MARCH 2002 WAJSOWICZ 973 A Modi®ed Sverdrup Model of the Atlantic and Caribbean Circulation ROXANA C. WAJSOWICZ* Department of Meteorology, University of Maryland at College Park, College Park, Maryland (Manuscript received 9 October 2000, in ®nal form 6 August 2001) ABSTRACT An analytical model of the mean wind-driven circulation of the North Atlantic and Caribbean Sea is constructed based on linear dynamics and assumed existence of a level of no motion above all topography. The circulation around each island is calculated using the island rule, which is extended to describe an arbitrary length chain of overlapping islands. Frictional effects in the intervening straits are included by assuming a linear dependence on strait transport. Asymptotic expansions in the limit of strong and weak friction show that the transport streamfunction on an island boundary is dependent on wind stress over latitudes spanning the whole length of the island chain and spanning just immediately adjacent islands, respectively. The powerfulness of the method in enabling the wind stress bands, which determine a particular strait transport, to be readily identi®ed, is demonstrated by a brief explanation of transport similarities and differences in earlier numerical models forced by various climatological wind stress products. In the absence of frictional effects outside western boundary layers, some weaker strait transports are in the wrong direction (e.g., Santaren Channel) and others are too large (e.g., Old Bahama Channel). Also, there is no western boundary current to the east of Abaco Island. Including frictional effects in the straits enables many of these discrepancies to be resolved. Sensitivity in strait transport to friction parameter is explored for the Caribbean island chain. Transport reversal in the minor passages around the Bahama Banks and Windward Passage as the friction parameter increased is noted. The separation latitude of the western boundary currents on Cuba's east coast moves southward as the friction parameter increases from zero, so making the Great Inagua Passage transport a better proxy for the Windward Passage transport. Major discrepancies with observations, namely, eastward instead of westward ¯ow in Grenada Passage, a southward instead of northward Guyana Current, and hence a Caribbean circulation and Florida Current fed wholly by water masses of North Atlantic origin, cannot be resolved. However, they are simply overcome by extending the model to three layers with the wind-driven and upper limb of the thermohaline circulation con®ned to the top layer, and the lower limb of the thermohaline circulation to the bottom layer. If it is assumed that over the latitudes of the Caribbean there is no signi®cant upwelling/downwelling between the layers, then the thermohaline-driven circulation is effectively a western boundary current, and all of the results for the analytical wind-driven-only model carry over, but with the value of the upper-layer transport streamfunction on the boundary of the American continent set to the magnitude of the thermohaline circulation rather than that on Africa. Exploration of strait transport sensitivity to friction parameter gives that realistic transports through the passages of the Windward Islands are only obtained if the friction coef®cient in these passages is an order of magnitude larger than that in the western passages. Windward Passage transport reverses from south to north for a smaller value of the friction parameter than in the absence of the thermohaline circulation; Anegada and Mona Passages are robust in¯ow passages for the Caribbean Sea. South Atlantic water masses enter the Caribbean Sea through the passages from Grenada Passage to Martinique Passage. As the friction coef®cient in the Windward Islands passages increases from zero, South Atlantic water mass is partially de¯ected northward along the outer arc of the islands and enters the Caribbean Sea through the passages up to Anegada Passage. The model suggests that for realistic friction parameters, South Atlantic water masses are unlikely to be found in the more western passages, or in the western boundary current skirting the edge of the Bahama Banks. 1. Introduction subject of much controversy since Leetmaa et al.'s Whether models based on Sverdrup dynamics explain (1977) note that the observed magnitude of Florida the circulation of the North Atlantic Ocean has been the Strait transport is consistent with that required to bal- ance the southward Sverdrup transport in the ocean in- terior. Wunsch and Roemmich (1985) showed that the * Additional af®liation: Earth System Science Interdisciplinary Center, University of Maryland at College Park, College Park, Maryland. diagnosed northward heat transport for the North At- lantic is not consistent with a Sverdrup model in which the ¯ow through Florida Strait is the return ¯ow of the Corresponding author address: Roxana Wajsowicz, Dept. of Me- northern subtropical gyre. Also inconsistent with this teorology, University of Maryland, 3433 Computer and Space Science Bldg., College Park, MD 20742-2425. simple type of Sverdrup model is evidence of South E-mail: [email protected] Atlantic water masses ¯owing through the passages of q 2002 American Meteorological Society Unauthenticated | Downloaded 10/02/21 04:15 PM UTC 974 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 32 the Lesser Antilles (Wilson and Johns 1997), and as tilles and exit through the Florida Straits. The exact much as 11 Sv (Sv [ 106 m3 s21) through Florida Strait pathway for the South Atlantic water mass depends on (Schmitz and Richardson 1991). However, realistic the amount of frictional resistance in the passages. The GCM simulations [see, e.g., Maltrud et al.'s (1998) Plate results are summarized and discussed in section 5. 2] show that a Sverdrup model actually describes well the mean transports in the ocean interior of the North 2. The multiple island rule Atlantic over the latitudes of interest from 108 to 308N. Observations of South Atlantic water masses pene- The island rule and multiple-island rule were de- trating the Caribbean can be reconciled with Leetmaa scribed in general form in Wajsowicz (1993). Their der- et al.'s (1977) note if it is recognized that estimating ivation is recapped below in section 2b for the case of transports from the Sverdrup balance does not neces- frictional effects con®ned to oceanic western boundary sarily imply anything about the water mass origin of the layers and assuming that all of the passages are dynam- ¯ow. The properties of the western boundary layer in ically wide and deep. In section 2c, modi®cations to the which the Sverdrupian gyres close are crucial, as de- rules, assuming frictional effects are important, are de- scribed in Wajsowicz (1999b) in the context of the In- scribed with emphasis on the in¯uence of wind stresses donesian Through¯ow. With this revised perspective, for outside the latitude band of the island under con- the wind-driven circulation within the North Atlantic sideration. Asymptotic solutions in the limit of small and Caribbean is reexamined. Sverdrup dynamics are and large friction coef®cient are presented for an ar- shown to be consistent with observations provided a bitrary length island chain, assuming a simple north- thermohaline circulation, which is con®ned to the west- west±southeast skew. ern boundary layer over the domain of interest, is in- cluded, as noted by Townsend et al. (2000). Also, the a. Equations of motion transports through certain straits need to be limited; fric- tional effects are assumed. The streamfunction on island To keep the discussion succinct, the description is boundaries, and so strait transports, are calculated using given in terms of quasi-steady motion of an active layer a frictional form of the multiple-island rule (Wajsowicz above an inert deep layer in which all bottom topog- 1993). This is a quite powerful result, as it enables the raphy is assumed con®ned; the only external forcing is wind stress bands determining a strait transport to be due to surface wind stresses. Let c describe the transport identi®ed, and so in turn the sensitivity of the transport streamfunction of the active layer so that the depth- to changes in the wind stress and strength of the ther- integrated zonal and meridional velocities for the layer mohaline overturning circulation to be better under- are given by u 52cy, y 5 cx. Then, the depth-inte- stood. grated momentum equations are The basic multiple-island rule (Wajsowicz 1993) is P t x 2 f c 52x 1 1F x (2.1a) recapped in section 2, and several extensions appropri- x rr ate for the Caribbean derived. The wind-driven trans- oo ports through the major passages of the Caribbean are P t y f c 52y 1 1F y, (2.1b) calculated using the multiple-island rule and Hellerman y rr and Rosenstein (1983) wind stress climatology in sec- oo tion 3. The cases of dynamically wide and narrow chan- where f is the Coriolis parameter, P is the depth-inte- x y nels are considered. Determining strait transports by the grated pressure, t 5 (t , t ) is the wind stress, ro is the x y multiple-island rule enables the effect of using different density of the layer, and F 5 (F , F ) is the depth wind stress climatologies to be readily deduced, and the integrated friction term. The number of boundary con- variety of behavior Townsend et al. (2000) found for ditions required depends on the form of F. However, 11 different wind stress climatologies is easily ex- the no-normal ¯ow condition reduces to c 5 const on plained. These wind-driven multiple-island rule results boundaries. are described in detail, as adding a thermohaline cir- culation does not alter the basic dependencies. b. Dynamically wide passages The model is extended to three layers in section 4 to From Wajsowicz (1993), if it is assumed that fric- include a meridional overturning thermohaline circu- tional effects are unimportant outside western boundary lation.