Subinertial Flows and Transports in Cozumel Channel

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. 0, XXXX, doi:10.1029/2002JC001456, 2003

Subinertial flows and transports in Cozumel Channel Gabriela Cha´vez,1 Julio Candela, and Jose´ Ochoa Departamento de Oceanografıá Fı´sica, Centro de Investigacioń Cientı´fica y de Educacioń Superior de Ensenada, Me´xico Received 29 April 2002; revised 18 July 2002; accepted 23 July 2002; published XX Month 2003.

[1] The subinertial flow of the Cozumel Channel is examined with nearly six months of current, subsurface pressure and meteorological data in order to (a) verify the validity of the geostrophic balance in Cozumel Channel and analyze the influence of other terms of the momentum equation in observed ageostrophic variations, and (b) estimate the transport through the Channel using a set of continuous current profile observations at the Channel’s center and the cross section velocity maps obtained from shipboard ADCP observations. Over periods longer than a month, the momentum balance in the channel is mainly geostrophic, but on alternative periods of similar duration, intense ageostrophic fluctuations are found that have timescales of days to weeks and up to 1 m/ s amplitudes. There is evidence that the advective nonlinear terms are the most probable cause of the lack of geostrophy over these periods. Other terms such as the local acceleration and the wind stress are found to contribute minimally in the ageostrophic fluctuations. A mean transport of approximately 5 Sv toward the Gulf of Mexico is estimated for the 5 months of measurements (December 1996 to May 1997), although with great variability: a minimum of 1.3 Sv around January, a maximum of 7.5 Sv by the beginning of May, and a standard deviation of 1.2 Sv. Neither surface currents nor the geostrophically deduced current is suitable for estimating the observed transport in the Channel. INDEX TERMS: 4512 Oceanography: Physical: Currents; 4508 Oceanography: Physical: Coriolis effects; 4556 Oceanography: Physical: Sea level variations; 4576 Oceanography: Physical: Western boundary currents; 4243 Oceanography: General: Marginal and semienclosed seas; KEYWORDS: channel dynamics, geostrophy, coastal circulation, Cozumel Channel

Citation: Chavez, G., J. Candela, and J. Ochoa, Subinertial flows and transports in Cozumel Channel, J. Geophys. Res., 108(0), XXXX, doi:10.1029/2002JC001456, 2003.

1. Introduction Current impinges upon the Yucatan Peninsula. A drifter release experiment [Badan et al., 2001] shows the surface [2] The Cozumel Channel is a narrow passage (18 km Cayman Current approaching the Yucatan Peninsula and wide by 50 km long and 400 m deep) about 70 km turning north. The Cozumel Island divides the Yucatan southwest of the Yucatan Channel in the Caribbean Sea Current; part of it flows to the east of the island in the (Figure 1); it is bounded by the Yucatan Peninsula on the Caribbean Sea proper and about 20% of the mean trans- west and the Cozumel Island on the east and has a very port, as will be shown in this study, flows through the regular bathymetry with no sills. There are no known Cozumel Channel (Figure 1). reports about the physical oceanography of this channel. [3] Channels and straits are peculiar zones of the About 24 Sv (1 Sv = 106 m3 s1) pass through the oceans as many of them are small spatial extensions Caribbean Sea-Gulf of Mexico System [Sheinbaum et connecting basins with different characteristics [Pierini al., 2002; Ochoa et al., 2001]. This transport is part of and Rubino, 2001]. They have been studied in the past the North Atlantic Subtropical Gyre [Schmitz and McCart- because the oceanographic characteristics in the neigh- ney, 1993; Johns et al., 2002]. On the western Caribbean boring areas are linked to the channels’ dynamics. Sea a meandering current, the Cayman Current, flows Cozumel Channel is a strip of water that does not join westward around 19N carrying those 24 Sv. As these two distinct basins but forms a passageway for the current approaches the Yucatan Peninsula, it turns north- dominant current in the region (i.e., the Yucatan Current) ward, takes the name of Yucatan Current, and feeds the identified clearly by strong flows to the northeast. These Loop Current inside the Gulf of Mexico. The Cozumel flows enter the Gulf of Mexico, feed the Loop Current, Channel lies north of the latitude where the Cayman and exit through the Strait of Florida in order to form

1 the beginning of the Gulf Stream (Figure 1). The Now at Dirreccio´n Municipal de Proteccio´n Civil, Tijuana, Baja possibility of monitoring the Yucatan Current and the California, Me´xico. transports from the Caribbean Sea into the Gulf of Copyright 2003 by the American Geophysical Union. Mexico by means of measuring in the more accessible 0148-0227/03/2002JC001456$09.00 Cozumel Channel is one idea behind the measurements

X - 1 X - 2 CHAVEZ ET AL.: SUBINERTIAL FLOWS AND TRANSPORTS IN COZUME CHANNEL

Figure 1. Maps of the study area indicating the location of places and currents discussed in the text. (a) The sketch of two streamlines that give a characteristic path of the flow through the region. (b) Details of the Cozumel Channel area. Depth contours at 50, 200, 500, 1000, 2000, and 3000 are indicated. Also shown are the locations of the ADCP (large dot) and bottom mounted pressure sensors (large +) used in this study. used in this study. For this set of measurements there studies make evident the need to confirm the validity of were no simultaneous measurements of transport in the the assumption of geostrophy in a channel if we are to use Yucatan Channel, therefore as a previous step in that it for other estimations. If a barotropic geostrophic balance direction, this study documents for the first time the proves to hold in a channel, the opportunity exists of oceanography of the channel. measuring the current (and the transport) indirectly by [4] Earlier studies in other channels and straits, such as using pressure sensors accessible in both sides of the Garrett and Toulany [1981, 1982] in the Strait of Belle channel, as opposed to setting up much more complicated Isle, Candela et al. [1989, 1990] in the Gibraltar Strait, and expensive moorings within it. Even if the geostrophic and Tsimplis [1997] in the Strait of Euripus, suggest that a balance has an intense baroclinic contribution, the sea geostrophic balance can be expected in the transversal level fluctuations can accurately infer transport variations momentum balance in channels like Cozumel Channel. if the barotropic and baroclinic contributions are highly That is, the cross-channel pressure gradient balances the coherent. along-channel velocity component via the Coriolis term. [5] The data used in this study shows that the across- The assumption that the ocean’s interior is in geostrophic channel momentum balance in the Cozumel Channel has balance is a good approximation for subinertial flows, but geostrophic periods, but ageostrophic fluctuations are also surface currents may have an important ageostrophic found. Thus we examine the influence of other terms component that would affect transport estimates that rely looking for the cause of ageostrophy. Even though, by on this assumption. Feng et al. [2000] report about studies scaling arguments, the nonlinear terms can be expected to of Kuroshio Current’s fluctuations inferred through the be small in most situations, in the presence of turbulent or variations of the sea level in Tokara Strait; they argue that structured motions, these terms may become important and the subsurface structure of the current in the zone is not cause ageostrophic deviations above the measurements well known. This implies a lack of certainty with the noise level. Hence turbulent stresses and advective terms usage of sea level to estimate the transport by assuming a are also explored as causes of the observed ageostrophic barotropic geostrophic balance, since it may not be repre- fluctuations. sentative of the actual current structure. On the other hand, [6] The following section describes the available obser- Johns et al. [2001] found a vertical barotropic structure in vations. The third section presents the assumptions for the Kuroshio Current, which makes it possible to infer the different simplified dynamical models. The same section transport variations efficiently with sea level. All of these includes tests, some of them rather crude by necessity, of the CHAVEZ ET AL.: SUBINERTIAL FLOWS AND TRANSPORTS IN COZUME CHANNEL X - 3

Table 1. Description and Location of the Instruments Used and Length of the Time Series Used in This Work Beginning of End of Instrument Location Depth Measurements Measurements Cozumel Pressure Sensor 2028.790N8658.520W At 10 m in protected zone (dock) 1996/12/15 1997/05/27 Calica Pressure Sensor 2034.210N8707.0290W At 10 m in protected zone (dock) 1996/12/16 1997/05/28 Isla Mujeres Pressure Sensor 2115.2540N8644.7870W Approx. 3 m in protected zone (dock) 1996/12/12 1997/05/30 Cozumel Channel ADCP 2034.2050N870.9410W At 427 m, measuring from 250 m, in 10 m intervals 1996/12/14 1997/05/29 validity of such dynamical models. The fourth section in Isla Mujeres to the north of the Channel. We also use shows the transport estimate through the channel. The last shipboard ADCP measurements from five oceanographic section gives the conclusions. cruises that took place in December 1996, May–June 1997, March–May 1998, January–February 1999, and June–July 2000. 2. Observations [8] Figure 1 shows the location of the instruments, and [7] This paper is based on moored ADCP and subsur- Table 1 gives their description. The shipboard ADCP data face pressure measurements obtained during the pilot stage of the five cruises studied is shown in Figure 2. Table 2 of the CANEK Program from December 1996 to May gives the period in which they were obtained, as well as 1997. The ADCP was moored at the center of the channel the number of channel crossings performed during each at a depth of 270 m over a 427 m bottom measuring cruise. currents hourly every 10 m from 250 to 30 m depth. [9] In order to work with across- and along-channel Subsurface pressure was obtained at three locations: two components, we rotated the data 34.22.Inthisnew across Cozumel Channel at Calica and Cozumel and one coordinate system the cross-channel component will be

Figure 2. Shipboard ADCP measurements done on the Cozumel Channel during five oceanographic cruises, i.e., CANEK0, CANEK1, CANEK3, CANEK4, and CANEK5. The currents shown are half hourly averages centered at a depth of 50 m. X - 4 CHAVEZ ET AL.: SUBINERTIAL FLOWS AND TRANSPORTS IN COZUME CHANNEL

Table 2. Dates of Beginning and End of Each Cruise and Number specify the momentum balance equation in the following of Full Cross-Channel Shipboard ADCP Sections Done During form: Each Cruise @hui @ðÞhuihui @ðÞhuihvi @ðÞhuihwi 1 @hPi Cruise Start End No. of Crossings þ þ þ f hvi¼ Canek 0 3 Dec 96 21 Dec 96 1 @t @x @y @z ro @x Canek 1 23 May 97 12 Jun 97 5 @hu0u0i @hu0v0i @hu0w0i Canek 3 27 Jan 99 6 Feb 99 1 : ð1Þ Canek 4 25 Aug 99 14 Sep 99 1 @x @y @z Canek 5 16 Jun 00 10 Jul 00 8 where t is time; u, v, and w are the current components along x, y and z coordinates; z is the vertical coordinate considered positive upwards; P is pressure; f is the Coriolis parameter the x component and the along-channel will be the y given by f =2 sinq (with q the typical latitude, i.e., q = 0 3 component. 2031.5 ); =2p/(24 3600 s); and ro = 1028 kg m . [10] A very persistent northeasterly current that presents The triangular parentheses denote the mean or persistent no reversals over the observed period characterizes the flow fraction, and the primes represent the fluctuating part of the in the center of Cozumel Channel. Tidal currents, both field (e.g., u = hui + u0). An ideal averaging operation, diurnal and semidiurnal, are less than 10 cm/s in magnitude, indicated by hi, should fulfill hhuii = hui, for any variable; while subinertial along-channel currents can reach magni- that is, the average of the average remains intact thus tudes close to 200 cm/s. The across-channel subinertial producing hu0i = 0. This implies hhuihvii = huihvi and currents at the center of the channel are about an order of hhuiv0i = huihv0i = 0, although hu0v0i is not necessarily zero, magnitude smaller than the along-channel currents but can precisely when the fluctuations are correlated. The matrix reach magnitudes up to 20 cm/s. Figure 3 shows the along- xx and across-channel subinertial current components observed t txy txz hu0u0ihu0v0ihu0w0i at 30 m depth. tyx tyy tyz ¼r hv0u0ihv0v0ihv0w0i o [11] The vertical profile of the current at the center of the tzx tzy tzz hw0u0ihw0v0ihw0w0i Channel presents a very smooth, persistent, and regular profile, with maximum currents at around 40 meters depth defines the Reynolds stress tensor. Last, any spatial or decaying by about 50% in magnitude at the deepest meas- temporal derivative must be commutative with the aver- ured depth of 250 meters. Figure 4 gives the first mode of aging operation (i.e., @hvi/@x = h@v/@xi). the EOF analysis of the principal axis subinertial current [13] Tomakeestimatesoftermsinequation(1),we profile, which represents 98% of the subinertial current approximate the averaging operation (i.e., the operator hi) mean square value. with a low-pass filter of the hourly data. The filter has a mean power cutoff at a period of 38 hours. Therefore this averaging method only satisfies partially the requirements 3. Geostrophic Balance of the ideal operator. [12] By considering variables as consisting of a mean and [14] For the moment we put aside the terms that present a fluctuating component [Pond and Pickard, 1983], we can horizontal spatial derivatives in equation (1); we deal with

Figure 3. Along- (a) and across-channel (b) current components observed at 30 meters depth in the center of Cozumel Channel. CHAVEZ ET AL.: SUBINERTIAL FLOWS AND TRANSPORTS IN COZUME CHANNEL X - 5

Figure 4. Mode 1 of the Empirical Orthogonal Function (EOF) analysis of the subinertial (periods > 38 hours) principal axis current profile observed at the center of Cozumel Channel. (a) The spatial vertical structure of the current profile for this mode that explains 98% of the variance. (b) The time evolution of this mode. This analysis is done with the mean included in the current series. them later. As for the terms involving vertical spatial redundant. For the estimation of some of the terms in the derivatives, the advective nonlinear term is neglected equation we will use somewhat crude finite differences to because the vertical component of the velocity is very small approximate spatial derivatives. In short, the reduced compared with the horizontal components. The case of the momentum in equation (2) assumes a geostrophic balance turbulent term that remains (the last term of equation (1)) modified by Ekman effects and the local acceleration, thus a requires more consideration. The term @hw0u0i/@z can be simple linear forced system, of which we have measure- approximated using, instead of derivatives, finite differ- ments of all terms. ences and the surface stress: [15] The first task is to compare the velocity term associated to Coriolis and the cross-channel pressure gra- @hu0w0i @txz txz txz txz dient term. The shallowest ADCP measurement available in r ¼ surf deep layers surf ; o @z @z H H the center of the channel is at a depth of 30 m, and it is considered as the surface velocity for the momentum xz xz if tdeep_layers is neglected, where, tsurf is the cross channel balance verification. By fitting a plane surface to the wind stress, and H is the vertical scale of the surface stress observed pressure at the three available locations at every influence. ro is a known constant, unlike H whose exact sample in time, we estimate the pressure gradients, i.e., value is not well determined. H represents the depth of solving the system influence of the surface stress, i.e., the Ekman depth, given 2 30 1 0 1 by H2 =2m/f, where m is a turbulent viscosity coefficient 1 x1 y1 c0 P1 4 5@ A @ A [see, e.g., Cushman-Roisin, 1994]. In most oceanic condi- 1 x2 y2 c1 ¼ P2 : ð3Þ tions, this scale is on the order of tens of meters; here we 1 x3 y3 c2 P3 will consider a constant H of 30 m, an assumed value which, as seen shortly, does not change the results. The where x and y are the location of the pressure (P) xz 2 neglect of tdeep layers , which is proportional to u or u measurements, and c1 and c2 are the cross- and along- depending on the type of parameterization used, is channel gradients, respectively (i.e., c1 = @P/@x and c2 = consistent with having u small throughout the channel and @P/@y). A simpler estimation of the cross-channel gradient necessarily null at the boundaries. Thus the reduced cross- via the difference of the Calica and Cozumel pressure channel momentum equation, without advective terms, is sensors is indistinguishable, within the round off error, from this plane fitting. The difference among these two estimates @u 1 @P 1 @txz fv ¼ þ ; ð2Þ has an RMS 10 orders of magnitude smaller than the RMS @t ro @x ro @z of either one, which is 0.01 Pa/m. Fitting a plane to the pressure field permits us to obtain both components of the where we have dropped, for simplicity, the notation with pressure gradient in one step, although in this study we do brackets (i.e. hi), since for the terms in equation (2) it is not use the @P/@y information. X - 6 CHAVEZ ET AL.: SUBINERTIAL FLOWS AND TRANSPORTS IN COZUME CHANNEL

Figure 5. (a) The across channel pressure gradient divided by fro (thin line) and the along channel current velocity component (thick line). (b) The along channel velocity minus the across channel pressure gradient divided by fro, i.e. the ageostrophic anomaly (dashed trace). Also plotted are, in continuous thin xz line, @u/@t divided by f, and in continuous thick line, tsurf divided by froH, i.e., the other linear terms in the across-channel momentum equation (see equation (2)).

[16] Figure 5 shows the time series of v and (c1/ro f ) has a larger variance than where we can observe that although a geostrophic balance can be appreciated for some periods (i.e. A1 and A2), 1 @P v ; there are others in which large ageostrophic fluctuations f ro @x occur (i.e., B1 and B2). The correlation coefficient between these series is 0.96, 0.10, 0.87, and 0.24 for xz in addition, this remains to be true when either @u/@t or tsurf A1, B1, A2, and B2, respectively. The next task is then to are not included. check if the other terms in equation (2) can explain the [18] The analysis proved that the term @u/@t in the ageostrophic fluctuations. equation has no influence over the balance, neither on the [17] We estimate the local acceleration (first term in complete time series nor on the separate periods (which equation (2)) by a simple forward-finite difference in time. presented a correlation coefficient of 0.94 for a geostrophic To assess the weight of the last term in equation (2), balance and with the addition of the local derivative and the synoptic meteorological data was downloaded from the wind stress term did not improve, but slightly decreased). NCEP/NCAR Global Reanalysis Project web page and local There is also no reduction in the variance of dv by changing winds in Cozumel Island from the NCDC-NOAA web page, the assumed H = 30 m because the correlation between frov the latter to corroborate the former. Comparing the two data xz @P/@x (or frov @P/@x ro@u/@t) and tsurf is too low (see sources, it was noted that the synoptic winds follow the Figure 5b). winds measured at the Cozumel airport very closely and [19] By having justifiably neglected the wind stress and were therefore considered representative of the true wind local acceleration and having verified that the discrepancies variability over the region. The residual defined as occurring during the B periods were not produced by instrumental errors, we now turn our attention to the previously ignored remaining nonlinear terms (terms 2, 3, 1 @P 1 @u 1 txz dv ¼ v þ surf ; 7, and 8 on equation (1)). We will refer to these terms f ro @x f @t f ro H collectively as ‘‘horizontal nonlinear terms’’ since they CHAVEZ ET AL.: SUBINERTIAL FLOWS AND TRANSPORTS IN COZUME CHANNEL X - 7

Figure 6. Qualitative estimation of the nonlinear horizontal terms for the across-channel balance. The plots have different scaling in meters per second. (a) The balance between the cross-channel pressure gradient and the along channel current velocity component. (b–c) The nonturbulent advective terms and (d–e) the Reynolds stresses. involve a horizontal derivative. Because of the lack of an there is no argument to generalize this scaling. These are, adequate instrumental array during the time of measure- therefore, only crude estimates of the order of magnitude of ment, these spatial derivatives cannot be quantified reliably, such terms. i.e., we only have point measurements of the current and [20] The horizontal nonlinear terms estimated with these therefore cannot evaluate its spatial gradients. However, considerations are presented in Figure 6, as they would be considering that the current decreases to zero at the lateral added to the pressure gradient in the geostrophic balance boundaries, a reasonable order of magnitude estimate of the (that is, divided by f ). In Figure 6a, the time series of the across-channel derivatives can be obtained by considering two main components of the balance is presented for Áx = L/2, where L is the channel’s width. To estimate the comparison. It is interesting to observe that the advective order of magnitude of the y derivatives, we consider Áy = terms time series follow a similar behavior with little Áx = L/2. We use, then, the same spatial scaling in the activity during periods A and high activity during the two along-channel as well as in the across-channel directions periods of prominent ageostrophic fluctuations (B). It has to even though only on the latter there are physical conditions be noted that the vertical scales of the plots in Figure 6 are to justify it. Although this procedure could be justifiable not the same for all the terms; the term @(huihvi)/@y is the when considering the particular situation of a traveling only one comparable in magnitude with the ageostrophic circular eddy with a diameter equal to the channels width, fluctuations (Figure 6a). Figure 7 shows the time series of

1 Figure 7. The thick line is the ageostrophic velocity (hvi(ro f ) @hPi/@x), compared with the potentially important advective term @(huihvi)/@y. X - 8 CHAVEZ ET AL.: SUBINERTIAL FLOWS AND TRANSPORTS IN COZUME CHANNEL

Figure 8. Position of the shipboard ADCP profiles used for each section. On the upper part for each section cruise number, consecutive section number, and average date for the crossing are indicated. Each crossing took about an hour. The asterisk shows the location of the moored ADCP. The dots represent 5- min averages of the shipboard measurements. the crude order of magnitude of this term compared with the vertical and 4 km in the horizontal, describes the ‘‘small’’ ageostrophic anomaly (e.g., the ageostrophic velocity). This scale variability and another pair, 400 m and 18 km, comparison shows that the horizontal nonlinear terms are describes the ‘‘large’’ scale, or background, variability. the probable cause of the ageostrophic fluctuations and that Two additional parameters, equal to 0.1 and 0.05, describe the term @(huihvi)/@y is potentially the most important of the noise variance for each scale respectively. them. Notice that these crude estimates do not differentiate [22] Figure 9a presents a very structured velocity field between hvi@hui/@y and @(huihvi)/@y. and an identifiable principal current core (with the highest velocities) close to the surface. However, an EOF analysis of the 16 observed sections (Figure 9b) reveals that the first 4. Transport in Cozumel Channel mode, which contributes with 93.4% of the mean square [21] The transversal velocity structure in the channel was value representing the prevailing current structure in the studied using the shipboard ADCP data collected during channel, has a very regular and smooth structure across the five oceanographic cruises (see Figure 2). There are 16 section. complete sections across the channel. Figure 8 shows the [23] For each section we identified the shipboard ADCP profile positions that build up each of the 16 crossings. The profile closest to the position of the moored ADCP and then dots in each frame of Figure 8 show the mean location of compared at each depth the current measured in that profile the 5-min shipboard ADCP averages which produce one to the cross-channel average current of the section as vertical velocity profile. We then proceeded to interpolate measured by the rest of the profiles of the shipboard ADCP. these profiles to get transversal sections of the current With this procedure we find a weight profile for each velocity (Figure 9a). The asterisk in Figure 8 shows the section that indicates how well a current profile measured position of the moored ADCP whose measurements were at the moored ADCP location represents the average current used in section 3 and which was not measuring simulta- across the whole section. Averaging the 16 weight profiles neously to any of the sections obtained with the shipboard thus obtained an average weight profile is calculated (Figure ADCP. We obtain current contours for the complete section 10). The product of the average weight profile multiplied by (Figure 9a) through an objective interpolation. A six param- the current velocity measured with the moored ADCP and eter objective mapping, as described by Roemmich [1983], the corresponding cross-sectional area at each depth and was used in which one pair of length scales, 100 m in the then adding up over all depth bins produces an estimate of CHAVEZ ET AL.: SUBINERTIAL FLOWS AND TRANSPORTS IN COZUME CHANNEL X - 9

Figure 9. (a) Contours of along-channel current component (in meters per second) of the shipboard ADCP crossings of the channel correspondent to the sections shown in Figure 8. Indicated on the lower left corner of each plot is the instantaneous transport (in Sv) for each section. (b) Empirical Orthogonal Function (EOFs) analysis of the 16 shipboard ADCP sections shown in Figure 9a. Only the first three modes are shown, and the percentage of the variance of each of them is indicated. The three plots on the left represent the spatial weights of the modes, while the three panels on the right represent the temporal weight of each corresponding mode associated with each of the sections used. These EOFs are computed with the mean included in each section analyzed. The number in the lower left of the spatial weight plots are the average transport for the 16 sections associated with each mode. the transport at each time step. In a more primitive way we to include all the available sections in the study area to have could just consider the moored ADCP current profile and an objective extrapolation of the middle channel current multiply it by its respective transversal area at every depth. profile to the whole section. The transport estimation by this These two methods will not be so different as the average method is shown in Figure 11; its difference with the weight profile used is close to one, but we consider it better transport estimate using unitary weights has a 0.07 Sv X - 10 CHAVEZ ET AL.: SUBINERTIAL FLOWS AND TRANSPORTS IN COZUME CHANNEL

son, 1973], but the shortness of the time series makes this hypothesis unreliable. A harmonic analysis of the time series gives an annual signal with amplitude of 1.2 Sv and maximum at the end of May. Notice that the transport variations are of considerable magnitude, from 1.2 Sv up to 7.5 Sv. [24] We compute the time series of the depth at which the velocity coincides with the transport estimate divided by the total transversal area. If such depth does not vary too much, a single current meter at that level gives a direct estimate of the transport. Since in this particular channel there is a high vertical coherence of the currents, many levels are a good choice, the best one being that at which the current has the highest correlation with the transport. The depth that seems the natural choice is where the velocity multiplied by the total area equals the transport, which happens to coincide with the depth levels of higher correlation with the transport. Such time series has an average of 160 m and a standard deviation of 20 m. The use of this level in the moored ADCP produces a transport time series with slightly higher fre- quency fluctuations than the one shown in Figure 11; the difference of both estimates has an RMS of 0.55 Sv. The comparison between the transport estimated using the average weight profile with respect to using the mean cross- sectional area multiplied by the average current between 140 to 180 m gives very similar results; hence the idea to measure between those depths to infer the transport is an effective one (correlation coefficient of 0.93 between the series). The comparison between the transports estimated via the geostrophically deduced or measured near surface current with the more reliable estimation using the weight profile proves the two former estimates to be unreliable approximations for the Channel’s transport (correlation coefficient of 0.22 and 0.75, respectively). The surface currents have less correlation than the intermediate currents with the transport. If transports are to be estimated with Figure 10. Weight profiles for each section, i.e., the ratio currents deduced from the across-channel pressure gradient, between the across-channel average of velocity and the supposing a geostrophic balance, the errors will be gross, velocity measured at the moored ADCP’s location at every especially during periods of ageostrophic behavior as the depth. The wide line is the average weight profile. ones observed, even implying transport reversals at times, something that has not been observed. rms. The mean transport for this period is 5.05 Sverdrups (1 Sv = 106 m3 s1) with a tendency to increase from winter 5. Conclusions to summer. This could be indicative of a seasonal signal, as [25] The momentum balance in the Cozumel Channel is has been found for the Florida Channel [Niiler and Richard- geostrophic during some periods of the measurements, but

Figure 11. Time series of the estimated transport in the Cozumel Channel in Sverdrups (thin line, 1 Sv =106 m3 s1) using the time series of currents from the moored ADCP at the center of the Channel and the average weight profile obtained from the shipboard ADCP channel crossings. The thick line is a seasonal harmonic fit to the estimated transports. CHAVEZ ET AL.: SUBINERTIAL FLOWS AND TRANSPORTS IN COZUME CHANNEL X - 11 other periods exist with high ageostrophic fluctuations. The Candela, J., C. Winant, and A. Ruiz, Tides in the Strait of Gibraltar, local acceleration and the wind stress terms do not contrib- J. Geophys. Res., 95, 7313–7335, 1990. Cushman-Roisin, B., Introduction to Geophysical Fluid Dynamics, 320 pp., ute to account for the ageostrophic variations, even for the Prentice-Hall, Old Tappan, N. J., 1994. periods where a geostrophic balance dominates. By suppos- Feng, M., H. Mitsudera, and Y. Yoshikawa, Structure and variability of the ing a characteristic scaling of Áx = Áy = L/2 (with L =the Kuroshio Current in Tokara Strait, J. Phys. Oceanogr., 30, 2257–2276, 2000. channel’s width), the nonlinear horizontal term potentially Garrett, C., and B. Toulany, Variability of the flow through the Strait of important in the balance to explain the ageostrophic fluctu- Belle Isle, J. Mar. Res., 39, 163–189, 1981. ations is @(huihvi)/@y. This calls for a more realistic deter- Garrett, C., and B. Toulany, Sea level variability due to meteorologically forcing in the Northeast Gulf of St. Lawrence, J. Geophys. Res., 87, mination of velocity derivatives as a step to settle the cause 1968–1978, 1982. of the intense ageostrophic fluctuations. The nonlinear Johns, W. E., T. N. Lee, D. Zhang, R. Zantopp, C. Liu, and Y. Yang, The turbulent terms (Reynolds stresses) show some activity for Kuroshio East of Taiwan: Moored transport observations from the the periods of ageostrophic fluctuations, but their crude WOCE PCM-1 Array, J. Phys. Oceanogr., 31, 1031–1053, 2001. Johns, W. E., T. L. Townsend, D. M. Fratantoni, and W. D. Wilson, On order of magnitude estimate is small. Other specific meas- the Atlantic inflow to the Caribbean Sea, Deep-Sea Res., 49, 211–243, urements are necessary to determine their importance in the 2002. cross-channel balance. Niiler, P. P., and W. S. Richardson, Seasonal variability of the Florida Current, J. Mar. Res., 31, 144–167, 1973. [26] The mean transport estimated between December Ochoa, J., J. Sheinbaum, A. Badan, J. Candela, and W. D. Wilson, Geos- 1996 and May 1997 in the Cozumel Channel is 5 Sv, with trophy via potential vorticity invertion in the Yucatan Channel, J. Mar. an RMS of 1.2 Sv. The optimal depth for the estimation of Res., 59, 725–747, 2001. Pierini, S., and A. Rubino, Modeling the oceanic circulation in the area of the transport using a single current velocity measurement is the Strait of Sicily: The remotely forced dynamics, J. Phys. Oceanogr., between 140 and 180 m. The estimation of the transport 31, 1397–1412, 2001. using the measured surface current or the geostrophic Pond, S., and G. L. Pickard, Introductory Dynamical Oceanography, 329 deduced current is not appropriate. pp., Butterworth-Heinemann, Woburn, Mass., 1983. Roemmich, D., Optimal estimation of hydrographic station data and derived fields, J. Phys. Oceanogr., 13, 1544–1549, 1983. [27] Acknowledgments. We thank all the participants of the Canek Schmitz, W. J., Jr., and M. S. McCartney, On the North Atlantic Circulation, Program of which this is a contribution, in particular our colleagues Rev. Geophys., 31, 29–49, 1993. Antonio Badan, Julio Sheinbaum, and Ignacio Gonza´lez, and the technical Sheinbaum, J., J. Candela, A. Badan, and J. Ochoa, Flow structure and staff Joaquin Garcı´a, Miguel Ojeda, Carlos Flores, Armando Ledo, and transport in Yucatan Channel, Geophys. Res. Lett., 29(3), 1040, Benjamı´n Pe´rez. We also thank the crew of the B/O Justo Sierra and Rich doi:10.1029/2001GL013990, 2002. Limeburner. This study was funded by CICESE and CONACYT and forms Tsimplis, M. N., Tides and sea-level variability at the Strait of Euripus, part of the M.Sc. Thesis of the first author. Estuarine Coastal Shelf Sci., 44, 91–101, 1997.

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