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Loop Current Growth and Eddy Shedding Using Models and Observations: 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 MARCH 2013 C H A N G A N D O E Y 669 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, 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 Gulf of Mexico 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 ocean (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 Ó 2013 American Meteorological Society Unauthenticated | Downloaded 10/07/21 06:48 PM UTC 670 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 43 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 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 North Atlantic Current’s northward intrusion b is the upstream vortic- Ocean and the American continent (see CO2012’s Fig. 2a ity divided by Coriolis parameter f (z/f) at the western and their online supporting materials). The Caribbean edge of the boundary current 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 Unauthenticated | Downloaded 10/07/21 06:48 PM UTC MARCH 2013 C H A N G A N D O E Y 671 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.
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