Numerical Process Experiments and Satellite Altimetry Data

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Loop Current Growth and Eddy 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 Loop Current’s variability in the Gulf of Mexico 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 Sea 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, consistent 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 vorticity fluxes through the Yucatan Channel.

1. Introduction The intrusion and retraction of the Loop Current in the eastern Gulf of Mexico and eddy shedding (i.e., separation of warm rings from the Loop) constitute one of the most fascinating geophysical fluid dynamical phenomena in the ocean (see Oey et al. 2005 for a review). The resulting circulation is the source of much of the variability in the Gulf of Mexico. Sea surface height (SSH) constructed from satellite altimetry data shows that the Loop Current behaves in a complex and seemingly chaotic fashion. An improved understanding of when an eddy is likely to shed from the Loop Current is of interest both scientifically and for practical applications. In this work and in Xu et al. (2013), we attempt to contribute to the knowledge

Corresponding author address: L.-Y. Oey, Princeton University, 70 Washington Road, Princeton, NJ 08540. E-mail: [email protected] DOI: 10.1175/JPO-D-12-0139.1 Ó 2013 American Meteorological Society

of eddy shedding through model and observational analyses. The shedding of Loop Current eddies can be interpreted as being a result of competing imbalance between the volume influx (Q) through the Yucatan Channel, which grows the Loop, and westward Rossby wave (velocity Ci ’ 2bR2o , Ro 5 Rossby radius based on the matured eddy), which tends to ‘‘peel’’ the eddy from the Loop; this will be referred to as the Pichevin– Nof mechanism (Pichevin and Nof 1997; Nof 2005).1,2 The Loop and eddies are approximated as being active in the upper layer only (i.e., reduced-gravity).

1

Hurlburt and Thompson (1980) demonstrated the process numerically, while Pichevin and Nof solved it analytically. 2 The growth rate should be said more accurately to be a function of Q and the eddy’s westward velocity a function of bR2o . Formulae for zero-PV eddy (e.g., from Nof 2005) are growth rate 5 8g0 Q/3pf 2 R3E and westward velocity 5 22bR2o /3 , where RE(t) ; (Qt)1/4 is the (growing) eddy’s radius, which itself depends on Q.

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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 Rossby wave dynamics (squiggly arrow represents Rossby wave) overcomes the inflow rate, and an eddy may be shed.

The mechanism applies to a northward (for Northern Hemisphere), strong (nonlinear), and less-dense narrow outflow debouching into a straight-coast ocean on a b-plane, and requires neither the existence of a lower layer, nor flow instability, nor forcing (other than Q), nor topography (other than the narrow channel and the straight coast). Knowing Q, the eddy growth rate (Cy), and shedding period (P 5 time taken for the eddy to grow and break away from the outflow) are calculated; Nof (2005) shows that Cy ; Qn, where n = ;1/4–2/5, and P ; Q21/5. The relevant time scale is O(bRo)21 or longer [.(10–30) days for Ro ’ (30–50) km; Nof 2005], so the idea may be approximately applied to a slowly-varying Q with time scales of, say, a few months, or longer. The mechanism then suggests that an increased Q would accelerate eddy growth, so that if Q subsequently decreases the Ci–Cy imbalance can provide a favorable condition for the eddy to shed (Fig. 1). Besides Q, another parameter that affects the Loop Current’s northward intrusion b is the upstream vorticity divided by Coriolis parameter f (z/f) at the western edge of the boundary current in Yucatan Channel (Oey et al. 2003; Oey 2004). Using long-term OGCM (Ocean General Circulation Model) integrations forced by 22 years of reanalysis winds, Chang and Oey (2012, hereafter referred to as CO2012) found that the linear regression between b and z/f is significant and high (r2 ’ 0.83, see their Fig. 2c): the modeled Loop Current extends far into the Gulf as the Yucatan Current, hence z/f and the y-velocity y, intensify.3 While the regression relation is empirical, it is consistent with Reid (1972)’s equation (see also Oey et al. 2003) based on PV-conservation:

3 CO2012 used a western width of 50 km averaged from surface to 200 m to define z and y.

2 1/2 z z 2y 1 (1 2 cosu) , b5 1 b b b

(1)

where u is the anticlockwise angle the inflow Yucatan Current makes with the x (eastward) axis. The b is plotted in Fig. 2, which shows that b is most sensitive to z especially for positive z’s (Figs. 2a,b; consistent with CO2012’s result), moderately sensitive to y [Figs. 2a,c; consistent with Nof (2005) that the Loop’s growth rate Cy ; Qn is moderately sensitive to Q because of the fractional nth power], and insensitive to u (Figs. 2b,c). Since an increased y (or Q) invariably leads also to increased z, it is difficult to separate their effects; but both are positively correlated with b (Fig. 2). The trade winds over the Caribbean Sea and Gulf of Mexico are significantly biannual and 1808 out of phase with respect to each other, due to the combined forcing of various centers of action over the North Atlantic Ocean and the American continent (see CO2012’s Fig. 2a and their online supporting materials). The Caribbean (Gulf of Mexico) trade wind weakens (strengthens) from summer to fall and from winter to spring, and strengthens (weakens) from spring to summer and from fall to winter. The variation is asymmetric, such that the Caribbean (Gulf of Mexico) trade wind weakens (strengthens) more dramatically from summer to fall than from winter to spring. CO2012 show that the Caribbean’s wind and wind stress curl correlate (negatively, since trade wind is westward and wind stress curl is also negative) significantly with the Yucatan transport which therefore also varies biannually and moreover also asymmetrically; the transport decreases more dramatically from summer to fall than from winter to spring (CO2012’s Fig. 2b). Based on 5-year shipboard ADCP measurements, Rousset and Beal (2010, their Fig. 4b) also found a significant biannual transport variation. However, the data

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CHANG AND OEY TABLE 1. Reduced-gravity model parameters. Parameters

Meanings

Values

g H Dx, Dy

gDr/ro Mean upper-layer depth Variable x and y grid spacings

Hcoast

Isobath where coastline is defined Horizontal viscosity Newtonian cooling coefficient Quadratic drag coefficient

0.01 m s22 600 m ;10 km in the Gulf of Mexico 200 m

0

AH aN Cb

FIG. 2. Contours of b (km) as a function of (a) z and y (fixed u 5 908); (b) z and u (fixed y 5 1 m s21); and (c) u and y (fixed z 5 2 3 1026 s21) according to the Reid’s (1972) formula: Eq. (1).

shows no asymmetry, a discrepancy which is yet to be investigated. Because of the above biannual forcing, CO2012 show that their simulated Loop Current tends to shed more eddies in summer and winter compared to fall and spring; there is also an asymmetry: the summer-fall difference in the number of shed eddies is greater than the winter– spring difference. These findings indicate a close connection between the inflow (z, y, or transport) and the Loop Current growth and eddy shedding, which is very much consistent with Pichevin–Nof mechanism and Reid’s theory. That Loop Current variability may be biannual was proposed by several Gulf of Mexico pioneers: Leipper (1970), Behringer et al. (1977), Molinari et al. (1978), and Sturges and Evans (1983) (see review in CO2012). The idea was subsequently dismissed, in particular after Hurlburt and Thompson (1980) demonstrated numerically that the Loop Current can shed eddies without the need for a time-dependent transport forcing. On the

100 m2 s21 1.25 3 1023 day21 1024

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 examine if the bimodal variability is dominant in satellite observations. This work examines the above ideas with process experiments 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 observations. The outline of the paper is as follows. Section 2 describes reduced-gravity experiments to explore the Pichevin–Nof mechanism and Reid’s (1972) theory applied to biannual transport forcing by wind. This is followed in section 3 with analyses of the satellite SSH data. Section 4 concludes the paper.

2. Reduced-gravity experiments The reduced-gravity model was described previously (Chang and Oey 2010, CO2012). The domain is the northwest Atlantic Ocean 58–508N and 1008–558W [see Fig. 1 in Chang and Oey (2010).] Table 1 gives various model parameters and their meanings. Although realistic [e.g., National Centers for Environmental Prediction (NCEP) reanalysis 1 satellite] wind may be used (e.g., CO2012), our goal here is to understand responses under clearly defined forcing, and we want to control the mean and fluctuating parts of the transport that passes through the Yucatan Channel. We therefore specify a steady zonal wind stress with curl (i.e., latitudinal 0–p cosine variation) east of 808W (i.e., in the Atlantic Ocean only), and its magnitude is adjusted to drive (through Sverdrup dynamics) a steady westward transport ’ 21.5 Sv (1 Sv [ 106 m3 s21) 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 (see caption)

Difference in No. of eddies between months with most and least eddies

Standard deviation based on actual SeH

Steady22Sv (1) GOM (1) 1 (2) Carib (1) 1 (3) GOMCarib (1) 1 (2) 1 (3)

2 (actual), 1 (smoothed)

1.0

None

7, 8


0.9

None

6, 7, 8


1.7

June and December–January

6, 7, 8, 9


2.6

June and December–January

4, 5, 6, 7, 8, 9

referred to as the Steady22Sv experiment. Three time-dependent transport experiments are then conducted (cf. CO2012), each forced by biannual wind, which qualifies as being slowly varying. A semiannual sinusoidal function is used: maximum westward in December and June, and minimum in March and September; these drive biannual transport variation (see below). The model wind therefore idealizes the biannual cycle of the observed zonal wind, which as mentioned above is actually asymmetric: maximum westward in January and July, and minimum in May and September (note the 1–2-month shift between model and observed wind maxima and minima). The wind is specified in the northwestern Caribbean Sea (158N , latitude , 228N, 878W , longitude , 808W). Wind stress amplitude of 2 3 1024 m2 s22 is used to (approximately) match the monthly-mean Yucatan transport fluctuations of ’ 61 Sv based on the 22-yr OGCM simulation (see CO2012’s Fig. 2b). This experiment is called Exp.Carib. The zonal wind in the Gulf of Mexico is also biannual and is 1808 out of phase from that in the Caribbean Sea (CO2012). Westward wind in the Gulf drives an eastward momentum flux and delays eddy-shedding (Chang and Oey 2010). A biannual zonal momentum flux which is in phase with the Caribbean wind is therefore also included to model this effect in the second Exp. GOMCarib, which then specifies both the Caribbean Sea and Gulf of Mexico winds. Finally, Exp. GOM specifies the semiannual momentum flux over the Gulf of Mexico only, that 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 integrated for 15 years from a state of rest; the model Loop Current sheds eddies at a quasi-regular period in about 3 years. The last 12 yr results are used for analysis.

Calendar month(s) with most eddies

Shedding periods (months)

a. Eddy-shedding characteristics We first discuss some general characteristics of the eddy-shedding results (Table 2 and Fig. 3). Rather than ‘‘pick-and-choose’’ from snapshots of the 12-yr data, we conduct an unbiased, monthly composite analysis and the significances of these composites are then judged by calculating the corresponding standard errors. This procedure anticipates that the solution is periodic, which turns out to be true as judged from the smallness of the standard errors in nearly all of the parameters we have examined below. For each experiment, the calendar months when eddies are shed are recorded. Table 2 (second column) lists the difference in the number of eddies between months with most and least eddies. From the distribution of number of eddies as a function of the calendar months, which will be referred to as the Seasonal Histogram (SeH) (CO2012), the standard deviation is calculated and listed in the third column.4 The calendar months with most eddies (taken into account also of statistical significance—described below) are then listed in the fourth column. Finally, eddy-shedding periods defined as time differences between present minus preceding eddies are listed in the last column. The SeH is plotted as black curves in Figs. 3b–d for Exp.GOM, Carib, and GOMCarib. The corresponding SeH for the Steady22Sv experiment is also included in Fig. 3b as the dashed gray curve. A 3-month weighted averaging (1 1 2 1 1)/4 has been applied to the SeH to account for

4 T. Sturges (2012, personal communication) mentioned that the word ‘‘seasonal’’ may be confused with ‘‘annual variation.’’ Here we follow the Oxford English dictionary to mean it as ‘‘happening during a particular season’’ without necessarily implying it to be 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 0 and min–max scales are 62 3 1024 m2 s22. 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.

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ambiguity, which may result when eddies are shed near the beginning and end of the month. This is because the separation of an eddy from the Loop Current is generally a gradual process which can take ;(1–3) weeks from the time that a peanut shape (with shell) with a narrow ‘‘neck’’ develops to complete detachment. Both the smoothed and actual values (Table 2) are used below. The behaviors of the reduced gravity model with constant transport forcing have previously been thoroughly analyzed and discussed (Hurlburt and Thompson 1980; Pichevin and Nof 1997; Nof 2005; Chang and Oey 2010, CO2012). For the present study, the Steady22Sv experiment is used to establish a baseline case for judging the significance of seasonal shedding preferences in other experiments. The Steady22Sv experiment sheds 19 eddies: 15 eddies have an 8-month period and 4 eddies have 7 months (see the eddy-shedding histogram EsH in Fig. 3e). The shedding period of ;(7–8) months is similar to that found in previous studies. The dominant 8-month period is the natural shedding period of the present reduced-gravity system (see, e.g., Oey et al. 2003). CO2012 show that the 8-month shedding period can yield three preferred peaks for eddy shedding in the corresponding SeH. However, because of the existence of the 7-month period, albeit weak, the 3 peaks tend to be smeared and, for a large enough sample of eddies, the preferred shedding months become indistinguishable from the background mean, as shown by the dashed curve in Fig. 3b. The difference in the number of eddies between months with most and least eddies is 2 (51 for the smoothed SeH; Table 2, second column), and the corresponding standard deviation is ’1 (Table 2, third column). These values for the Steady22Sv experiment will serve as the baseline to judge the significance of monthly preferences of eddy-shedding in other experiments. The Exp.GOM is dominated by shedding periods of 7 and 8 months and only one eddy has a 6-month period (Fig. 3e). The corresponding SeH is strongly smeared by the dominant 7-month period (Fig. 3b). The difference in the number of eddies between months with most and least eddies is 2 (51 for the smoothed SeH; Table 2, second column), and the corresponding standard 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 Exp.GOM are not significant. This conclusion is confirmed by the upper-layer h-contour at 908W across, which the Loop Current extends and/or eddies pass, plotted as a function of month (the Hovmo¨ller plot; Fig. 3b, background color); this shows no distinct

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maxima for any particular month(s). It is interesting that despite the biannual forcing within the Gulf of Mexico, Exp.GOM produces no preferred month of shedding in stark contrast to the Caribbean Sea forcing experiments to be described next. The Gulf forcing therefore acts only to delay shedding through eastward momentum flux and upper-layer convergence in the eastern Gulf, especially in fall (cf. CO2012; see also Chang and Oey 2010, 2011). For Exp.Carib (Fig. 3c) and Exp.GOMCarib (Fig. 3d), differences in the number of eddies between months with most and least eddies are 4 and 8, respectively (52 and 4 for the smoothed SeH; Table 2, second column), and the corresponding standard deviations are 1.7 and 2.6 (Table 2, third column). These values exceed those for the Steady22Sv experiment, and the peaks in their SeH’s are therefore significant. The preference months when eddies are shed are June and ;(December–January) (Figs. 3c,d, and Table 2, fourth column), and they are confirmed by the corresponding h-Hovmo¨ller maps along 908W (colors in Figs. 3c,d) that, unlike the map for Exp.GOM (Fig. 3b), display distinct biannual maxima.5 Note that these h maxima precede the months of maximum eddy counts by approximately 1 month. This is because the model Loop Current generally extends pass 908W prior to shedding an eddy. By comparing Figs. 3c,d, we see that Exp.GOMCarib and Exp.Carib are similar, but the former has more distinct peaks in its SeH and is therefore closer to the observation (see Fig. 1a of CO2012). The latter conclusion is consistent with the results of the more elaborate 3D OGCM in CO2012. In Exp.GOMCarib, stronger easterlies in fall (and spring) over the Gulf of Mexico produce convergence that accumulates mass in the eastern Gulf, and eastward momentum flux which delays eddy-shedding, thus accentuating the difference in eddy counts between fall and winter (spring and summer). Finally, from Figs. 3d,g, we also conclude that, while the eddy-shedding histogram (Fig. 3g) containing a range of periods from ;(4–9) months may seem to suggest chaos, the system is actually remarkably regular and sheds eddies at quasi-periodic intervals that are obviously linked to the (wind and transport) forcing.

5 The model’s months of maximum and minimum shedding are ;(1–2) months earlier than observed. However, the idealized wind is perfectly biannual rather than asymmetric as observed, and has maxima and minima which are also ;(1–2) months earlier. Therefore, for the purpose of studying biannual shedding mechanism, shedding time is only relevant with respect to the phase of the wind; see below.

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b. Interpretations We now relate the above biannual regularity in eddy shedding to the forcing, and interpret them in terms of Pichevin–Nof mechanism and Reid’s theory. The results for both Exp.Carib and Exp.GOMCarib are similar, so only the former (with simplest wind forcing) is discussed here. We conduct an EOF analysis based on the 12-yr h data, then describe the process based on monthly composites. Figure 4 shows the leading EOFs 1 and 2, which together explain 70% of the total variance. Both eigenvectors (EV-1 and 2) show a train of h anomalies of opposite signs emanating from Cuba and extending northward then westward into the Gulf of Mexico. The EV-2 is in fact simply EV-1 shifted in that direction, and its principal component (PC-2) is highly correlated with PC-1 and lags PC-1 by 55 days (correlation coefficient 5 0.92 at 99% significance).6 Both PCs are significantly biannual as shown by the amplitudes of their monthly composites which are significantly greater than the standard errors. The sequences that lead to eddy-shedding are compactly described by these 2 EOFs (Fig. 5). In mid-June (mid-December), the PC-1 is near a positive maximum while PC-2 ’ 0 as a warm anomaly forms southwest of Cuba, and the Loop grows as the warm EV-1 at 878W strengthens (Fig. 4a). Approximately 55 days later, in early August (early February), PC-2 is near a positive maximum while PC-1 ’ 0, the warm anomaly is squeezing through the Yucatan Channel, creating a weak high northwest of Cuba; meanwhile the Loop continues to expand westward through the EV-2 high near 888W (Fig. 4b). By mid-September (mid-March), PC-1 is near a negative maximum while PC-2 again becomes ’0, and the Cuban warm anomaly has now completely squeezed through the Yucatan Channel (Fig. 4a). At the same time, the strong warm anomaly due to EV-1 has expanded further westward to (25.58N, 898W) near the tip of the model Loop Current (Fig. 4a). At this time, a cold anomaly is formed southwest of Cuba. In early November (or early May), PC-2 now becomes a negative maximum while PC-1 is again ’0. The Cuban warm anomaly pushes north-northwestward, and the strong warm anomaly in the Gulf of Mexico also shifts westward, being now centered at (268N, 90.58W; Fig. 4b).

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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 (Lin et al. 2007; Oey 2008), and Caribbean eddies (Alvera-Azcarate et al. 2009). For the present application, the simpler EOFs are much more straightforward.

This is also the time, or shortly thereafter (December or June), when the majority of eddies are shed from the model Loop Current (Fig. 3c). The westward propagation velocity is ’23.3 cm s21. The model Caribbean is driven by the oscillating trade wind, which will be seen below to produce upper-layer anomalies through the sloshing back-and-forth of the (zonal) Caribbean current. This Caribbean variance is contained in EOF3 (not shown), which explains 12% of the total variance, has a strong biannual signal, is in phase with PC-1, and its EV-3 is dominated by the Cuban southwest anomaly, but stronger and larger filling up the northern half of the northwestern Caribbean Sea; the EOF-3 is weak inside the Gulf of Mexico. Figure 4 (fourth row) shows the homogeneous correlation (HC) maps between h and PCs 1 and 2. For each mode, the HC2 (3100) gives the percentage of local variance explained by that mode. While the link between the Gulf of Mexico and Caribbean Sea is crucial, only a relatively small percentage (’10%) of the Caribbean variance covaries with the Gulf of Mexico. The reason is due to a mismatch in the oscillations between the Gulf (e.g., eddy-shedding) and Caribbean Sea (e.g., wind-driven). An analogous situation will be seen for satellite data. Figure 6 plots the Yucatan inflow relative vorticity z and northward velocity y, Loop Current’sÐ Ðnorthern boundary (LCNB), Loop’s volume VLoop 5 h dx dy, where the double integral is area of the Loop bounded by latitude 228N, longitude 848W and the Loop’s edge defined by h 5 625 m, LCBN from the Reid’s (1972) formula [Eq. (1)], and the Yucatan transport TrYuc. The trade wind stress (t ox , 0) is specified to be strongest in June (December). The z, y, and TrYuc all lag the wind by 2 months (Figs. 6a,b,e) and become maximum in August (February). The lag is due to the finite time taken for warm water to accumulate against the Yucatan Peninsula coastline during the increased trade wind from spring to summer. The process is analyzed by calculating the mass balance within a control volume in northwestern Caribbean Sea: bounded by the Yucatan coast in the west, Honduras coast to the south, Yucatan Channel to the north and a south-tonorth transect from Honduas to Cuba in the east (see Fig. 7a). The continuity is ›h ›hu ›hy 1 1 5 2aN h, ›t ›x ›y

(2)

where 2aN h is the Newtonian cooling term with aN 5 1/800 day21 and h 5ÐhÐ – H (see Table 1). Integrating over 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% significance, contour interval 5 0.2).

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FIG. 5. (top to bottom) The January–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.

678


ðð

›h dx dy 1 ›t I

ðN S

huE dy 1

ðE

II

The first term (I) is the rate of mass accumulation (depletion if ,0) inside the control volume. The second term (II) represents the Caribbean mass influx (uE , 0) across the eastern boundary. The third term (III) is the Yucatan outflow into the Gulf of Mexico (yN . 0). The last term (IV) accounts for the Newtonian cooling term. Average the entire 12 years, we find that term I 5 0, II 5 221.5 Sv, III 5 121.2 Sv and IV 5 10.3 Sv. Term IV leads III by 1 month but its fluctuation is very small ’60.04 Sv, and it will henceforth be neglected. Terms I, II, and III and wind stress are plotted in Fig. 7e. As the trade wind strengthens from March to maximum in June, warm anomaly (higher pressure) develops along the southern coast of Cuba as the upper layer deepens, and by geostrophy the westward Caribbean transport also becomes maximum (Figs. 7a,e). From mid-April through mid-July, warm water accumulates and the high pressure moves up againstÐ Ðthe Yucatan’s eastern coast, as indicated by the positive (›h/›t) dx dy during the same period of increased trade wind (Fig. 7e). Near the end of this period of warm-water convergence, at end of July to beginning of August, the anticyclone associated with the high pressure is strongest, and it forces also strong northward Yucatan transport that peaks in August (Figs. 7b,e). This is also when y and z in the western Yucatan Channel become maximum (Figs. 6a,b). The Reid’s formula [Fig. 6d, Eq. (1)] mimics more closely the z variation rather than the y variation showing its greater sensitivity to the former (see Fig. 2a), and it too peaks in August. The strong Yucatan transport produces a more rapid growth of the Loop Current according to Pichevin–Nof theory, as seen by the rapid increase in the volume of the Loop VLoop, which becomes maximum ;(1–2) months later in ;(September– October) (Fig. 6c). The model LCNB also shifts north as shown in Fig. 6c, and becomes a maximum in September, approximately one month after maximum z, y, and Yucatan transport. After September, both LCNB’s rapidly drop (Figs. 6c,d) as the Caribbean anticyclone ‘‘squeezes’’ through the Yucatan Channel (Fig. 5, August–October) and both z and y decrease (Figs. 6a,b). The ‘‘squeezed’’ anticyclone adds mass into the Loop as seen in the continued growth of VLoop from September– October (Fig. 6c). From August–October, the negative ÐÐ (›h/›t) dx dy (Fig. 7e) indicates that the Caribbean anticyclone rapidly shrinks and the (westward) Caribbean transport is weakest (i.e., its anomaly is positive

W

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ðð hy N dx 1 III

aN h dx dy 50.

(3)

IV

maximum; Figs. 7c,e) as an anomalous low develops south of Cuba. In ;(October–November), the anticyclone is replaced with a strong cyclonic anomaly (Figs. 7d and 5), and the Yucatan transport, y, z, and LCNB’s all reach minima, while the VLoop reaches its minimum one month later in December (Fig. 6). At this time, the decreased supply of warm water into the Loop Current, which has in previous months grown and expanded, cannot balance the Rossby wave speed associated with the matured Loop—that is, the Pichevin–Nof mechanism. Eddies, then, tend to separate around this time or shortly thereafter (Fig. 3c). The westward volume flux carried by the separated eddy can be estimated by noting that near the time of its minimum the Yucatan inflow is stationary (Fig. 6e: November or May), so that the flux must equal to the VLoop-deficit between shedding month (December or June) and the month before. The value is ’0.6 Sv, which taking the eddyshedding period of 6 months yields an eddy of about 150 km in diameter as seen in the simulation (plots not shown). Because of the biannual forcing, the above descriptions apply also for the first half year from December–June. There is some asymmetry between the June shedding and ;(November–January) shedding (Fig. 3c) which is also seen in the model LCNB (Fig. 6c). This may be due to the existence of the natural shedding period [;(7–8) months, Fig. 3e], as well as the forcing (the asymmetry largely disappears for Exp.GOMCarib, not shown). The consequence of the asymmetry is relatively minor, however, and also it is not seen in other time series (Figs. 6 and 7e); we therefore do not further pursue its cause. In summary, eddy-shedding tends to occur shortly (;1 month) after the minimum Yucatan z and y following a period of strong inflow forced by piling up of warm water against the western Caribbean Sea by the strong trade wind. That a minimum inflow z and y tends to favor eddy shedding was found by Oey (2004) in a 3D OGCM. In the reduced-gravity model, the chain of events takes approximately 6 months so that one cycle that culminates in the shedding of an eddy is immediately followed by the start of the next cycle. To check that minimum z and y are not merely coincidental, we reran Exp.Carib using annual rather than biannual trade wind forcing. The results are shown in the appendix (Fig. A1), which is seen to have the same characteristics as the biannual

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FIG. 6. Monthly (a) z (s21) and (b) y (m s21) averaged within the western 50 km of the Yucatan Channel at 228N; (c) latitude of Loop Current’s northern boundary (LCNB) defined by h 5 625 m (the purple contour in Fig. 5) along a line from Yucatan Channel to Mississippi Delta (black curve), and Loop’s volume VLoop (gray curve, 1013 m3; see text); (d) LCBN from the Reid’s (1972) formula using z and y with u 5 908. (e) Yucatan transport in Sv. Bars are the standard errors equal to 6s/N1/2 where s 5 standard deviation for each parameter and N 5 number of samples.

forcing case that eddy shedding occurs after the minimum z and y. Thus, there exists a preference shedding month (Fig. A1a) in accordance with the annual forcing, even though the EsH shows a range of shedding periods from ;(4–11) months (Fig. A1e). Shedding events tend to (i.e., maximum SeH) occur ;1 month after the minimum z and y (Figs. A1a,b,c). Finally, maximum transport is approximately 2 months after the peak of the trade wind (Fig. A1d).

3. Satellite observations and comparison with model With periodic forcing that simulates the biannual variation of the wind, the reduced-gravity model produces also biannual growth of the Loop Current and

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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 approximately 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 increase from summer to fall [;(August–October)] also with approximately doubled amplitude than from winter to spring [;(January–May)]—see Fig. 8a. Because 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 minimum 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 found July–September preferences for eddy-shedding. These results are consistent with the reduced-gravity results that decreased transports (hence also z and y) are triggers of eddy shedding, and suggest that the simpler model may harbor a large portion of the Loop Current physics. Satellite SSH data provides a relatively long-term (1993–2010 is used here) information of Loop Current and eddy shedding. This information was neither available nor completely without ambiguity in prealtimetry years. The data we use is SSH anomaly (SSHA) from Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO; http://www.aviso.oceanobs. com/) from October 1992 to December 2010 on 1/ 38 3 1/ 38 Mercator grid. The mean SSH field is from Rio et al. (2011). This has a resolution of 1/ 48 3 1/ 48 and was constructed by combining the Gravity Recovery and Climate Experiment (GRACE) geoid, drifting buoy velocities, profiling float and hydrographic temperature and salinity data. These data allow one to discern eddy-shedding dates (hence periods), which are generally consistent with those obtained from a data-assimilated analysis dataset we have conducted for the Bureau of Ocean Energy Management (see, e.g., Lin et al. 2007; Yin and Oey 2007; 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 monthly transport anomalies (Sv 5 106 m3 s21) 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. Gray curve is the specified zonal wind stress in m2 s22. Plots are repeated every 2 years.

Leben (2005). The eddy-shedding dates and periods were used in CO2012. Here we use the AVISO data to examine the growth and wane of the Loop. Based on the experience gained from the reducedgravity model experiments, we look again for some regularity in the 18-year satellite data.7 Alvera-Azcarate et al. (2009) analyzed the AVISO data (October 1992– February 2006) but focusing on the Caribbean Sea where they found strong annual steric variation. Therefore, prior to any analysis, we remove from the data the annual steric height variation, which amounts to an SSH difference of 0.14 m between the September maximum and March minimum. Thus, regularity in the signal is a dynamical one. Lin et al. (2010) conducted an EOF analysis using the AVISO SSHA. The leading EOF modes 1 and 2 together explain 50% of the total variance, and the authors described the connection of these EOFs with Yucatan transport. It is significant that their EOF principal components display strong annual variations (see their Figs. 3c,d), which therefore suggest some seasonal regularity.8

7

The correctness of this presumption will be seen a priori. The authors did not mention if the annual steric signal was removed prior to their analysis, but we have confirmed their results with steric removed using their EOF domain. 8

a. Monthly composites We again conduct an unbiased, monthly composite analysis. Figure 8c shows the composite Loop Current edges at the indicated months and Fig. 8d shows Hovmo¨ller SSHA maps along the 26.58N latitude line across the Loop. What is striking is the appearance of two highs in Fig. 8d: a weak one in winter (January) and a strong and larger one in summer [;(June–August)], which is also more westward extended. This biannual mode is significantly separated (i.e., it is not indistinguishable from being just one mode) as judged by the fact that the difference between either of the two highs (summer and winter) and the low’s (fall and spring) is greater than two standard errors (60.03 m). However, the summer-to-fall amplitude is much more distinct than the winter-to-spring amplitude, which is barely significant, as shown by the plot of maximum SSH and standard error in Fig. 8e. These behaviors are consistent with the independently derived conclusions based on the simulated Yucatan transport variation (i.e., Fig. 8b) and 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 growth-and-wane signal that is unrelated to static responses to seasonal heating and cooling of the upper ocean. The response is strongest and more clearly

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FIG. 8. Monthly (a) zonal wind stresses (m2 s22) 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– spring). The cause is a dynamical one that is primarily forced by the wind (in particular the trade wind in the Caribbean Sea), which also shows a seasonal asymmetry. With these in mind, we focus in the northwestern

Caribbean Sea and compare in Fig. 9 the reduced-gravity model composites of the upper-layer anomalies with the corresponding composites of AVISO SSHA from May through December. From May through July when the 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)].

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anomaly against the Yucatan coast just south of the Yucatan Channel evolves from cold to warm in agreement with the model. From August to October when the trade wind weakens, the warm anomaly weakens and turns into a cold anomaly, which reaches its maximum (cyclonic) strength in November (Fig. 9d). These warm and cold anomalies presumably force stronger and weaker Yucatan transports, and the timings are also consistent with the maximum and minimum transports, respectively, in Fig. 6e using the reduced-gravity model. Despite the simplicity of the reduced-gravity physics and the idealized nature of the specified wind forcing, there is therefore some correspondence between model and AVISO. In Fig. 9e, the AVISO SSHA and model h both averaged over the northwestern Caribbean Sea 17.58–22.58N and 878–808W are compared. The correspondence is obvious especially for the second half year, and both 0-lag and 1-month-lag (AVISO lags) correlations are significant. The discrepancy is in part attributed to the idealized nature of the model wind, which does not exactly follow the observed, asymmetric wind variation (see section 2; also Fig. 8a). The 1-month lead by model is consistent with the fact that the idealized wind is specified to be at a maximum in June and December, which leads the observed wind maxima by approximately 1 month (July and January). Finally, the AVISO data also shows a close connection between the sea surface height fluctuations in the Caribbean Sea and the Loop Current’s expansion and retraction, as can be readily seen by comparing Fig. 9e and Fig. 8e. They show for example that as the warm anomaly in the Caribbean Sea strengthens in July, the Loop Current extends northward in ;(June–August), while the Loop retracts in November as the Caribbean cold anomaly is strongest. These inferences are now quantified using EOF.

b. EOF analysis EOFs of SSHA using the same domain as in the reduced-gravity case are computed (Fig. 10). The EOF1 accounts for 30% of the total variance (Fig. 10a). Its eigenvector (EV-1) shows a tripolar structure which during the positive phase of the principal component (PC-1) has a strong high at its center pole near (258N, 878W) flanked by two weaker (by ;50%) lows: one to the west and the other one to the southeast. Mode-2 EOF explains 17% of the total variance. The EV-2 also has a strong high at its center pole near (278N, 88.38W) flanked by two weaker low’s west and east. Both EV’s thus display a train of SSHA of opposite signs emanating from Cuba, and the EV-2 pattern is just EV-1 shifted west-northwestward. Monthly composites of both PC-1 and PC-2 (Fig. 10a, third row) show a significant annual

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cycle and are in fact significantly correlated (at 99% significance level) with maximum correlation 50.63 when PC-1 leads by 3 months. They are therefore 908 out of phase. As in the reduced-gravity EOFs1 and 2, the AVISO EOFs 1 and 2 also represent propagating features, and again may be analyzed using complex EOF’s (Merrifield and Guza 1990). It is however much more straightforward to use the simpler EOFs and, taking advantage of their significant seasonal cycles, to analyze them together with monthly SSHA-composites (Fig. 11) for physical interpretations. Starting in May, the Loop Current begins to grow (Figs. 8d,e), EOF-2 is weak and EOF-1 dominates (Figs. 10 and 11). From June through August, EOF-1 weakens (Fig. 10); the variability is now dominated by EOF-2 whose center pole represents the west-northwestward growth and expansion of the Loop during these 3 months (Fig. 11), while its southeastern pole (a cyclone) contributes to the ‘‘necking’’ of the Loop near (258N, 868W). From September, EOF-1 strengthens and reaches its strong negative phase when a strong low anomaly in Fig. 11 develops near EV-1’s dominant center pole (878W, 258N), cutting across the Loop Current, while the EOF-2’s center pole then becomes the separating eddy. Then, from October through December, because of the shifts in both pattern and phase between EOFs 1 and 2, their western poles together describe the westward propagation of this eddy: EOF-1 (October) / EOF-1 1 -2 (November) / EOF-2 (December). From January through February, the winter growth phase of the Loop Current begins, described primarily by the strong EOF-1s (Figs. 10 and 11). In March and April, the Loop Current weakens, but the process is much less well defined (Fig. 11) and cannot be explained by EOFs 1 and 2 alone; higher EOF’s also contribute to the composite (not shown). In summary, the growths of the Loop Current in winter and early summer, as well as the Loop’s retraction in fall are primarily described by EOF-1. The EOF-2, on the other hand, describes the west-northwestward expansion of the Loop and subsequent eddy shedding in summer to fall. Eddy shedding preferentially occurs from summer to fall, particularly in late fall. In spring, weakening of the Loop Current is more complicated, requiring many modes. We compare EOF’s from AVISO (Fig. 10) and reducedgravity model (Fig. 4). As to be expected, the total variance explained by the observed EOFs 1 and 2 (47%) is lower than the modeled 70%. Both EV patterns show trains of anomalies extending west-northwestward from Cuba into the Gulf of Mexico; wavelength of the pattern in observation is longer, probably because the observed Loop and eddies are much more energetic (individual 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 Current growth and eddy shedding are also analogous. To reveal the connection with fluctuations in the Caribbean Sea, we plot in Fig. 10 (last row) the homogeneous correlation (HC) maps between PCs 1 and 2 and SSHA. The correlation indicates how well the SSH in Caribbean (and other) region covaries with the dominant fluctuations in the Loop Current.9 Approximately 10% of the Caribbean Sea’s variance covaries with Gulf of Mexico. Similar feature as the southwest Cuban anomaly, described previously in conjunction with the reduced-gravity EOFs, and how the anomaly progresses from mode 1 to mode 2 as the Loop Current expands and sheds eddies, is now also discernible in Fig. 10. Similarly to the HC-maps for the reduced-gravity model (Fig. 4), the weak Caribbean-Gulf covariance is due to a mismatch in the dynamical oscillations between the two basins. The upstream connection with the SSH fluctuations in the Caribbean Sea is of interest (e.g. Murphy et al. 1999; Oey et al. 2003). Figure 12 extends HC’s to the entire Caribbean Sea, and shows also EOF 3. In HC-1, west of 808W, eddy-like features are generally consistent with wind-forced piling-up (and retreat) of warm water, since this tends to be maximum (minimum) in summer (fall) (Figs. 9b,d and 10). The Loop also covaries with the generation region of the so-called Hispaniola Eddy near (168N, 758W), where Oey et al. (2003) show that a localized anticyclonic wind stress curl can periodically spin up warm eddies, which then drift westward to affect Loop Current eddy shedding. Similar eddy-like features are also seen in HC-3. Here, large-scale effect of the trade wind in producing the fluctuating, geostrophicallybalanced Caribbean Current is also evident. The HC-2 shows a covarying component that is confined around Cuba, which appears to be consistent with Lin et al.’s (2010) findings, and it contributes to the Yucatan transport fluctuations. The Lin et al. (2010) theory depends on the existence of a ‘‘topographic form drag’’ which is absent from the reduced-gravity model. The latter shows nonetheless strong h-fluctuations off the southwestern tip of Cuba (Figs. 4 and 9a,c), which coincides with the significant HC-2 there (Fig. 12b). These different processes contribute to mass and vorticity (;=2h) fluxes in Yucatan Channel, to the growth and wane of the Loop Current, and to eddy shedding.

9

Strictly speaking, with the dominant fluctuations of the EOF 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 eastern Gulf only: 22.58–288N and 928–828W, which is the region used by Lin et al. (2010).

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4. Conclusions The expansion, eddy shedding, and retraction of the Loop Current are complex phenomena with multiple temporal and spatial scales. This paper attempts to find some regularity in the process, motivated by recent findings that eddy shedding may preferentially occur in summer and winter. Here are the conclusions. 1) Satellite altimetry observations show that the Loop Current displays a significant biannual expansion and retraction cycle, from summer to fall (S2F), and then from winter to spring (W2S); these cycles are unrelated to the annual steric height variation because of heating and cooling. 2) The S2F-cycle is particularly strong, and is often followed by eddy-shedding. 3) Both the S2F cycle and eddy shedding are represented well by the first two leading EOF modes, which are well-correlated in space and time except that they are shifted relatively to each other (i.e., 908 phase shift) and therefore also describe the westward propagation of the detached eddy. 4) The W2S-cycle is much less well-defined; nonetheless, it is significant, though barely. 5) The existence of S2F and W2S cycles, and their asymmetry, is suggestive of forced responses by the Caribbean and Gulf of Mexico wind system, which is also similarly asymmetric. 6) The wind-forced dynamics is contained in a reducedgravity model, which includes coastline but otherwise ignores topography, and which assumes a quiescent lower layer. For the S2F cycle, the simple model gives upper-layer variation in northwest Caribbean Sea that is in good agreement with satellite observation. 7) The forced response first occurs in the northwestern Caribbean Sea through upper-layer thickening by warm water that piles up along the Yucatan peninsula, followed by transport and vorticity fluctuations in the Yucatan Channel that force the Loop Current to expand, shed eddy, and retract. The dynamics can be explained in terms of the Pichevin–Nof mechanism and Reid’s theory, and eddy-shedding tends to occur near minimum z and y. 8) Finally, the Loop Current’s growth and wane are 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 primarily a forced system, so that the Loop’s growth may be approximately determined based on the biannual transport forcing because of the wind. Shedding of 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. SeH); (b) Yucatan inflow z (s21); (c) y (m s21); (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). For this experiment, the maximum trade (i.e., westward) wind stress (522 3 1024 m2 s22) is specified to be in September.

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especially during the large decrease in transport from summer to fall (CO2012). The observed asymmetric response between summer-to-fall and winter-to-spring shedding characteristics is explained by smaller-amplitude change in the trade wind in the latter compared to the former, by approximately half, producing a correspondingly fourfold smaller contrast in the transport that influences eddy shedding. The biannual wind therefore modulates the natural shedding so the Loop Current is more prone to shed eddies when large-amplitude weakening in transport occurs. On the other hand, the exact timing of when an eddy is shed can depend on the Loop’s intrinsic variability including dynamical instability and upper–lower-layer coupling, etc., as well as on the undeterministic nature of the forcing itself. These ideas are taken up in Xu et al. (2013) based on a realisticcase model experiment of Loop Current eddy shedding. Acknowledgments. Comments from 2 anonymous reviewers help improve the manuscript. We acknowledge the supports by the Bureau of Ocean Energy Management Contract M08PC20007 (SAIC subcontract).

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Leben, R. R., 2005. Altimeter-derived Loop Current metrics. Circulation in the Gulf of Mexico: Observations and Models, Geophys. Monogr., Vol. 161, Amer. Geophys. Union, 181– 201. Leipper, D. F., 1970: A sequence of current patterns in the Gulf of Mexico. J. Geophys. Res., 75, 637–657. Lin, X., L.-Y. Oey, and D.-P. Wang, 2007: Altimetry and drifter assimilations of Loop Current and eddies. J. Geophys. Res., 112, C05046, doi:10.1029/2006JC003779. Lin, Y., R. J. Greatbatch, and J. Sheng, 2010: The influence of Gulf of Mexico Loop Current intrusion on the transport of the Florida Current. Ocean Dyn., 60, 1075–1084. Lugo-Fernandez, A., 2007: Is the Loop Current a chaotic oscillator? J. Phys. Oceanogr., 37, 1455–1469. Merrifield, M. A., and R. T. Guza, 1990: Detecting propagating signals with complex empirical orthogonal functions: A cautionary note. J. Phys. Oceanogr., 20, 1628–1633. Molinari, R. L., J. F. Festa, and D. Behringer, 1978: The circulation in the Gulf of Mexico derived from estimated dynamic height fields. J. Phys. Oceanogr., 8, 987–996. Murphy, S. J., H. E. Hurlburt, and J. J. O’Brien, 1999: The connectivity of eddy variability in the Caribbean Sea, the Gulf of Mexico, and the Atlantic Ocean. J. Geophys. Res., 104 (C1), 1431–1453. Nof, D., 2005: The momentum imbalance paradox revisited. J. Phys. Oceanogr., 35, 1928–1939. Oey, L.-Y., 2004: Vorticity flux in the Yucatan Channel and Loop Current Eddy shedding in the Gulf of Mexico. J. Geophys. Res., 109, C10004, doi:10.1029/2004JC002400. ——, 2008: Loop current and deep eddies. J. Phys. Oceanogr., 38, 1426–1449. ——, H. Lee, and W. J. Schmitz, 2003: Effects of winds and Caribbean eddies on the frequency of Loop Current eddy shedding. J. Geophys. Res., 108, 3324, doi:10.1029/2002JC001698. ——, T. Ezer, and H. J. Lee, 2005: Loop Current, rings, and related circulation in the Gulf of Mexico: A review of numerical models and future challenges. Circulation in the Gulf of Mexico: Observations and Models, Geophys. Monogr., Vol. 161, Amer. Geophys. Union, 31–56. Pichevin, T., and D. Nof, 1997: The momentum imbalance paradox. Tellus, 49, 298–319. Reid, R. O., 1972: A simple dynamic model of the Loop Current. Contributions on the Physical Oceanography of the Gulf of Mexico, Vol. II, L. R. A. Capurro and J. L. Reid, Eds., Gulf Publishing Co., 157–159. Rio, M. H., S. Guinehut, and G. Larnicol, 2011: New CNES-CLS09 global mean dynamic topography computed from the combination of GRACE data, altimetry, and in situ measurements. J. Geophys. Res., 116, C07018, doi:10.1029/2010JC006505. Rousset, C., and L. M. Beal, 2010: Observations of the Florida and Yucatan Currents from a Caribbean cruise ship. J. Phys. Oceanogr., 40, 1575–1581. Sturges, W., and J. C. Evans, 1983: Variability of Loop Current in Gulf of Mexico. J. Mar. Res., 41, 639–653. Xu, F., Y. Chang, L. Oey, and P. Hamilton, 2013: Loop Current growth and eddy shedding using models and observations: Analyses of the July 2011 eddy-shedding event. J. Phys. Oceanogr., in press. Yin, X.-Q., and L.-Y. Oey, 2007: Bred-ensemble ocean forecast of Loop Current and eddies. Ocean Modell., 17, 300–326.