the Loop; this will be referred to as the Pichevin– surface height (SSH) constructed from satellite al- Nof mechanism (Pichevin and Nof 1997; Nof 2005).1,2 timetry data shows that the Loop Current behaves in The Loop and eddies are approximated as being ac- a complex and seemingly chaotic fashion. An improved tive in the upper layer only (i.e., reduced-gravity). understandingofwhen an eddy is likely to shed from the Loop Current is of interest both scientifically and for practicalapplications.InthisworkandinXuetal. 1 Hurlburt and Thompson (1980) demonstrated the process nu- (2013), we attempt to contribute to the knowledge merically, while Pichevin and Nof solved it analytically. 2 The growth rate should be said more accurately to be a func- b 2 tion of Q and the eddy’s westward velocity a function of Ro. Corresponding author address: L.-Y. Oey, Princeton University, Formulae for zero-PV eddy (e.g., from Nof 2005) are growth rate 5 0 p 2 3 52 b 2 ; 70 Washington Road, Princeton, NJ 08540. 8g Q/3 f RE and westward velocity 2 Ro/3 , where RE(t) E-mail: [email protected] (Qt)1/4 is the (growing) eddy’s radius, which itself depends on Q.

DOI: 10.1175/JPO-D-12-0139.1

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FIG. 1. A schematic plot of (left) an extended Loop Current when the Yucatan inflow is strong following, say, a maximum westward wind in the Caribbean Sea; and (right) when the inflow weakens and westward dynamics (squiggly arrow represents Rossby wave) overcomes the inflow rate, and an eddy may be shed.

The mechanism applies to a northward (for Northern z z 2 y 1/2 5 1 1 2 2 u Hemisphere), strong (nonlinear), and less-dense narrow b b b b (1 cos ) , (1) outflow debouching into a straight-coast ocean on a b-plane, and requires neither the existence of a lower u layer, nor flow instability, nor forcing (other than Q), where is the anticlockwise angle the inflow Yucatan nor topography (other than the narrow channel and the Current makes with the x (eastward) axis. The b is straight coast). Knowing Q, the eddy growth rate (C ), plotted in Fig. 2, which shows that b is most sensitive to y z z and shedding period (P 5 time taken for the eddy to especially for positive ’s (Figs. 2a,b; consistent with y grow and break away from the outflow) are calculated; CO2012’s result), moderately sensitive to [Figs. 2a,c; n consistent with Nof (2005) that the Loop’s growth rate Nof (2005) shows that Cy ; Q ,wheren = ;1/4–2/5, and 2 2 ; n P ; Q 1/5. The relevant time scale is O(bR ) 1 or longer Cy Q is moderately sensitive to Q because of the o u [.(10–30) days for R ’ (30–50) km; Nof 2005], so the fractional nth power], and insensitive to (Figs. 2b,c). o y idea may be approximately applied to a slowly-varying Since an increased (or Q) invariably leads also to in- z Q with time scales of, say, a few months, or longer. The creased , it is difficult to separate their effects; but both mechanism then suggests that an increased Q would ac- are positively correlated with b (Fig. 2). celerate eddy growth, so that if Q subsequently de- The trade winds over the Caribbean Sea and Gulf of Mexico are significantly biannual and 1808 out of phase creases the Ci–Cy imbalance can provide a favorable condition for the eddy to shed (Fig. 1). with respect to each other, due to the combined forc- Besides Q, another parameter that affects the Loop ing of various centers of action over the ’s northward intrusion b is the upstream vortic- Ocean and the American continent (see CO2012’s Fig. 2a ity divided by parameter f (z/f) at the western and their online supporting materials). The Caribbean edge of the in Yucatan Channel (Oey (Gulf of Mexico) trade wind weakens (strengthens) from et al. 2003; Oey 2004). Using long-term OGCM (Ocean summer to fall and from winter to spring, and strengthens General Circulation Model) integrations forced by 22 (weakens) from spring to summer and from fall to winter. years of reanalysis winds, Chang and Oey (2012, The variation is asymmetric, such that the Caribbean hereafter referred to as CO2012) found that the linear (Gulf of Mexico) trade wind weakens (strengthens) more regression between b and z/f is significant and high dramatically from summer to fall than from winter to (r2 ’ 0.83, see their Fig. 2c): the modeled Loop Current spring. CO2012 show that the Caribbean’s wind and wind extends far into the Gulf as the Yucatan Current, stress curl correlate (negatively, since trade wind is hence z/f and the y-velocity y,intensify.3 While the westward and wind stress curl is also negative) signifi- regression relation is empirical, it is consistent with cantly with the Yucatan transport which therefore also Reid (1972)’s equation (see also Oey et al. 2003) based varies biannually and moreover also asymmetrically; on PV-conservation: the transport decreases more dramatically from sum- mer to fall than from winter to spring (CO2012’s Fig. 2b). Based on 5-year shipboard ADCP measurements, 3 CO2012 used a western width of 50 km averaged from surface Rousset and Beal (2010, their Fig. 4b) also found a sig- to 200 m to define z and y. nificant biannual transport variation. However, the data

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TABLE 1. Reduced-gravity model parameters.

Parameters Meanings Values

0 22 g gDr/ro 0.01 m s H Mean upper-layer depth 600 m Dx, Dy Variable x and y grid spacings ;10 km in the Gulf of Mexico Hcoast Isobath where coastline 200 m is defined 2 21 AH Horizontal viscosity 100 m s 23 21 aN Newtonian cooling coefficient 1.25 3 10 day 24 Cb Quadratic drag coefficient 10

other hand, if the Loop Current is in part forced by the biannual wind (and Yucatan transport), then the system may not be entirely chaotic (Lugo-Fernandez 2007). Therefore, in view of the recent evidences that biannual transport variation exists both in observations (Rousset and Beal 2010) and models (CO2012), it seems useful to further explore the dynamics using process as well as realistic experiments with data assimilation, and to ex- amine if the bimodal variability is dominant in satellite observations. This work examines the above ideas with process ex- periments using a reduced-gravity model and analyses of satellite observations. A follow-up study (Xu et al. 2013) examines a realistic-case analysis of the 2011 summer shedding event using satellite and in situ obser- vations. The outline of the paper is as follows. Section 2 FIG. 2. Contours of b (km) as a function of (a) z and y (fixed u 5 2 describes reduced-gravity experiments to explore the 908); (b) z and u (fixed y 5 1ms 1); and (c) u and y (fixed z 5 2 3 2 2 10 6 s 1) according to the Reid’s (1972) formula: Eq. (1). Pichevin–Nof mechanism and Reid’s (1972) theory ap- plied to biannual transport forcing by wind. This is fol- lowed in section 3 with analyses of the satellite SSH data. shows no asymmetry, a discrepancy which is yet to be Section 4 concludes the paper. investigated. Because of the above biannual forcing, CO2012 show 2. Reduced-gravity experiments that their simulated Loop Current tends to shed more eddies in summer and winter compared to fall and spring; The reduced-gravity model was described previously there is also an asymmetry: the summer-fall difference (Chang and Oey 2010, CO2012). The domain is the in the number of shed eddies is greater than the winter– northwest 58–508N and 1008–558W [see spring difference. These findings indicate a close con- Fig. 1 in Chang and Oey (2010).] Table 1 gives various nection between the inflow (z, y, or transport) and the model parameters and their meanings. Although realistic Loop Current growth and eddy shedding, which is very [e.g., National Centers for Environmental Prediction much consistent with Pichevin–Nof mechanism and (NCEP) reanalysis 1 satellite] wind may be used (e.g., Reid’s theory. CO2012), our goal here is to understand responses under That Loop Current variability may be biannual was clearly defined forcing, and we want to control the mean proposed by several Gulf of Mexico pioneers: Leipper and fluctuating parts of the transport that passes through (1970), Behringer et al. (1977), Molinari et al. (1978), the Yucatan Channel. We therefore specify a steady and Sturges and Evans (1983) (see review in CO2012). zonal wind stress with curl (i.e., latitudinal 0–p cosine The idea was subsequently dismissed, in particular after variation) east of 808W (i.e., in the Atlantic Ocean only), Hurlburt and Thompson (1980) demonstrated numeri- and its magnitude is adjusted to drive (through Sverdrup cally that the Loop Current can shed eddies without the dynamics) a steady westward transport ’ 21.5 Sv 2 need for a time-dependent transport forcing. On the (1 Sv [ 106 m3 s 1) in the Caribbean Sea. This will be

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TABLE 2. Reduced-gravity model experiments and their SeH and EsH parameters. In column 2, actual indicates eddy counts based on the unsmoothed SeH, while smoothed is based on the 3-month weighted-smoothed SeH (i.e., black curves in Figs. 3b–d; see text). Wind: (1) Steady wind stress curl in North Atlantic Ocean east of 808W to drive ;22 Sv through Yucatan Channel; (2) semiannual wind in Gulf of Mexico; (3) semiannual wind in northwestern Caribbean Sea.

Experiment Wind Difference in No. of eddies between Standard deviation Calendar month(s) Shedding periods (see caption) months with most and least eddies based on actual SeH with most eddies (months) Steady22Sv 2 (actual), 1 (smoothed) 1.0 None 7, 8 (1) GOM 2 (actual), 1 (smoothed) 0.9 None 6, 7, 8 (1) 1 (2) Carib 4 (actual), 2 (smoothed) 1.7 June and December–January 6, 7, 8, 9 (1) 1 (3) GOMCarib 8 (actual), 4 (smoothed) 2.6 June and December–January 4, 5, 6, 7, 8, 9 (1) 1 (2) 1 (3)

referred to as the Steady22Sv experiment. Three a. Eddy-shedding characteristics time-dependent transport experiments are then con- ducted (cf. CO2012), each forced by biannual wind, We first discuss some general characteristics of the which qualifies as being slowly varying. A semiannual eddy-shedding results (Table 2 and Fig. 3). Rather than sinusoidal function is used: maximum westward in ‘‘pick-and-choose’’ from snapshots of the 12-yr data, we December and June, and minimum in March and conduct an unbiased, monthly composite analysis and September; these drive biannual transport variation the significances of these composites are then judged (see below). The model wind therefore idealizes the by calculating the corresponding standard errors. This biannual cycle of the observed zonal wind, which as procedure anticipates that the solution is periodic, which mentioned above is actually asymmetric: maximum turns out to be true as judged from the smallness of westward in January and July, and minimum in May the standard errors in nearly all of the parameters we and September (note the 1–2-month shift between have examined below. model and observed wind maxima and minima). The For each experiment, the calendar months when wind is specified in the northwestern Caribbean Sea eddies are shed are recorded. Table 2 (second column) (158N , latitude , 228N, 878W , longitude , 808W). lists the difference in the number of eddies between 2 2 Wind stress amplitude of 2 3 10 4 m2 s 2 is used to months with most and least eddies. From the distribu- (approximately) match the monthly-mean Yucatan tion of number of eddies as a function of the calendar transport fluctuations of ’61 Sv based on the 22-yr months, which will be referred to as the Seasonal His- OGCM simulation (see CO2012’s Fig. 2b). This ex- togram (SeH) (CO2012), the standard deviation is cal- periment is called Exp.Carib. The zonal wind in the culated and listed in the third column.4 The calendar Gulf of Mexico is also biannual and is 1808 outofphase months with most eddies (taken into account also of from that in the Caribbean Sea (CO2012). Westward statistical significance—described below) are then lis- wind in the Gulf drives an eastward momentum flux ted in the fourth column. Finally, eddy-shedding pe- and delays eddy-shedding (Chang and Oey 2010). A riods defined as time differences between present minus biannual zonal momentum flux which is in phase with preceding eddies are listed in the last column. The SeH is the Caribbean wind is therefore also included to plotted as black curves in Figs. 3b–d for Exp.GOM, model this effect in the second Exp. GOMCarib, which Carib, and GOMCarib. The corresponding SeH for then specifies both the Caribbean Sea and Gulf of the Steady22Sv experiment is also included in Fig. 3b as Mexico winds. Finally, Exp. GOM specifies the semi- the dashed gray curve. A 3-month weighted averaging annual momentum flux over the Gulf of Mexico only, that (1 1 2 1 1)/4 has been applied to the SeH to account for is, no wind in the Caribbean Sea. Other supporting experiments were also carried out and they will be mentioned below as appropriate. All experiments were 4 integrated for 15 years from a state of rest; the model T. Sturges (2012, personal communication) mentioned that the word ‘‘seasonal’’ may be confused with ‘‘annual variation.’’ Here Loop Current sheds eddies at a quasi-regular period we follow the Oxford English dictionary to mean it as ‘‘happening in about 3 years. The last 12 yr results are used for during a particular season’’ without necessarily implying it to be analysis. annual.

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FIG. 3. The reduced-gravity experiments: specified zonal (a) momentum flux in the Gulf of Mexico (solid) and wind stress in the northwestern Caribbean Sea (dash); green dashed line is 2 2 0 and min–max scales are 62 3 10 4 m2 s 2. The 12-yr monthly ensemble upper-layer depth h (m) at 908W (colors) for latitude (258–288N) and repeating calendar months, January– December; and: monthly number of eddy shedding (black curve) (i.e., SeH) for experiments (b) GOM, (c) Carib, and (d) GOMCarib; scale is on the right ordinate normalized (0–1) by the number shown on lower-left corner of each panel; 3-month weighted (1/4 –½–1/4) smoothing is applied (CO2012). (e)–(g) Plots of number of eddies shed as a function of their periods (shown from 1–15 months) for the three experiments, respectively. In (b) and (e), the corresponding plot for the Steady22Sv experiment are shown as gray-dashed curve (same scale as Exp.GOM) and open bars, respectively.

Unauthenticated | Downloaded 10/07/21 06:48 PM UTC 674 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 43 ambiguity, which may result when eddies are shed near maxima for any particular month(s). It is interesting that the beginning and end of the month. This is because the despite the biannual forcing within the Gulf of Mexico, separation of an eddy from the Loop Current is gen- Exp.GOM produces no preferred month of shedding in erally a gradual process which can take ;(1–3) weeks stark contrast to the Caribbean Sea forcing experiments from the time that a peanut shape (with shell) with a to be described next. The Gulf forcing therefore acts narrow ‘‘neck’’ develops to complete detachment. Both only to delay shedding through eastward momentum the smoothed and actual values (Table 2) are used flux and upper-layer convergence in the eastern Gulf, below. especially in fall (cf. CO2012; see also Chang and Oey The behaviors of the reduced gravity model with 2010, 2011). constant transport forcing have previously been thor- For Exp.Carib (Fig. 3c) and Exp.GOMCarib (Fig. 3d), oughly analyzed and discussed (Hurlburt and Thompson differences in the number of eddies between months 1980; Pichevin and Nof 1997; Nof 2005; Chang and Oey with most and least eddies are 4 and 8, respectively (52 2010, CO2012). For the present study, the Steady22Sv and 4 for the smoothed SeH; Table 2, second column), experiment is used to establish a baseline case for judg- and the corresponding standard deviations are 1.7 and ing the significance of seasonal shedding preferences in 2.6 (Table 2, third column). These values exceed those other experiments. The Steady22Sv experiment sheds for the Steady22Sv experiment, and the peaks in their 19 eddies: 15 eddies have an 8-month period and 4 SeH’s are therefore significant. The preference months eddies have 7 months (see the eddy-shedding histo- when eddies are shed are June and ;(December–January) gram EsH in Fig. 3e). The shedding period of ;(7–8) (Figs. 3c,d, and Table 2, fourth column), and they are months is similar to that found in previous studies. The confirmed by the corresponding h-Hovmo¨ ller maps dominant 8-month period is the natural shedding pe- along 908W (colors in Figs. 3c,d) that, unlike the map riod of the present reduced-gravity system (see, e.g., for Exp.GOM (Fig. 3b), display distinct biannual Oey et al. 2003). CO2012 show that the 8-month maxima.5 Note that these h maxima precede the months shedding period can yield three preferred peaks for of maximum eddy counts by approximately 1 month. eddy shedding in the corresponding SeH. However, be- This is because the model Loop Current generally ex- cause of the existence of the 7-month period, albeit tends pass 908W prior to shedding an eddy. By com- weak, the 3 peaks tend to be smeared and, for a large paring Figs. 3c,d, we see that Exp.GOMCarib and enough sample of eddies, the preferred shedding Exp.Carib are similar, but the former has more distinct months become indistinguishable from the back- peaks in its SeH and is therefore closer to the obser- ground mean, as shown by the dashed curve in Fig. 3b. vation (see Fig. 1a of CO2012). The latter conclusion is The difference in the number of eddies between consistent with the results of the more elaborate 3D months with most and least eddies is 2 (51forthe OGCM in CO2012. In Exp.GOMCarib, stronger east- smoothed SeH; Table 2, second column), and the erlies in fall (and spring) over the Gulf of Mexico corresponding standard deviation is ’1(Table2,third produce convergence that accumulates mass in the column). These values for the Steady22Sv experiment eastern Gulf, and eastward momentum flux which de- will serve as the baseline to judge the significance of lays eddy-shedding, thus accentuating the difference monthly preferences of eddy-shedding in other experi- in eddy counts between fall and winter (spring and ments. summer). Finally, from Figs. 3d,g, we also conclude The Exp.GOM is dominated by shedding periods of that, while the eddy-shedding histogram (Fig. 3g) 7 and 8 months and only one eddy has a 6-month period containing a range of periods from ;(4–9) months (Fig. 3e). The corresponding SeH is strongly smeared may seem to suggest chaos, the system is actually re- by the dominant 7-month period (Fig. 3b). The differ- markably regular and sheds eddies at quasi-periodic ence in the number of eddies between months with intervals that are obviously linked to the (wind and most and least eddies is 2 (51 for the smoothed SeH; transport) forcing. Table 2, second column), and the corresponding stan- dard deviation is ’0.9 (Table 2, third column). These are same or less than the values for the Steady22Sv experiment, and we conclude that the peaks in SeH for 5 The model’s months of maximum and minimum shedding are Exp.GOM are not significant. This conclusion is con- ;(1–2) months earlier than observed. However, the idealized wind firmed by the upper-layer h-contour at 908W across, is perfectly biannual rather than asymmetric as observed, and has maxima and minima which are also ;(1–2) months earlier. which the Loop Current extends and/or eddies pass, Therefore, for the purpose of studying biannual shedding mecha- plotted as a function of month (the Hovmo¨ ller plot; nism, shedding time is only relevant with respect to the phase of the Fig. 3b, background color); this shows no distinct wind; see below.

Unauthenticated | Downloaded 10/07/21 06:48 PM UTC MARCH 2013 C H A N G A N D O E Y 675 b. Interpretations This is also the time, or shortly thereafter (December or June), when the majority of eddies are shed from the We now relate the above biannual regularity in eddy model Loop Current (Fig. 3c). The westward propa- shedding to the forcing, and interpret them in terms of 2 gation velocity is ’23.3 cm s 1. Pichevin–Nof mechanism and Reid’s theory. The results The model Caribbean is driven by the oscillating trade for both Exp.Carib and Exp.GOMCarib are similar, so wind, which will be seen below to produce upper-layer only the former (with simplest wind forcing) is dis- anomalies through the sloshing back-and-forth of the cussed here. We conduct an EOF analysis based on the (zonal) . This Caribbean variance is 12-yr h data, then describe the process based on monthly contained in EOF3 (not shown), which explains 12% of composites. the total variance, has a strong biannual signal, is in Figure 4 shows the leading EOFs 1 and 2, which to- phase with PC-1, and its EV-3 is dominated by the Cu- gether explain 70% of the total variance. Both eigen- ban southwest anomaly, but stronger and larger filling vectors (EV-1 and 2) show a train of h anomalies of up the northern half of the northwestern Caribbean opposite signs emanating from and extending Sea; the EOF-3 is weak inside the Gulf of Mexico. northward then westward into the Gulf of Mexico. The Figure 4 (fourth row) shows the homogeneous corre- EV-2 is in fact simply EV-1 shifted in that direction, and lation (HC) maps between h and PCs 1 and 2. For each its principal component (PC-2) is highly correlated with mode, the HC2 (3100) gives the percentage of local PC-1 and lags PC-1 by 55 days (correlation coefficient 5 variance explained by that mode. While the link be- 0.92 at 99% significance).6 Both PCs are significantly tween the Gulf of Mexico and Caribbean Sea is cru- biannual as shown by the amplitudes of their monthly cial, only a relatively small percentage (’10%) of the composites which are significantly greater than the stan- Caribbean variance covaries with the Gulf of Mexico. dard errors. The reason is due to a mismatch in the oscillations The sequences that lead to eddy-shedding are com- between the Gulf (e.g., eddy-shedding) and Caribbean pactly described by these 2 EOFs (Fig. 5). In mid-June Sea (e.g., wind-driven). An analogous situation will be (mid-December), the PC-1 is near a positive maximum seen for satellite data. while PC-2 ’ 0 as a warm anomaly forms southwest of Figure 6 plots the Yucatan inflow relative vorticity z Cuba, and the Loop grows as the warm EV-1 at 878W and northward velocity y, Loop Current’s northern strengthens (Fig. 4a). Approximately 55 days later, in ÐÐ boundary (LCNB), Loop’s volume V 5 hdxdy, early August (early February), PC-2 is near a positive Loop where the double integral is area of the Loop bounded maximum while PC-1 ’ 0, the warm anomaly is squeez- by latitude 228N, longitude 848W and the Loop’s edge ing through the Yucatan Channel, creating a weak high defined by h 5 625 m, LCBN from the Reid’s (1972) northwest of Cuba; meanwhile the Loop continues to formula [Eq. (1)], and the Yucatan transport Tr . expand westward through the EV-2 high near 888W Yuc The trade wind stress (tox , 0) is specified to be (Fig. 4b). By mid-September (mid-March), PC-1 is near strongest in June (December). The z, y,andTr all a negative maximum while PC-2 again becomes ’0, and Yuc lag the wind by 2 months (Figs. 6a,b,e) and become the Cuban warm anomaly has now completely squeezed maximum in August (February). The lag is due to the through the Yucatan Channel (Fig. 4a). At the same finite time taken for warm water to accumulate against time, the strong warm anomaly due to EV-1 has ex- the Yucatan Peninsula coastline during the increased panded further westward to (25.58N, 898W) near the tip trade wind from spring to summer. The process is an- of the model Loop Current (Fig. 4a). At this time, alyzed by calculating the mass balance within a control a cold anomaly is formed southwest of Cuba. In early volume in northwestern Caribbean Sea: bounded by November (or early May), PC-2 now becomes a nega- the Yucatan coast in the west, Honduras coast to the tive maximum while PC-1 is again ’0. The Cuban warm south, Yucatan Channel to the north and a south-to- anomaly pushes north-northwestward, and the strong north transect from Honduas to Cuba in the east (see warm anomaly in the Gulf of Mexico also shifts west- Fig. 7a). The continuity is ward, being now centered at (268N, 90.58W; Fig. 4b).

›h ›hu ›hy 1 1 52a h, (2) ›t ›x ›y N 6 EOFs 1 and 2 therefore describe propagating features and the data may be analyzed using complex EOFs (Merrifield and Guza 1990) as were previously done for studying Loop Current eddies where 2a h is the Newtonian cooling term with a 5 (Lin et al. 2007; Oey 2008), and Caribbean eddies (Alvera-Azcarate N N 21 h 5 et al. 2009). For the present application, the simpler EOFs are much 1/800 day and ÐÐh – H (see Table 1). Integrating over more straightforward. the control volume, () dx dy:

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FIG. 4. Exp.Carib (h) EOFs (a),(left) mode-1 and (b),(right) mode-2: (first row) EV’s (m); (second row) PCs (12 yr, arbitrary 1991–2002; the maximum correlation of PC1 and PC2 5 0.92 at 99% significance and PC1 leads by 55 days); and (third row) their monthly composites with standard errors. (last row) The PC and SSH correlations (colored if above 95% sig- nificance, contour interval 5 0.2).

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FIG.5.(toptobottom)TheJanuary–December composites of EOFs 1 1 2 (m; color and contour interval 5 5 m, 0 contour is omitted) for reduced-gravity h. The magenta contour is monthly composite h 5 600 m indicating edge of the model Loop Current and eddies.

Unauthenticated | Downloaded 10/07/21 06:48 PM UTC 678 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 43 ðð ð ð ðð › N E h 1 1 y 1 a h 5 dx dy huE dy h N dx N dx dy 0. (3) ›t S W I II III IV

The first term (I) is the rate of mass accumulation (de- maximum; Figs. 7c,e) as an anomalous low develops pletion if ,0) inside the control volume. The second south of Cuba. In ;(October–November), the anticy- term (II) represents the Caribbean mass influx (uE , 0) clone is replaced with a strong cyclonic anomaly (Figs. across the eastern boundary. The third term (III) is the 7d and 5), and the Yucatan transport, y, z,andLCNB’s

Yucatan outflow into the Gulf of Mexico (yN . 0). The all reach minima, while the VLoop reaches its minimum last term (IV) accounts for the Newtonian cooling term. one month later in December (Fig. 6). At this time, the Average the entire 12 years, we find that term I 5 0, II 5 decreased supply of warm water into the Loop Current, 221.5 Sv, III 5121.2 Sv and IV 510.3 Sv. Term IV which has in previous months grown and expanded, leads III by 1 month but its fluctuation is very small cannot balance the Rossby wave speed associated with ’60.04 Sv, and it will henceforth be neglected. Terms the matured Loop—that is, the Pichevin–Nof mecha- I, II, and III and wind stress are plotted in Fig. 7e. nism. Eddies, then, tend to separate around this time or As the trade wind strengthens from March to maxi- shortly thereafter (Fig. 3c). The westward volume flux mum in June, warm anomaly (higher pressure) develops carried by the separated eddy can be estimated by along the southern coast of Cuba as the upper layer noting that near the time of its minimum the Yucatan deepens, and by geostrophy the westward Caribbean inflow is stationary (Fig. 6e: November or May), so transport also becomes maximum (Figs. 7a,e). From that the flux must equal to the VLoop-deficit between mid-April through mid-July, warm water accumulates shedding month (December or June) and the month and the high pressure moves up againstÐÐ the Yucatan’s before. The value is ’0.6 Sv, which taking the eddy- eastern coast, as indicated by the positive (›h/›t) dx dy shedding period of 6 months yields an eddy of about during the same period of increased trade wind (Fig. 7e). 150 km in diameter as seen in the simulation (plots not Near the end of this period of warm-water convergence, shown). at end of July to beginning of August, the anticyclone Because of the biannual forcing, the above descriptions associated with the high pressure is strongest, and it apply also for the first half year from December–June. forces also strong northward Yucatan transport that There is some asymmetry between the June shedding peaks in August (Figs. 7b,e). This is also when y and z and ;(November–January) shedding (Fig. 3c) which is in the western Yucatan Channel become maximum also seen in the model LCNB (Fig. 6c). This may be due (Figs. 6a,b). The Reid’s formula [Fig. 6d, Eq. (1)] mimics to the existence of the natural shedding period [;(7–8) more closely the z variation rather than the y variation months, Fig. 3e], as well as the forcing (the asymmetry showing its greater sensitivity to the former (see Fig. 2a), largely disappears for Exp.GOMCarib, not shown). and it too peaks in August. The strong Yucatan transport The consequence of the asymmetry is relatively minor, produces a more rapid growth of the Loop Current however, and also it is not seen in other time series according to Pichevin–Nof theory, as seen by the rapid (Figs. 6 and 7e); we therefore do not further pursue its increase in the volume of the Loop VLoop, which be- cause. comes maximum ;(1–2) months later in ;(September– In summary, eddy-shedding tends to occur shortly (;1 October) (Fig. 6c). The model LCNB also shifts north as month) after the minimum Yucatan z and y following shown in Fig. 6c, and becomes a maximum in September, a period of strong inflow forced by piling up of warm approximately one month after maximum z, y,and water against the western Caribbean Sea by the strong Yucatan transport. After September, both LCNB’s trade wind. That a minimum inflow z and y tends to favor rapidly drop (Figs. 6c,d) as the Caribbean anticyclone eddy shedding was found by Oey (2004) in a 3D OGCM. ‘‘squeezes’’ through the Yucatan Channel (Fig. 5, In the reduced-gravity model, the chain of events takes August–October) and both z and y decrease (Figs. 6a,b). approximately 6 months so that one cycle that culmi- The ‘‘squeezed’’ anticyclone adds mass into the Loop as nates in the shedding of an eddy is immediately followed seen in the continued growth of VLoop from September– by the start of the next cycle. To check that minimum z ÐÐOctober (Fig. 6c). From August–October, the negative and y are not merely coincidental, we reran Exp.Carib (›h/›t) dx dy (Fig. 7e) indicates that the Caribbean using annual rather than biannual trade wind forcing. anticyclone rapidly shrinks and the (westward) Carib- The results are shown in the appendix (Fig. A1), which is bean transport is weakest (i.e., its anomaly is positive seen to have the same characteristics as the biannual

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preferences of eddy shedding. In reality, the biannual variation based on long-term (22 years) wind data is asymmetric. As shown by CO2012, the trade wind over the Caribbean Sea shows a more rapid drop from summer to fall [;(July–September)] with approxi- mately doubled amplitude than from winter to spring (January ;May). For convenience, their wind plot (their Fig. 2a) is repeated here as Fig. 8a. The westward wind over the Gulf of Mexico is nearly 1808 out of phase, but is otherwise also asymmetric, showing a more rapid in- crease from summer to fall [;(August–October)] also with approximately doubled amplitude than from winter to spring [;(January–May)]—see Fig. 8a. Be- cause of these asymmetries in the wind, the long-term (22 years), OGCM-estimated Yucatan transport is also asymmetric, showing a much more distinct and larger decrease from its maximum in summer (July) to its min- imum in early fall (September) than the corresponding decrease from early winter to spring [;(January–May); see CO2012’s Fig. 2b, also replotted here for convenience as Fig. 8b]. The summer–fall wind amplitude is 2 times the winter–spring amplitude, while it is 4 times for the Yucatan transport, because transport is forced by wind stress, which varies like the square of wind. In response, long-term GCM simulations forced by the realistic winds consistently show also a larger difference in the number of shed eddies from summer to fall than from winter to spring (CO2012’s Fig. 3). Alvera-Azcarate et al. (2009) also 21 21 FIG. 6. Monthly (a) z (s ) and (b) y (m s ) averaged within the found July–September preferences for eddy-shedding. western 50 km of the Yucatan Channel at 228N; (c) latitude of These results are consistent with the reduced-gravity 5 Loop Current’s northern boundary (LCNB) defined by h 625 m results that decreased transports (hence also z and y) (the purple contour in Fig. 5) along a line from Yucatan Channel to are triggers of eddy shedding, and suggest that the sim- Mississippi Delta (black curve), and Loop’s volume VLoop (gray curve, 1013 m3; see text); (d) LCBN from the Reid’s (1972) formula pler model may harbor a large portion of the Loop Cur- using z and y with u 5 908. (e) Yucatan transport in Sv. Bars are the rent physics. 1/2 standard errors equal to 6s/N where s 5 standard deviation for Satellite SSH data provides a relatively long-term 5 each parameter and N number of samples. (1993–2010 is used here) information of Loop Current and eddy shedding. This information was neither avail- able nor completely without ambiguity in prealtimetry forcing case that eddy shedding occurs after the mini- years. The data we use is SSH anomaly (SSHA) from mum z and y. Thus, there exists a preference shedding Archiving, Validation, and Interpretation of Satellite month (Fig. A1a) in accordance with the annual forcing, Oceanographic data (AVISO; http://www.aviso.oceanobs. even though the EsH shows a range of shedding periods com/) from October 1992 to December 2010 on 1/3831/38 from ;(4–11) months (Fig. A1e). Shedding events tend Mercator grid. The mean SSH field is from Rio et al. to (i.e., maximum SeH) occur ;1 month after the min- (2011). This has a resolution of 1/4831/48 and was con- imum z and y (Figs. A1a,b,c). Finally, maximum trans- structed by combining the Gravity Recovery and Climate port is approximately 2 months after the peak of the Experiment (GRACE) geoid, drifting buoy velocities, trade wind (Fig. A1d). profiling float and hydrographic temperature and salinity data. These data allow one to discern eddy-shedding 3. Satellite observations and comparison with model dates (hence periods), which are generally consistent with those obtained from a data-assimilated analysis dataset With periodic forcing that simulates the biannual we have conducted for the Bureau of Ocean Energy variation of the wind, the reduced-gravity model pro- Management (see, e.g., Lin et al. 2007; Yin and Oey 2007; duces also biannual growth of the Loop Current and Chang et al. 2011), as well as with those documented in

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FIG. 7. (a)–(d) Schematic illustrations of the dominant flow anomalies in the northwestern Caribbean Sea for the indicated months based on Fig. 5; arrow at the top show the total (i.e., not anomaly) wind. (e) The 12-yr composite of 2 monthly transport anomalies (Sv 5 106 m3 s 1) in the control volume shown in the rectangle in (a); see Eq. (3) in text. The mean 6 fluctuation (Sv) for each term is shown with a small Newtonian cooling term, ’0.3 60.04 Sv omitted. 2 Gray curve is the specified zonal wind stress in m2 s 2. Plots are repeated every 2 years.

Leben (2005). The eddy-shedding dates and periods were a. Monthly composites used in CO2012. Here we use the AVISO data to ex- We again conduct an unbiased, monthly composite amine the growth and wane of the Loop. analysis. Figure 8c shows the composite Loop Current Based on the experience gained from the reduced- edges at the indicated months and Fig. 8d shows gravity model experiments, we look again for some Hovmo¨ ller SSHA maps along the 26.58N latitude line regularity in the 18-year satellite data.7 Alvera-Azcarate across the Loop. What is striking is the appearance of et al. (2009) analyzed the AVISO data (October 1992– two highs in Fig. 8d: a weak one in winter (January) and February 2006) but focusing on the Caribbean Sea where a strong and larger one in summer [;(June–August)], they found strong annual steric variation. Therefore, which is also more westward extended. This biannual prior to any analysis, we remove from the data the mode is significantly separated (i.e., it is not indis- annual steric height variation, which amounts to an tinguishable from being just one mode) as judged by the SSH difference of 0.14 m between the September maxi- fact that the difference between either of the two highs mum and March minimum. Thus, regularity in the signal (summer and winter) and the low’s (fall and spring) is is a dynamical one. Lin et al. (2010) conducted an EOF greater than two standard errors (60.03 m). However, analysis using the AVISO SSHA. The leading EOF the summer-to-fall amplitude is much more distinct than modes 1 and 2 together explain 50% of the total vari- the winter-to-spring amplitude, which is barely signifi- ance, and the authors described the connection of these cant, as shown by the plot of maximum SSH and stan- EOFs with Yucatan transport. It is significant that their dard error in Fig. 8e. These behaviors are consistent with EOF principal components display strong annual var- the independently derived conclusions based on the iations (see their Figs. 3c,d), which therefore suggest simulated Yucatan transport variation (i.e., Fig. 8b) and some seasonal regularity.8 eddy-shedding statistics (CO2012’s Fig. 3) mentioned above; they are also consistent with the reduced-gravity model processes explained in the previous section. Thus the observed Loop Current displays a biannual 7 The correctness of this presumption will be seen a priori. 8 The authors did not mention if the annual steric signal was growth-and-wane signal that is unrelated to static re- removed prior to their analysis, but we have confirmed their results sponses to seasonal heating and cooling of the upper with steric removed using their EOF domain. ocean. The response is strongest and more clearly

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2 22 FIG. 8. Monthly (a) zonal wind stresses (m s ) in the Caribbean Sea (left ordinate) and Gulf of Mexico (right ordinate) and (b) simulated Yucatan transport (Sv), both from CO2012. (c) Loop Current edges defined by SSH 5 0 composited from 18-yr (1993–2010) of AVISO at the indicated months. (d) Monthly composites of AVISO SSH plotted as a Hovmo¨ ller map (magenta contour is max 5 0.18 m) along the 26.58N latitude line cutting across the northern edge of the Loop, as shown by the dashed line in (c). Two repeat cycles are shown. Annual steric height has been removed and the standard error (m) shown as a dashed contour. (e) Maximum SSH (m) from (d) and the standard error. defined from ;(summer–fall) than from ;(winter– Caribbean Sea and compare in Fig. 9 the reduced-gravity spring). The cause is a dynamical one that is primarily model composites of the upper-layer anomalies with the forced by the wind (in particular the trade wind in the corresponding composites of AVISO SSHA from May Caribbean Sea), which also shows a seasonal asymmetry. through December. From May through July when the With these in mind, we focus in the northwestern trade wind strengthens, AVISO shows that the SSH

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FIG. 9. (a) May–August composites of the reduced-gravity model Exp.Carib h (colors) and (u, y) vectors for comparison with (b) the corresponding composites AVISO SSHA; red and blue are 650 m, respectively for h, and 60.1 m for AVISO. Similarly, the September– December months are compared in (c) for Exp.Carib and (d) for AVISO. (e) Monthly AVISO SSHA and Exp.Carib h (divided by 50 to scale to same order as AVISO) averaged in 17.58–22.58N and 878–808W in the northwestern Caribbean Sea; the standard error is shown. [Correlation, 95% significance 5 (0.66, 0.52) when model leads by 1 month, while at 0 lag they are (0.57, 0.53)].

Unauthenticated | Downloaded 10/07/21 06:48 PM UTC MARCH 2013 C H A N G A N D O E Y 683 anomaly against the Yucatan coast just south of the cycle and are in fact significantly correlated (at 99% sig- Yucatan Channel evolves from cold to warm in agree- nificance level) with maximum correlation 50.63 when ment with the model. From August to October when the PC-1 leads by 3 months. They are therefore 908 out of trade wind weakens, the warm anomaly weakens and phase. As in the reduced-gravity EOFs1 and 2, the turns into a cold anomaly, which reaches its maximum AVISO EOFs 1 and 2 also represent propagating fea- (cyclonic) strength in November (Fig. 9d). These warm tures, and again may be analyzed using complex EOF’s and cold anomalies presumably force stronger and (Merrifield and Guza 1990). It is however much more weaker Yucatan transports, and the timings are also straightforward to use the simpler EOFs and, taking consistent with the maximum and minimum transports, advantage of their significant seasonal cycles, to ana- respectively, in Fig. 6e using the reduced-gravity model. lyze them together with monthly SSHA-composites Despite the simplicity of the reduced-gravity physics (Fig. 11) for physical interpretations. and the idealized nature of the specified wind forcing, Starting in May, the Loop Current begins to grow there is therefore some correspondence between model (Figs. 8d,e), EOF-2 is weak and EOF-1 dominates (Figs. and AVISO. In Fig. 9e, the AVISO SSHA and model 10 and 11). From June through August, EOF-1 weakens h both averaged over the northwestern Caribbean Sea (Fig. 10); the variability is now dominated by EOF-2 17.58–22.58N and 878–808W are compared. The corre- whose center pole represents the west-northwestward spondence is obvious especially for the second half year, growth and expansion of the Loop during these 3 months and both 0-lag and 1-month-lag (AVISO lags) correla- (Fig. 11), while its southeastern pole (a cyclone) con- tions are significant. The discrepancy is in part attributed tributes to the ‘‘necking’’ of the Loop near (258N, 868W). to the idealized nature of the model wind, which does not From September, EOF-1 strengthens and reaches its exactly follow the observed, asymmetric wind variation strong negative phase when a strong low anomaly in (see section 2; also Fig. 8a). The 1-month lead by model is Fig. 11 develops near EV-1’s dominant center pole consistent with the fact that the idealized wind is specified (878W, 258N), cutting across the Loop Current, while the to be at a maximum in June and December, which leads EOF-2’s center pole then becomes the separating eddy. the observed wind maxima by approximately 1 month Then, from October through December, because of the (July and January). shifts in both pattern and phase between EOFs 1 and 2, Finally, the AVISO data also shows a close connec- their western poles together describe the westward tion between the sea surface height fluctuations in the propagation of this eddy: EOF-1 (October) / EOF-1 1 Caribbean Sea and the Loop Current’s expansion and -2 (November) / EOF-2 (December). From January retraction, as can be readily seen by comparing Fig. 9e through February, the winter growth phase of the Loop and Fig. 8e. They show for example that as the warm Current begins, described primarilybythestrongEOF-1s anomaly in the Caribbean Sea strengthens in July, the (Figs. 10 and 11). In March and April, the Loop Current Loop Current extends northward in ;(June–August), weakens, but the process is much less well defined (Fig. 11) while the Loop retracts in November as the Caribbean and cannot be explained by EOFs 1 and 2 alone; higher cold anomaly is strongest. These inferences are now EOF’s also contribute to the composite (not shown). quantified using EOF. In summary, the growths of the Loop Current in winter and early summer, as well as the Loop’s retraction in fall b. EOF analysis are primarily described by EOF-1. The EOF-2, on the EOFs of SSHA using the same domain as in the other hand, describes the west-northwestward expan- reduced-gravity case are computed (Fig. 10). The EOF1 sion of the Loop and subsequent eddy shedding in sum- accounts for 30% of the total variance (Fig. 10a). Its mer to fall. Eddy shedding preferentially occurs from eigenvector (EV-1) shows a tripolar structure which dur- summer to fall, particularly in late fall. In spring, weak- ing the positive phase of the principal component (PC-1) ening of the Loop Current is more complicated, requiring has a strong high at its center pole near (258N, 878W) many modes. flanked by two weaker (by ;50%) lows: one to the west We compare EOF’s from AVISO (Fig. 10) and reduced- and the other one to the southeast. Mode-2 EOF ex- gravity model (Fig. 4). As to be expected, the total vari- plains 17% of the total variance. The EV-2 also has ance explained by the observed EOFs 1 and 2 (47%) is a strong high at its center pole near (278N, 88.38W) lower than the modeled 70%. Both EV patterns show flanked by two weaker low’s west and east. Both EV’s trains of anomalies extending west-northwestward from thus display a train of SSHA of opposite signs emanating Cuba into the Gulf of Mexico; wavelength of the pattern from Cuba, and the EV-2 pattern is just EV-1 shifted in observation is longer, probably because the observed west-northwestward. Monthly composites of both PC-1 Loop and eddies are much more energetic (individual and PC-2 (Fig. 10a, third row) show a significant annual areas of highs and lows are larger). Descriptions of how

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FIG. 10. As in Fig. 4, but for AVISO SSH. The maximum correlation of PC1 and PC2 (50.63 at 99% significance and PC1 leads by 90 days).

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FIG. 11. (top to bottom) January–December composites of AVISO SSHA (m). First positive (negative) contour is 10.01 m (20.01 m) and subsequent contours have an interval 50.02 m; positive (negative) is solid (dashed). Annual steric height has been removed and the mean standard error is approximately 60.01 m. Thick magenta shows the 0 m contour of the SSH indicating the edge of the Loop Current (and eddies).

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EOFs 1 and 2 in each case contribute to the summer Loop 4. Conclusions Current growth and eddy shedding are also analogous. To The expansion, eddy shedding, and retraction of the reveal the connection with fluctuations in the Caribbean Loop Current are complex phenomena with multiple Sea, we plot in Fig. 10 (last row) the homogeneous cor- temporal and spatial scales. This paper attempts to find relation (HC) maps between PCs 1 and 2 and SSHA. The some regularity in the process, motivated by recent correlation indicates how well the SSH in Caribbean (and findings that eddy shedding may preferentially occur in other) region covaries with the dominant fluctuations in summer and winter. Here are the conclusions. the Loop Current.9 Approximately 10% of the Caribbean Sea’s variance covaries with Gulf of Mexico. Similar 1) Satellite altimetry observations show that the Loop feature as the southwest Cuban anomaly, described pre- Current displays a significant biannual expansion and viously in conjunction with the reduced-gravity EOFs, and retraction cycle, from summer to fall (S2F), and then how the anomaly progresses from mode 1 to mode 2 as from winter to spring (W2S); these cycles are un- the Loop Current expands and sheds eddies, is now also related to the annual steric height variation because discernible in Fig. 10. Similarly to the HC-maps for the of heating and cooling. reduced-gravity model (Fig. 4), the weak Caribbean-Gulf 2) The S2F-cycle is particularly strong, and is often covariance is due to a mismatch in the dynamical oscil- followed by eddy-shedding. lations between the two basins. 3) Both the S2F cycle and eddy shedding are repre- The upstream connection with the SSH fluctuations sented well by the first two leading EOF modes, in the Caribbean Sea is of interest (e.g. Murphy et al. which are well-correlated in space and time except 1999; Oey et al. 2003). Figure 12 extends HC’s to the that they are shifted relatively to each other (i.e., 908 entire Caribbean Sea, and shows also EOF 3. In HC-1, phase shift) and therefore also describe the westward west of 808W, eddy-like features are generally consistent propagation of the detached eddy. with wind-forced piling-up (and retreat) of warm water, 4) The W2S-cycle is much less well-defined; nonethe- since this tends to be maximum (minimum) in summer less, it is significant, though barely. (fall) (Figs. 9b,d and 10). The Loop also covaries with 5) The existence of S2F and W2S cycles, and their the generation region of the so-called Hispaniola Eddy asymmetry, is suggestive of forced responses by the near (168N, 758W), where Oey et al. (2003) show that Caribbean and Gulf of Mexico wind system, which a localized anticyclonic wind stress curl can periodically is also similarly asymmetric. spin up warm eddies, which then drift westward to af- 6) The wind-forced dynamics is contained in a reduced- fect Loop Current eddy shedding. Similar eddy-like fea- gravity model, which includes coastline but otherwise tures are also seen in HC-3. Here, large-scale effect of the ignores topography, and which assumes a quiescent trade wind in producing the fluctuating, geostrophically- lower layer. For the S2F cycle, the simple model gives balanced Caribbean Current is also evident. The HC-2 upper-layer variation in northwest Caribbean Sea that shows a covarying component that is confined around is in good agreement with satellite observation. Cuba, which appears to be consistent with Lin et al.’s 7) The forced response first occurs in the northwestern (2010) findings, and it contributes to the Yucatan trans- Caribbean Sea through upper-layer thickening by port fluctuations. The Lin et al. (2010) theory depends warm water that piles up along the Yucatan penin- on the existence of a ‘‘topographic form drag’’ which is sula, followed by transport and vorticity fluctuations absent from the reduced-gravity model. The latter shows in the Yucatan Channel that force the Loop Current nonetheless strong h-fluctuations off the southwestern to expand, shed eddy, and retract. The dynamics can tip of Cuba (Figs. 4 and 9a,c), which coincides with the be explained in terms of the Pichevin–Nof mecha- significant HC-2 there (Fig. 12b). These different pro- nism and Reid’s theory, and eddy-shedding tends to cesses contribute to mass and vorticity (;=2h) fluxes in occurnearminimumz and y. Yucatan Channel, to the growth and wane of the Loop 8) Finally, the Loop Current’s growth and wane are Current, and to eddy shedding. related to mass and vorticity fluctuations in the Caribbean Sea through their fluxes through the Yucatan Channel.

The upshot of this study is that the Loop Current is 9 Strictly speaking, with the dominant fluctuations of the EOF primarily a forced system, so that the Loop’s growth region, see Fig. 10. However, because of the dominance of the Loop, the result is very similar if the EOF region is limited to the may be approximately determined based on the bi- eastern Gulf only: 22.58–288N and 928–828W, which is the region annual transport forcing because of the wind. Shedding of used by Lin et al. (2010). eddies may therefore also be approximately determined

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FIG. 12. Correlations (color-shaded for values above 95% significance; contour interval 5 0.2) between Loop Current EOF (see Fig. 10): (a) PC-1, (b) PC-2, and (c) PC-3 and AVISO SSHA. Gray contours are 200- and 2000-m isobaths.

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FIG. A1. Results of the Exp.Carib but with annual (rather than biannual) trade wind forcing. (a) The 12-yr monthly ensemble upper-layer depth h (m) at 908W (shading) for latitude (258–288N) and calendar months, January–December; and monthly number of eddy shedding (black curve) (i.e. 2 2 SeH); (b) Yucatan inflow z (s 1); (c) y (m s 1); (d) transport (Sv); and (e) the Eddy-Shedding Histogram: plot of number of eddies shed as a function of their periods (shown from 1–15 months). 2 2 For this experiment, the maximum trade (i.e., westward) wind stress (522 3 10 4 m2 s 2)is specified to be in September.

Unauthenticated | Downloaded 10/07/21 06:48 PM UTC MARCH 2013 C H A N G A N D O E Y 689 especially during the large decrease in transport from Leben, R. R., 2005. Altimeter-derived Loop Current metrics. summer to fall (CO2012). The observed asymmetric re- Circulation in the Gulf of Mexico: Observations and Models, sponse between summer-to-fall and winter-to-spring Geophys. Monogr., Vol. 161, Amer. Geophys. Union, 181– 201. shedding characteristics is explained by smaller-amplitude Leipper, D. F., 1970: A sequence of current patterns in the Gulf of change in the trade wind in the latter compared to the Mexico. J. Geophys. Res., 75, 637–657. former, by approximately half, producing a corre- Lin, X., L.-Y. Oey, and D.-P. Wang, 2007: Altimetry and drifter spondingly fourfold smaller contrast in the transport assimilations of Loop Current and eddies. J. Geophys. Res., that influences eddy shedding. The biannual wind there- 112, C05046, doi:10.1029/2006JC003779. Lin, Y., R. J. Greatbatch, and J. Sheng, 2010: The influence of Gulf fore modulates the natural shedding so the Loop Cur- of Mexico Loop Current intrusion on the transport of the rent is more prone to shed eddies when large-amplitude . Ocean Dyn., 60, 1075–1084. weakening in transport occurs. On the other hand, the Lugo-Fernandez, A., 2007: Is the Loop Current a chaotic oscilla- exact timing of when an eddy is shed can depend on tor? J. Phys. Oceanogr., 37, 1455–1469. the Loop’s intrinsic variability including dynamical in- Merrifield, M. A., and R. T. Guza, 1990: Detecting propagating signals with complex empirical orthogonal functions: A cau- stability and upper–lower-layer coupling, etc., as well as tionary note. J. Phys. Oceanogr., 20, 1628–1633. on the undeterministic nature of the forcing itself. These Molinari, R. L., J. F. Festa, and D. Behringer, 1978: The circulation ideas are taken up in Xu et al. 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