Equatorial Upwelling in the Central Pacific Estimated from Moored

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Equatorial Upwelling in the Central Paci®c Estimated from Moored Velocity Pro®lers

ROBERT H. WEISBERG AND LIN QIAO Department of Marine Science, University of South Florida, St. Petersburg, Florida

(Manuscript received 9 March 1998, in ®nal form 16 February 1999)

ABSTRACT Horizontal divergence and vertical velocity (w) are estimated at 0Њ, 140ЊW using an array of ®ve subsurface moored acoustic Doppler current pro®lers deployed from May 1990 to June 1991 during the Tropical Instability Wave Experiment. The record-length mean ¯ow is divergent within the near-surface region and convergent within the thermocline, with maximum convergence located at the high speed core of the Equatorial Under- current (EUC). This pattern of divergence results in upwelling at and above the EUC core (with maximum value of 2.3 ϫ 10Ϫ5 msϪ1 located at 60-m depth) and downwelling below the core. The relative slopes in the zonal plane between the mean velocity vectors and the isotherms suggest a net diffusive heat ¯ux. Assuming that this occurs vertically, an entrainment velocity parameterization provides an estimate of the ``diapycnal vertical velocity'' pro®le that reverses sign at the EUC core depth. Several kinematical and dynamical consistency checks are developed on both the time-dependent and the mean motions to supplement a discussion of errors for the mean w pro®le. The time-dependent ¯uctuations in w may be an order of magnitude larger than the mean values, and on synoptic timescales w may be directed either up or down over the entire upper 250-m region sampled.

1. Introduction der 1990)], a better quantitative understanding of the Easterly winds acting upon a bounded equatorial fully three-dimensional equatorial ocean circulation is ocean cause the surface to slope so that the resulting necessary for improved climate prediction by coupled pressure gradient force opposes the wind-induced ver- ocean±atmosphere models. tical stress divergence. Due to the planetary ␤ effect, As part of a study on planetary waves seasonally poleward Ekman transports cause the near-surface cur- generated by unstable, near-surface equatorial currents, rents to be divergent (e.g., Cromwell 1953), which is a subsurface array of acoustic Doppler current pro®lers counteracted by a zonal pressure-gradient-induced geo- (ADCP) was deployed about 0Њ, 140ЊW from May 1990 strophic convergence. The ensuing circulation, consist- to June 1991. Data from this Tropical Instability Wave ing of a westward ¯owing South Equatorial Current Experiment (TIWE) are used to estimate the vertical (SEC) at the surface and an eastward ¯owing Equatorial component of velocity (w) through vertical integration Undercurrent (EUC) within the thermocline, is fully of the continuity equation. Such a procedure has been three-dimensional, and these zonally oriented currents used in several previous studies but not with high ver- are linked by the circulation in the meridional plane tical resolution, nor with an array that provides for cen- (e.g., Defant 1981; Fofonoff and Montgomery 1955). ter differencing. Stommel (1960) provided a theory for this linkage, and The paper is organized as follows. Section 2 reviews Knauss (1966) provided observational evidence on how background material on equatorial upwelling and pre- the meridional circulation cell feeds the near-surface vious estimates made with either in situ data or with equatorial upwelling. Such upwelling maintains the sea numerical circulation models. Section 3 presents the surface temperature (SST) gradients of the Tropics that ®eld program, a description of the data, the method of in turn control the air±sea interactions there (Bjerknes w estimation, and an overview of the various error 1966). Since tropical air±sea interactions determine sources. The record-length mean ®ndings are developed global climate variations on interannual timescales [e.g., in section 4. Section 5 then discusses supporting evi- the El NinÄo±Southern Oscillation (ENSO: e.g., Philan- dence in the form of kinematical and dynamical consistency checks drawn from both the time-dependent and the mean motions. Comparisons with previous results are discussed in section 6, along with implications Corresponding author address: Dr. Robert H. Weisberg, Dept. of Marine Science, University of South Florida, St. Petersburg, FL of these ®ndings for SST and other material property 33701. distributions. An appendix provides additional error an- E-mail: [email protected] alyses.

᭧ 2000 American Meteorological Society

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2. Background isopycnals. Maximum upwelling of magnitude 3 ϫ 10Ϫ5 msϪ1 was calculated above the EUC core at the base Poleward Ekman transports driven by easterly winds of the mixed layer. Halpern and Freitag (1987) and Hal- can extend into midlatitudes (e.g., Levitus 1988). As pern et al. (1989) using moored current meter obser- ¯uid moves equatorward geostrophically in compen- vations near 110ЊW, and at different zonal separations sation for this, conservation of potential vorticity re- between 140ЊW and 110ЊW, respectively, obtained re- quires the pycnocline to rise and the density gradient sults similar to Bryden and Brady (1985). Upwelling of across it to increase. Additionally, the zonal slope of magnitude of 2±3 (ϫ10Ϫ5 msϪ1) was found across the the pycnocline supported along the equator by easterly EUC, with maximum values either in or above the EUC wind stress suggests that ¯uid moving eastward within core. Equatorial Atlantic Ocean calculations by Gouriou the EUC rises en route. Equatorial upwelling therefore and Reverdin (1992) combining shipboard hydrography has a well-established, large-scale basis, the most ob- and velocity pro®les also produced results similar to vious manifestation of which is the equatorial cold Bryden and Brady (1985) in both magnitude and vertical tongue. Satellite imagery shows the cold tongue to be distribution. Contrary to Gouriou and Reverdin (1992), tightly con®ned to and symmetric about the equator, Weingartner and Weisberg (1991a) using moored cur- particularly west of 110ЊW in the Paci®c Ocean (Reyn- rent meters found a reversal from upwelling within and olds and Smith 1994). Despite this, and other measur- above the EUC core (maximum at the base of the mixed able effects of upwelling on material properties within layer) to downwelling over the lower portion of the the equatorial region, the smallness of w makes direct EUC. All of the time series studies using moored current measurements of it dif®cult. Equatorial upwelling has meters share a common ®nding that w is highly time been estimated indirectly by diagnostic calculations us- dependent. Other estimates of w are also available by ing linear dynamics, vertical integration of the conti- considerations of large-scale mass balances (e.g., Wyrtki nuity equation, or through the application of primitive 1981; Roemmich 1983; Wunsch 1984a; Johnson and equation, global circulation models. Luther 1994), tracer distributions (e.g., Broecker et al. Before reviewing previous w estimations an orien- 1978; Quay 1983; Fine et al. 1983; Wunsch 1984b), tation to the regional hydrography is useful. Repeated isotherm depth variations (e.g., Wyrtki and Eldin 1982), meridional sections in the central Paci®c between 17ЊS and by the estimates of horizontal divergence from sur- and 20ЊN from the Hawaii to Tahiti Shuttle program face drifters (e.g., Hansen and Paul 1984, 1987; Poulain (Wyrtki and Kilonsky 1984) show average distributions 1993). The existence of equatorial upwelling (after av- of the zonal component of velocity, temperature, salin- eraging out synoptic and equatorial wave adjustment ity, oxygen, nitrate, phosphate, and silicate. Common process variability) is unequivocal. At issue, however, to all of these dynamically active or passive tracers is is the vertical distribution of w, especially downwelling a rising of isopleths toward the equator within the region below the EUC core and how this bears upon material of the thermocline. Within a few degrees of the equator property and momentum balances. Numerical model es- and coincident with the EUC that is positioned within timates are of little help in clarifying this issue since the thermocline is an upward (downward) bowing of the structure of the fully three-dimensional circulation material property isopleths above (below) the EUC core. is dependent upon turbulence parameterization. The The dynamically passive tracers bow downward much same discrepancies found in the data analyses to date more steeply than the dynamically active ones in the also exist in the numerical models, for example, com- thermostad region beneath the EUC, suggestive of large pare Philander et al. (1987) or Harrison (1996) with vertical mixing there. Knauss (1966) from a similar (but Seager and Murtugudde (1997). less comprehensively sampled) suite of hydrographic measurement surmised that downwelling and mixing occurs below the EUC core, as contrasted with upwelling 3. Field program and methods and mixing above the core. a. The TIWE equatorial array Common to most near-equator estimates of w is a magnitude of a few meters per day and an upwelling The TIWE equatorial array (Fig. 1) consisted of ®ve maximum situated between the EUC core and the sur- subsurface moorings (designated TIW1±TIW5), each face. The vertical distribution of w and its meridional with an RD Instruments, Inc., 150-kHz ADCP and a extent, however, vary largely with estimation technique. Sea-Bird Electronics, Inc., SEACAT conductivity, tem- In a diagnostic study using historical hydrographic data perature, and depth recorder. Mooring locations, record for a box bounded by 5ЊN and 5ЊS, 150ЊW and 110ЊW lengths, and nominal instrument depths are given in between 500 db and the surface, Bryden and Brady Table 1. The ADCPs with 20Њ transducer con®guration (1985) used geostrophy and an assumed Ekman trans- yielded hourly velocity pro®les at nominal 8.67-m in- port distribution to estimate a w pro®le on the equator. tervals, roughly between 250 m and the surface. After Upwelling was found across the entire EUC above applying sound speed corrections and editing for surface 180-m depth, with smaller downwelling below. The ¯ow affects, these velocity pro®les were resampled at 10-m within the EUC was described as being primarily along intervals between 250 m and 30 m by linear interpo-

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FIG. 1. The TIWE equatorial array in relationship to the tropical Paci®c Ocean's climatological SST distribution for September (climatology courtesy of M. McCarty and M. McPhaden, NOAA/PMEL). lation. The 30-m bin was the closest one to the surface b. The horizontal velocity measurements found to be unbiased by surface re¯ection. Velocity estimates above 30 m were made by linearly extrapolating The evolution of the three-dimensional velocity vec- the shear observed between 40 m and 30 m to the sur- tor at the center of the TIWE array may be described face. Comparing the 20-m (nominally biased) sample in the context of an annual cycle. Upper-ocean vari- with the linear extrapolation generally showed good ability at this central Paci®c 0Њ, 140ЊW site is subject agreement. Further information on the mooring's per- to both western and eastern Paci®c in¯uences. The an- formance (all were stable with rms vertical excursions nual march of the ITCZ over the eastern side of the of only a few meters) and data editing procedures are basin (e.g., Mitchell and Wallace 1992) results in max- reported in Weisberg et al. (1991). Since this paper fo- imum (minimum) trade winds over the cold tongue re- cuses on mean ®elds and the low-frequency variations, gion in late boreal summer to fall (late boreal winter to all of the time series presented are low-pass ®ltered with spring). This causes the surface westward ¯owing SEC a cutoff periodicity of 10 days using a truncated Fourier and the subsurface eastward ¯owing EUC to vary such transform. that westward (eastward) currents tend to be maximum when the southeast trades are strongest (weakest). For the period of the TIWE observations, local wind mea- TABLE 1. TIWE equatorial array mooring positions and nominal instrument depths. surements from the TAO array (Fig. 5) show minimum easterlies during June and July 1990, relatively strong Instrument depth easterlies from August 1990 to February 1991, and rel- Mooring name Position (lat/long) (m) atively weak easterlies again during May and June 1991. TIW1 0Њ01.4ЈN 273.6 Along with the annual cycle of the trade winds at 0Њ, 141Њ50.6ЈW 140ЊW the ocean response there is also affected by the TIW2 0Њ57.8ЈS 280.5 integrated effects of the winds to both the east and the 139Њ57.5ЈW west (e.g., Yang et al. 1997). For instance, annual var- TIW3 0Њ02.4ЈN 281.5 iability at 0Њ, 140ЊW originating from the western Paci®c 137Њ57.7ЈW warm pool region includes reversing zonal current puls- TIW4 0Њ03.2ЈS 276.5 es forced by westerly wind bursts that generally occur 140Њ08.4ЈW in boreal winter west of the date line (e.g., Lau and TIW5 1Њ01.5ЈN 266.4 Chan 1985). The ocean's response to these wind bursts 139Њ57.4ЈW propagates eastward in the form of equatorial Kelvin

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FIG.2.Theu and ␷ (lower panel) components as functions of time and depth at 0Њ, 140ЊW. The data are low-pass ®ltered to remove oscillations at timescales shorter than 10 days, and the isotach contour interval is 0.2 m sϪ1. For the upper panel light stippling denotes the westward ¯owing SEC and dark stippling denotes eastward ¯ow within the EUC in excess of 0.8msϪ1. For the lower panel, stippling denotes northward ¯ow. waves (Knox and Halpern 1982). More complete de- denoted by dark stippling in Fig. 2, has zonal speeds scriptions of the ocean's annual cycle in the central from 0.8 to 1.6 m sϪ1, and it is positioned within the equatorial Paci®c may be found in Philander et al. thermocline (Fig. 5). For the ␷ component, stippling (1987) and McPhaden and Taft (1988). Halpern and denotes northward ¯owing water. The instability waves Weisberg (1989) draw comparisons between this region are recognized as the large, regularly occurring, near- and the central equatorial Atlantic, and Kessler et al. surface con®ned oscillations that appear most promi- (1995) discusses more recent observations of equatorial nently from August through December 1990. Kelvin waves. The u-component isotachs are representative of the The zonal (u) and meridional (␷) components of ve- zonally oriented equatorial currents. Speci®cally, there locity measured at the TIW4 mooring near 0Њ, 140ЊW is a highly variable, near-surface con®ned SEC over- are shown in Fig. 2, with isotachs contoured as a func- riding the EUC. Of the three latitudes sampled the EUC tion of time (May 1990±June 1991) and depth (the upper is maximum on and nearly symmetric about the equator, 250 m of the water column). For the u component, the while the SEC is maximum to the north of the equator lightly stippled region near the surface denotes the west- (as shown for the record-length mean pro®les in Fig. ward ¯owing SEC that is observed to be intermittent, 3). The primary variations in the EUC appear to be both extending down to 60-m depth. Elsewhere the ¯ow is annual and intraseasonal. Three periods of maximum -z ϭ 0) region, EUC transport are observed: July±August 1990, Deץ/uץ eastward. The EUC core (de®ned by

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FIG. 3. Record-length mean pro®les for the u and ␷ components at the ®ve mooring locations. The solid lines denote the three equator moorings (the thick one being 140ЊW) and the dashed (dotted) lines denote the moorings north (south) of the equator. cember 1990, and April±June 1991. During the summer are given by Qiao and Weisberg (1995) and Qiao and and spring periods the EUC is shallow, as contrasted to Weisberg (1998), respectively. the winter period when it is deeper. The shallow summer and spring maxima coincide with the annual cycle of c. Vertical velocity component estimation the southeast trade winds. These winds relax over the eastern half of the equatorial Paci®c in boreal spring, The smallness of w obviates its direct measurement for example, see Meyers (1979) and Yang et al. (1997), by the TIWE moored ADCPs. It is therefore estimated causing a concomitant eastward acceleration of the near- from the continuity equation: surface currents by the eastward-directed zonal pressure (z, (1ץ/wץy ϭϪץ/␷ץx ϩץ/uץ gradient force. The wintertime maximum occurs in response to westerly winds over the western equatorial where x, y, and z are positive to the east, north, and up, Paci®c. The SEC is most developed from August to respectively. Center differences are used for the hori- December 1990, in between the ®rst two EUC maxima, zontal divergence, which is then integrated downward and again from February to April 1991, in between the by a trapezoidal scheme in 10-m increments from an second two EUC maxima. Other than these two periods, assumed rigid-lid surface to get w. For synoptic and the SEC, as sampled by the TIWE equatorial array, is longer timescales the approximation that w ϭ 0atz ϭ relatively weak, and westward ¯ow is absent on the 0 is correct by a factor of 10Ϫ2 relative to w thus esti- equator from April to June 1991. mated. Excepting the instability wave oscillations, the ␷ com- The evolution of the terms in the the continuity equa- y (the meridionalץ/␷ץ ,(x (the zonal divergenceץ/uץ :ponent is generally much smaller than u, this anisotropy tion z (the horizontal divergence) isץ/wץbeing a consequence of vanishing Coriolis parameter on divergence), and Ϫ the equator. In 1990, the instability wave season lasted shown in Fig. 4, where stippled regions denote diver- from August to December. It started with the westward gence and clear regions denote convergence. The zonal acceleration of the SEC and ended with a wintertime divergence shows regular reversals near the surface dur- Kelvin wave pulse whose leading edge eastward accel- ing the instability wave season, and there is a general eration temporarily halted the SEC. The largest ampli- tendency for zonally divergent (convergent) ¯ow above tudes for the instability wave's velocity oscillations oc- (below) the EUC core. In contrast with this, the merid- curred within the westward ¯owing SEC. These am- ional divergence shows a general tendency for divergent plitudes decreased rapidly within the thermocline to rel- ¯ow near the surface and convergent ¯ow within the atively small values at and below the EUC core. The EUC. Summing these two components together to get ␷-component oscillations were also largest on the equa- the total horizontal divergence shows a tendency for tor, but they penetrated deeper with the SEC north of divergent ¯ow near the surface and convergent ¯ow at the equator. Descriptions of the instability wave's ki- depth. These tendencies are clearer upon record-length nematics and energetics from the TIWE equatorial array averaging as developed in section 4.

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FIG. 4. From top to bottom: the zonal, meridional, and vertical divergences estimated by ®nite differences at 0Њ, 140ЊW. Stippled regions denote divergence, clear regions denote convergence, and all time series are low-pass ®ltered to remove oscillations at timescales shorter than 10 days.

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Vertically integrating the horizontal divergence re- es. This problem manifests as ®nite differencing errors, sults in the w estimate as shown in Fig. 5, along with so the fundamental question is whether or not the array the surface zonal wind stress and the isotherm depths adequately resolves the principal physical processes that sampled at an adjacent TAO mooring. With the EUC give rise to divergence. The processes of primary in- core depth denoted by a bold line superimposed upon terest herein are the slowly varying seasonal circulation the isotherms, Fig. 5 shows that upwelling or down- and the instability waves. The array design was based welling may occur over the entire sampled water column upon previously estimated spatial scales for the insta- (with speeds of order 10Ϫ4 msϪ1 despite the tendency bility waves, and Qiao and Weisberg (1995) show that for upwelling (downwelling) to occur above (below) the the array did resolve these features. The spatial scales EUC core. The latter feature is evident in Fig. 6 upon for the slowly varying circulation are also resolved by record-length averaging, where the relationship between the array. Estimated by either inertial or linear equatorial u, ␷, and w is shown. On average, w is related to u, wave arguments, the meridional scales of the circulation with upwelling observed in and above the EUC core are (U/␤)1/2 or (C/␤)1/2, respectively, where U is the and downwelling observed below. This ®nding is con- EUC core speed and C is the equatorial wave speed. sistent with water converging onto the equator within Thus, if the horizontal velocity components vary the thermocline. Upon reaching the equator these con- smoothly across the array (as shown for the record- vergent waters ascend (descend) above (below) the ther- length mean ͗u͘ and ͗␷͘ in Fig. 4) and the derivatives mocline with the EUC within the thermocline being a are continuous across the equator, then the ®nite-dif- dynamical consequence of this convergent ¯ow. ferencing errors, while not quanti®able, should not be overwhelming either. In particular, the ®nite differenc- x due to the meridional structure ofץ/u͗͘ץ d. Estimation errors ing errors in ͗u͘ are shown to be small in the appendix. By virtue of Estimation errors for w derive in four general cate- a centered difference array, ®nite-differencing bias er- gories: random and systematic instrument errors and rors due to wave propagation are avoided, as was in- random and systematic geophysical sampling errors. vestigated using all possible differencing schemes avail- These are discussed below in ascending order of im- able from the array. Supporting kinematical and dynam- portance. ical arguments toward justifying these assertions are de- The random instrument errors are associated with the veloped in sections 4 and 5. ADCP's velocity calculation, which uses Doppler-shift- Systematic instrument errors, assuming correct beam ed frequencies from range-gated, re¯ected sound returns geometry (incorrect geometry would translate into ran- that are sampled at the source transducer. Standard de- dom errors since the instruments are free to rotate with viations determined by the manufacturer are a function of the sound returns per sampling interval (the ping rate) the mooring), are those related to compass calibration. and the water volume sampled by each ping (the range The manufacturer speci®es a Ϯ2Њ accuracy in the in- gating). For the setup parameters employed, the standard strument's compass. Spinning the compass shows that deviation for each hourly sample is 0.012 m sϪ1. With this error is generally inhomogeneous with respect to all subsequent calculations being linear and with each coordinate direction. This inhomogeneity is actually sample independent, the standard deviation for the ran- good since mooring motion then tends to randomize the dom instrument errors decreases with the square root of resulting error. The TIWE instrument compasses were the number of samples averaged. For the low-frequency checked to be within the manufacturer's speci®cations and record-length mean estimates presented, the random without constant offsets. Nevertheless, this is potentially instrument errors and their effect upon w are therefore the most serious source of error since, in view of large negligible. EUC speeds, a constant compass offset could largely Random geophysical errors are more problematic, but bias the horizontal divergence by rotating the u com- nevertheless quanti®able. They follow from the time ponent onto the ␷ component. The appendix considers series variances due to the sampled geophysical pro- this effect by assuming constant and oppositely directed cesses, the effective bandwidth of these processes and 2Њ compass errors at the off-equator, TIW2 and TIW5 hence the number of degrees of freedom, and the array locations (effectively a 4Њ compass error), and calcu- geometry as applied to the vertically integrated diver- lating what the vertically integrated effect of such er- gence calculation. These factors are developed in the roneously large geostrophic convergence would be on appendix where the standard deviations for the record- the estimated downwelling below the EUC. The effect length mean quantities, ͗u͘, ͗␷͘, ͗w͘, and their deriva- is the same order of magnitude as that estimated and it tives, as presented in section 4, are calculated. With would account for about two-thirds of the value given regard to these random geophysical errors the ®ndings (larger or smaller depending upon whether the compass presented herein are all well de®ned. errors point toward or away from the equator). On the Systematic geophysical sampling errors are less quan- other hand, if this were true, then dynamical inconsis- ti®able. They result from discrete sampling (in this case tencies (which are not observed) would occur as dis- spatial) limitations for continuous geophysical process- cussed in section 5.

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FIG. 5. The estimated w (middle panel) as a function of time and depth at 0Њ, 140ЊW. The contour interval is 5 ϫ 10Ϫ5 msϪ1 and stippled (clear) regions denoting upwelling (downwelling). The bottom panel shows the isotherm depths as a function of time from the adjacent TAO mooring, with the EUC core depth indicated by a bold line and the region of westward ¯ow near the surface indicated by stippling. The top panel is the zonal component of wind stress from the adjacent TAO mooring.

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cy, geostrophic limit, if the zonal pressure gradient (ZPG) is continuous across the equator, then ␷ ϭ 0on the equator by virtue of the Coriolis parameter changing sign across the equator). Within the near-surface region, a small but nonzero (in excess of one standard deviation of the mean) ͗␷͘ may be attributed to ageostrophic wind effects consistent with a southward Sverdrup transport by negative wind stress curl over the eastern half of the basin. Below the near-surface region, ͗␷͘ is zero within one standard deviation of the mean. The u component on the equator shows a westward ¯owing SEC con®ned to the upper 25 m. The mean position of the EUC core is at 110-m depth (Ϯ about 10 m to within one standard deviation of the mean) with a maximum speed of about 1.1msϪ1 (Ϯ about 0.1 m sϪ1 to within one standard deviation of the mean). For both ͗u͘ and ͗␷͘ the standard deviations are largest above the EUC core. The w component shows maximum upwelling at 60 m (corresponding to the base of the mixed layer as evidenced in Figs. 5 or 10) of magnitude 2.3 ϫ 10Ϫ5 msϪ1 (Ϯ about 0.4 ϫ 10Ϫ5 msϪ1 to within one standard deviation of the mean) and a zero crossing at 140 m (Ϯ about 10 m to FIG. 6. Record-length mean pro®les for u (solid line), ␷ (dashed within one standard deviation of the mean) just below line), and w (bold line). Note the change in scale (shown at the bottom) the EUC core. While the standard deviation of w is large, for w. Maximum upwelling of 2.3 ϫ 10Ϫ5 msϪ1 occurs above the the standard deviation of ͗w͘ (a measure of geophysical EUC core. random error) is small due to the large n in the mean value estimation. As a consequence, both the magnitude 4. Description of the mean velocity vector of ͗w͘ and the depths of maximum value and zero crossing are well de®ned with respect to random geophysical The velocity components averaged over the May error. Other errors, of course, may be larger. In sum- 1990±June 1991 record length are again shown in Fig. mary, the vertical velocity component, on average, at 7, with the solid, dotted, and dashed lines denoting the this central equatorial Paci®c location appears to be means (͗␷ i͘), the means Ϯ one standard deviation of the maximum at the base of the mixed layer with upwelling 2 1/2 time series (͗͘␷ i ) , and the means Ϯ one standard de- above the EUC core and downwelling (comparable in 2 1/2 viation of the means (͗͘␷ i /n) , respectively, where the magnitude to the upwelling) beginning below the EUC number of degrees of freedom, n, are determined by core. Such large downwelling within the lower portion integral timescale (see appendix). The equatorial cur- of the EUC is in contrast with several previous estimates rent's anisotropy is clearly evident (in the low-frequen- reviewed in section 2.

FIG. 7. Record-length mean pro®les for u, ␷, and w (solid lines), Ϯ the standard deviations of the time series from which they derive (dotted lines), and Ϯ the standard deviations of the means (dashed lines).

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-x is calculated, and the mean ␷ץ/u͗͘ץ FIG. 8. The mean u-component pro®les from which .y is calculatedץ/␷͗͘ץ component pro®les from which z as a residual (although aboveץ/w͗͘ץ y, leavingץ/␷͗͘ץ -With w estimated via vertical integration of the con tinuity equation, the contribution by the zonal and me- 40 m and below 140 m they are additive). A potential ridional portions of the horizontal divergence is of infor ®nite differencing error derives from the meridional x is similarlyץ/u͗͘ץ terest. Figure 8 shows ͗u͘ and ͗␷͘ as a function of depth structure of ͗u͘ as seen in Fig 3. If at the along-equator and the off-equator locations from distributed, then it might be appropriate to scale the z byץ/w͗͘ץ x in the estimate of theץ/u͗͘ץ y at magnitude ofץ/␷͗͘ץ x andץ/u͗͘ץ which the center differences for 0Њ, 140ЊW are calculated. For ͗u͘ it is noted that the a factor of about 0.8. Doing this does not materially EUC accelerates (decelerates) downstream above (be- alter our ®ndings, however, as shown in the appendix x is of lesser importance thanץ/u͗͘ץ low) 140 m, which coincides with the position at which (Fig. A1), since y, so decreasing it by a small amount is of littleץ/␷͗͘ץ w͘ϭ0. For ͗␷͘ it is noted that meridionally divergent͗ xץ/u͗͘ץ ow occurs near the surface, whereas meridionally con- consequence. Also, with the vertical average of¯ vergent ¯ow occurs within the region of the EUC, with being divergent, a lessening of its effect tends to in- maximum convergence occurring at the EUC core crease the magnitude of the downwelling below the depth. It is further noted that both the ¯ows away from EUC core, as opposed to decreasing it. For consistency the equator near the surface and toward the equator with previous work we retain the unscaled formulations within the EUC are larger south of the equator than of Fig. 9. Note that the slopes of the divergence terms north of the equator. This small asymmetry is consistent are all fairly constant above 60 m, suggesting that the with the zonal wind being larger on average south of extrapolation procedure for the horizontal velocity com- the equator, producing asymmetries in the poleward Ek- ponents at 20 m and above is not adversely in¯uencing man and equatorward geostrophic transports. This is the divergence calculation. The Fig. 9 vertical pro®les also consistent with the fact that the relatively high sa- are also smooth suggesting that the divergences, com- linity within the EUC is of Southern Hemisphere origin. puted independently at each 10-m interval, provide a Referring back to Fig. 3, however, it is evident that the consistent calculation of divergence within the standard meridional divergence (near the surface) and conver- errors of the mean value estimates. If the data them- gence (near the EUC core) are still centered on the selves were ``noisy'' due to random instrument errors, equator, on average. such smooth pro®les from independently sampled lo- While both components of divergences are important, cations would not have been obtained. Last, along with the primary contributor to the horizontal divergence is the meridional convergence being maximum at the EUC the meridional divergence. Figure 9 shows the vertical core, it tends toward zero at the base of the EUC where y, and the negative of the ZPG is small [Qiao and Weisberg (1997) suggestץ/␷͗͘ץ ,xץ/u͗͘ץ distributions for x to oppose that the ZPG is zero there to within the reference levelץ/u͗͘ץ z. The tendency is forץ/w͗͘ץ ,their sum

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FIG. 9. The record-length mean zonal, meridional, and vertical divergence pro®les (solid lines), Ϯ the standard deviations of the time series from which they derive (dotted lines), and Ϯ the standard deviations for the respective means (dashed lines). error of about 0.2 ϫ 10Ϫ4 NmϪ3]. Dynamical consis- Fig. 10 shows the vertical distribution in the equatorial tency is therefore achieved by the horizontal divergence zonal plane of the mean velocity vectors superimposed estimation. upon the mean isotherm slopes. With ͗␷͘ϭ0 on the In summary, both the zonal and the meridional di- equator, the degree of collinearity determines the ad- vergences contribute to the total mean horizontal di- vective temperature ¯ux balance. The 21ЊC isotherm is vergence. The zonal ¯ow is divergent (convergent) at the approximate point at which the isotherm and the and above (below) the EUC core where the EUC ac- velocity vector are collinear. Above (below) 21ЊC the celerates (decelerates) downstream. The meridional ¯ow velocity vectors are directed up (down) relative to the is divergent within the near-surface region in accordance isotherms, implying a reversal in sign of the net ad- with poleward Ekman transport by a mean easterly wind vective temperature ¯ux imbalance. The individual con- z (which tend toץ/T͗͘ץx and ͗w͘ץ/T͗͘ץstress and convergent within the EUC in accordance tributions of ͗u͘ with a geostrophic transport by an eastward directed cancel within and above the EUC core) and their sum ZPG force. The depth at which the geostrophic con- are shown in Fig. 11. The resulting advective temper- vergence exceeds the Ekman divergence is approxi- ature ¯ux imbalance is relatively small, positive, and mately 50 m. While the meridional convergence ap- nearly uniform above the EUC core. It is both larger proaches zero at about 220 m, the zonal convergence and negative below the EUC core. This imbalance re- remains nonzero due to the downstream deceleration of quires a turbulent heat transport that may be parame- the EUC. Consequently, the ¯ow ®eld remains hori- terized by an entrainment (or diapycnal) velocity: zontally convergent down to the 250-m limit of our (z. (2ץ/T͗͘ץ/[zץ/T͗͘ץx ϩ͗w͘ץ/T͗͘ץw ͘ϭ[͗u͗͘ sampling, and for this reason the estimated downwelling e magnitude continues to increase over the sampled do- A comparison between the estimated ͗we͘ and ͗w͘ is main. Omiting or scaling down the zonal portion of the given in Fig. 12. Assuming that the entire advective divergence would increase the magnitude of the down- temperature imbalance may be attributed to vertical welling found below the EUC core. eddy diffusion, the results suggest an upward (down- The literature provides discussions on vertical veloc- ward) turbulent heat ¯ux above (below) the EUC core ity in terms of isopycnal and diapycnal portions (e.g., and a diapycnal vertical velocity with magnitude com- Gouriou and Reverdin 1992). The diapycnal portion parable to that of the kinematical vertical velocity. Of arises as an advective imbalance in a material property's course these ®ndings must be tempered by the fact that total derivative. If such imbalance exists, then the ma- the velocity and the isotherm slopes were sampled over terial property must either change locally or diffuse. different scales. While the TIWE array did not include concomitant temperature measurements, the TAO array did provide tem- 5. Supporting analyses perature data on scales suf®cient for estimating a mean gradient. An advective temperature ¯ux imbalance, and Given an encouraging but inherently inconclusive er- consequently a vertical distribution of implied turbulent ror analysis, it is important to marshal ancillary infor- heat transport, may therefore be estimated for the rec- mation relative to the ®ndings presented. Such evidence ord-length mean. Using ͗u͘ and ͗w͘ from Fig. 7 and is drawn from both the time-dependent and the mean TAO temperature data from 0Њ, 170ЊW and 0Њ, 125ЊW motions. For the time-dependent motions the following

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FIG. 11. Vertical pro®le of the record-length mean advective temperature ¯ux imbalance (solid line) along with the individual con- z dottedץ/T͗͘ץx (dashed line) and ͗w͘ץ/T͗͘ץtributions made by ͗u͘ line).

cel the other with opposite sign. Inspection of Fig. 4 shows this to be the case within the surface layer during ,x is convergentץ/uץ the instability wave season. When .y is divergent and converselyץ/␷ץ

b. Velocity ®eld kinematics FIG. 10. Record-length mean velocity vectors superimposed upon Because of the ␤ effect, a near-surface water parcel mean isotherm slopes in the equatorial zonal plane at 0Њ, 140ЊW, where the isotherm slopes are from TAO array data at 0Њ, 170ЊW and transiting poleward from the equator is expected to sink 0Њ, 125ЊW. Velocity (and isotherm slope) scale is shown at the top. as vortex ®laments stretch. This behavior is observed in Fig. 13, wherein the ␷ component at 30-m depth on the equator during the instability wave season is su- -x perimposed upon the w component at 60-m depth esץ/uץ factors are examined: (a) the covariability between y; (b) the velocity ®eld kinematics; speci®cally, timated between the equator and 1ЊN (using a forwardץ/␷ץ and .(xץ/uץ y and a centered difference forץ/␷ץ the relationship between ␷ on the equator and w to the difference for north and south of the equator; (c) the vorticity balance The two time series covary out of phase, showing that on the equator, both near the surface and at the EUC when ␷ is northward, w is downward, and conversely. core; and (d) the relationship between w, the thermocline The 60-m depth is chosen since that is where w tends variations, and the local wind stress variations. For the to be a maximum on average. During the instability mean motions, the dynamical balances within the EUC wave season the time-dependent upwelling reaches are considered. These are developed individually below. speeds of 20 m dayϪ1, which is an order of magnitude larger than the average w on the equator. These mag- nitudes are consistent with the numerical model results yץ/␷ץ x andץ/uץ a. The covariability between of Harrison (1996). A corollary to this ®nding is that Ocean planetary waves, such as the instability waves, w south of the equator should covary opposite to w north should be only weakly divergent. What horizontal di- of the equator. This antisymmetric behavior is generally vergence exists should therefore be the residual between con®rmed upon comparing w as a function of time and y, each tending to can- depth at 0.5ЊN and 0.5ЊS in Fig. 14 (where forward andץ/␷ץ x andץ/uץ similar magnitude

Unauthenticated | Downloaded 10/01/21 09:37 AM UTC JANUARY 2000 WEISBERG AND QIAO 117 y and a centeredץ/␷ץ backward differences are used for x). During the instabilityץ/uץ difference is retained for wave season, particularly August to December, very regular, well-de®ned features appear at 0.5ЊN versus less well-de®ned features at 0.5ЊS. This observation matches the meridional inhomogeneity found for the instability waves in the numerical model simulation of Philander et al. (1986). Thus, for the instability waves a kinematical consistency occurs between water parcels crossing the equator and the w component estimated to the north and south of the equator, and both the magnitude and the breakdown in symmetry agrees with numerical model results. Symmetry properties at other timescales also apply. Equatorial wave theory (Matsuno 1966) includes wave modes for which ␷ is zero on the equator and w is in phase across the equator. Spectral analysis (not shown) identi®es another band of coherent vertical motions centered upon a 167-h periodicity that are in phase across the equator consistent with ®rst meridional mode inertial±gravity waves.

c. The vorticity balance on the equator The linearized vorticity balance on the equator de- FIG. 12. The record-length mean pro®le of ͗w͘ (solid line) in com- pends upon the ␤ effect and the time-averaged curvature parison with the ``diapycnal'' or entrainment velocity ͗we͘ pro®le of the ambient ¯ow ®eld. Near the surface, the transient (dotted line) derived from the advective temperature ¯ux imbalance nature of the SEC and its meridional structure are such and the mean vertical temperature gradient. Note that ͗we͘ is the difference between the estimated ͗w͘ and that required for ¯ow along that the mean curvature is zero. The linearized vorticity isotherms. balance near the surface is thus (t ϩ ␤␷ ϭ 0, (3ץ/␰ץ y is the relative vorticity. Figureץ/uץx Ϫץ/␷ץwhere ␰ ϭ 15 shows the coherence squared, phase, and transfer

FIG. 13. The ␷ component on the equator at 30-m depth (solid line) superimposed upon the w component estimated at 0.5ЊN at 60-m depth (dashed line) during the instability wave season.

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FIG. 14. Estimates of w as a function of time and depth at 0.5ЊN lower panel and 0.5ЊS (upper panel) along 140ЊW .x). Stippling denotes upwellingץ/uץ y and a centered difference forץ/␷ץ using forward and backward differences for) function amplitude at 30-m depth (left panels) between be taken into account. Thus, at the EUC core depth, -y 2 is large year-round, the linearized vorץ/2U ץ t (estimated by centered differences as in the whereץ/␰ץϪ1␤ divergence calculations) and ␷ on the equator. Within ticity balance is the instability wave band centered about 500-h periodicity, the coherence is high, the time series are out of (y 2)␷ ϭ 0. (4ץ/2Uץt ϩ (␤ Ϫץ/␰ץ phase, and the transfer function amplitude is close to 1.0. This agreement between theory and observations for the conservation of absolute vorticity using a ®nite- Figure 15 also shows the coherence squared, phase, and t and ␷ atץ/␰ץdifference-derived ␰ suggests that the ®nite differencing transfer function amplitude between ␤Ϫ1 errors are not overwhelming. Since the errors involved the EUC core depth (right panels). If the hypothesis is in the calculation of ␰ and w are similar, this linearized correct then these results should differ from those at vorticity balance provides implicit support for the w 30-m depth in the transfer function amplitude by a factor y 2 calculatedץ/2U ץ y2)] ϭ 0.34 (withץ/2U ץ) estimation. of ␤/[␤ Ϫ The linearized vorticity balance also holds at other by center difference between 1ЊN and 1ЊS). This value depths. As the mean curvature of the background cur- agrees with the transfer function amplitude found at the rents approaches ␤ in magnitude, curvature must also center of the instability wave band.

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t)/␤ andץ/␰ץ) FIG. 15. The coherence squared, phase, and transfer function amplitude between ␷ on the equator at depths of 30 m (left panels) and 120 m (right panels). The bandwidth for the calculation is 0.0009 cph resulting in about 17 degrees of freedom, and the associated 90% signi®cance level on coherence squared as given by the horizontal line. d. The estimated w relative to the thermocline and ward the later part of the record when the zonal winds the local wind stress variations are relatively weak and w is primarily downwelling. The ¯uctuations in w have many sources, some local and some far ®eld, as manifest through wave propa- e. Velocity ®eld kinematics in relation to the zonal gation. Along with the agreements found for the insta- momentum balance on the equator bility waves, qualitative agreements also exist between The fundamental theory for the existence of the equa- the estimated w and the longer timescale variations in torial undercurrent (e.g., Fofonoff and Montgomery the thermocline. For example, the three major zonal 1955) suggests that the meridional convergence of water current pulses in Fig. 5: July 1990, December 1990, and should be a maximum at the EUC core depth. If the April 1991 all have downwelling associated with them EUC is accelerating and rising downstream with the y shouldץ/␷ץ x andץ/uץ ,and an attendant increase in thermocline depth. The es- thermocline then, on average timated w is largest when the local zonal winds are have the vertical distributions observed in Fig. 9. The largest, and SST increases to its seasonal maximum to- sense of the meridional circulation and the vertical dis-

Unauthenticated | Downloaded 10/01/21 09:37 AM UTC 120 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30 tribution and magnitude of the mean w above the EUC depth. Integrating vertically over this region and mul- core agrees with the shipboard measurement-derived re- tiplying by ␳Cp results in a net upward entrainment of sults of Knauss (1966). It is dif®cult to quantify what relatively cold water from between the EUC core and the meridional divergence should be at the surface on the surface amounting to about 80 W mϪ2. This matches the equator since that would require knowledge of the the annually averaged net surface heating in the vicinity vertical distribution of the Ekman divergence there. The of 0Њ, 140ЊW to within the uncertainty given by the values obtained are nevertheless in agreement with those various surface ¯ux estimates for the cold tongue region of Hansen and Paul (1987), or Poulain (1993), from (e.g., Hastenrath and Lamb 1978; Esbensen and Kushnir surface drifters when calculated over similar meridional 1981; Philander et al. 1987; Oberhuber 1988). Two separations. But even that comparison is dif®cult since statements follow: First, the agreement provides a ther- the meridional shear (Fig. 9) varies linearly with depth modynamic consistency check on the near-surface es- from a zero crossing at 50 m to a maximum value at timate of upwelling. Second, if this is the way that the the surface. Since surface drifters have a 10-m drogue cold tongue is maintained, on annual average, then small deployed on a 30-m tether, some of which break free, interannual changes in the three-dimensional circulation the depth at which surface drifters estimate divergence associated with the EUC will result in interannual is unclear. Quantifying the meridional divergence at and changes in the cold tongue temperature, unless accom- below the EUC core depth is simpler, however, since panied by corresponding changes in the net surface heat there the observed covergence is controlled geostroph- ¯ux. ically by the ZPG. Assuming that the ZPG is symmetric The magnitude of the downward mixing of heat over about the equator, the meridional divergence due to geo- the lower portion of the EUC appears to be much larger strophic ¯ow occurring ⌬y degrees from the equator is than the upward mixing of heat above the core. Inte- given by grating the temperature ¯ux imbalance vertically between 100 m and 250 m depths results in about 680 W (x. (5ץ/Pץy ϭϪ[␳␤⌬y 2]Ϫ1ץ/␷ץ mϪ2. Is it physically reasonable for this amount of heat The vertical pro®le of the TIWE averaged ZPG on the ¯ux to be accounted for by vertical eddy diffusion? The equator, as given by Qiao and Weisberg (1997), has its question is approached in two ways. The ®rst is to con- maximum value at the surface, and it deceases mono- sider the eddy diffusivity at the 250-m depth necessary tonically to negligibly small values between 220 m and to accommodate such ¯ux, and the second is to consider 250 m depths [supported by the Mangum and Hayes the eddy diffusive ¯ux divergence between 130 m and (1984) analysis of hydrographic data referenced to 1000 180 m where the advective ¯ux imbalance is greatest. db]. Assuming that the ZPG decreases poleward from The formulations are similar: 1) Qd ϭ ␳CpKdT/dz, the equator proportional with the u component (similar where K is the eddy coef®cient and Qd (the ¯ux at 250-m Ϫ2 2 2 to an equatorial Kelvin wave) quantitative agreement is depth) is 680 W m , and 2) dQ/dz ϭ ␳CpKd T/dz , Ϫ1 y where (␳Cp) dQ/dz (the imbalance from 130 m to 180ץ/␷ץ found between the geostrophic and the estimated (Fig. 9) from the EUC core depth to 250 m. Not only m) is 1.7 ϫ 10Ϫ6 ЊCsϪ1. Estimating the appropriate is the magnitude at the core the same to within 10%, temperature derivatives at 250 m and at 150 m (albeit -y approaches zero between 220 m and 250 m from a poorly resolved mean vertical pro®le) gives simץ/␷ץ but along with the ZPG. ilar values for K of about 4 ϫ 10Ϫ3 m 2 sϪ1. While this Finally, in the Qiao and Weisberg (1997) diagnosis is large, it is within the range of microstructure mea- of the zonal momentum balance, the vertical advection surements reported by Gregg (1987). Coincidentally, of momentum is as equally important as the other terms. these heat ¯ux estimates from beneath the EUC in the When all terms are combined and vertically integrated, central Paci®c agree with previous estimates made for the record length averaged zonal wind stress quantita- the equatorial Atlantic by Weingartner and Weisberg tively balances the ZPG in the vicinity of the EUC core. (1991b) based on a more limited dataset. Such conver- Also, when the vertical frictional stress pro®le is cal- gence below the EUC core and hence a downward ad- culated as a residual between the material acceleration vective temperature ¯ux imbalance is also consistent at each depth and the ZPG, it shows a zero crossing with the observation of a thermostad region beneath the within 10 m of the EUC core, as expected. If the errors EUC and the steep downward bowing of dynamically in w were overwhelming, it is unlikely that these dy- passive tracers relative to dynamically active ones as namical balances could have been realized. noted in section 2. Using the same dataset, but with an independent analysis of the zonal momentum balance, versus the heat balance, Qiao and Weisberg (1997) ar- 6. Discussion and summary rived at a similarly large value for the eddy diffusion The ͗w͘ pro®le implies an advective temperature ¯ux coef®cient for momentum. For both quantities, heat and imbalance (Figs. 10 and 11). Is the vertical distribution momentum, the requirement for large vertical mixing of this imbalance consistent with local heat ¯uxes, both follows directly from the downwelling estimated over at the surface and at depth? Consider ®rst the positive the lower portion of the EUC. A dynamical basis for region of the temperature ¯ux imbalance above 100-m the connection between downwelling and mixing is giv-

Unauthenticated | Downloaded 10/01/21 09:37 AM UTC JANUARY 2000 WEISBERG AND QIAO 121 en by Charney (1960) and Charney and Spiegel (1971). are sampled too coarsely for process experimentation. Robinson (1966) found best agreement between theory Required for improved understandings of the equatorial and observation for a vertical eddy diffusivity that var- cold tongues and the transport pathways that link the ied in qualitative agreement with that found here, and Tropics with the equator is a process-oriented dataset Philander (1973) also concluded that downwelling oc- suf®cient to determine the relative importances of the curs below the EUC core. equatorial ocean circulation and the net surface heat and The entrainment velocity estimated from the advec- buoyancy ¯uxes in determining both SST and the down- tive temperature ¯ux imbalance is found to increase ward mixing of material properties. linearly between the EUC core and the near surface. Since the mixed layer is about 60 m deep, it may be Acknowledgments. Support was provided by the physically more appropriate to terminate the entrain- Ocean Sciences Division, National Science Foundation, ment velocity calculation at 60 m where its magnitude Grant Numbers OCE-8813378 and OCE-9302811. Ϫ5 Ϫ1 is about 0.8 ϫ 10 ms . Improved estimates of ma- Messrs. R. Cole and J. Donovan assisted with the in- terial property ¯uxes and derived quantities such as en- strumentation, ®eld deployments, and data analyses. Dr. trainment velocity will require improved measurements C. Wang provided many helpful discussions. The of®- of the material property gradients. cers and crew of the R/V Wecoma and the R/V Alpha The primary difference between our estimates of w Helix made the sea-going operations safe, successful, and those obtained by Bryden and Brady (1985), or and pleasurable. M. McPhaden and L. Mangum others using the continuity equation with sparsely sam- (NOAA/PMEL) kindly provided the TAO array data pled data (section 2), is in the vertical pro®le. Our results used in this study. show upwelling within and above the EUC core and downwelling of equal magnitude below, as opposed to upwelling across almost the entire EUC. It is this dif- APPENDIX ference in vertical velocity below the core that has important implications both for dynamical and material Error Analysis property balances. Numerical models, particularly those employing bulk Richardson-number-dependent vertical a. Random geophysical errors eddy diffusion coef®cients, also tend to show upwelling The procedure for estimating the random geophysical across the entire EUC, in contrast to our ®ndings. This errors for the TIWE horizontal velocity component may be attributed to the fact that vertical diffusion below mean values is the same as given in Qiao and Weisberg the EUC core in such models is very small. With small dissipation and no opposing pressure gradient force, ¯u- (1997). It is assumed that these measured quantities de- id cannot downwell within the EUC because there is no rive from stationary, Gaussian distributed, random var- means of decelerating the ¯uid between the EUC core iables satisfying the ergodic hypothesis. The divergence -z, and w are estiץ/w͗͘ץ ,yץ/␷͗͘ץ ,xץ/u͗͘ץ ,and the slower region below (Qiao and Weisberg 1997). constituents In other words the fully three-dimensional circulation mated by linear operations upon u and ␷ so their dis- associated with the EUC is critically dependent upon tributions are also Gaussian. Thus, their variance esti- the dissipation that occurs within it. Since this circu- mates all follow from lation determines the equatorial ocean cold tongues, it var{X} ϭ ␶ T Ϫ1C (0), (A1) follows that an unequivocal determination of the fully 0 x three-dimensional circulation structure associated with where var{ } is the variance operator, x is a stationary the EUC is a necessary step toward improving ocean random variable, X is its record length (T) averaged models of the Tropics, particularly those coupled with mean value estimate, C (0) is its autocovariance at zero atmosphere models. Only through an independent da- x lag, and ␶ 0 is its integral timescale (e.g., Tennekes and taset is it possible to test whether a coupled ocean± Lumley 1972) given by atmosphere model simulates SST for the correct reason. In summary, the TIWE equatorial array provides es- T C (␶) d␶ timates of the vertical velocity pro®le within the upper ͵ x 250 m in the central Paci®c at 0Њ, 140ЊW. The array ϪT ␶0 ϭ . (A2) appears to resolve the primary producers of upper-ocean Cx(0) divergence on seasonal and synoptic scales, thereby pro- viding physically plausible estimates of volume ¯ux. Standard deviations are calculated as the positive square While plausible, important discrepancies exist that re- root of the variances, and the equivalent degrees of free- quire further testing, particularly the downwelling below dom, in analogy to band-limited white noise, is N ϭ Ϫ1 the EUC core and the implied large mixing rates. The T␶ 0 . With the exception of the u component in the TIWE array lacked adequate temperature and salinity vicinity of the EUC core, for which N is as small as 15, measurements for properly assessing heat and other ma- all other time series, including the divergence constit- terial property budgets, and data from the TAO array uents and w have values of N greater than 30.

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c. Systematic compass calibration errors Let (u, ␷) be the horizontal velocity components in the conventional (x, y) coordinate system directed positive to the east and north, respectively. In the event of a constant compass offset by ␣ degrees, the ADCP will yield velocity components (uЈ, ␷Ј) in the rotated coordinate system (xЈ, yЈ). For an anticlockwise rotation the coordinate transformation is uЈϭu cos␣ Ϫ ␷ sin␣, (A3) ␷Јϭu sin␣ ϩ ␷ cos␣. (A4) Consider the case of a 2Њ compass offset whereby cos␣ ϭ 1 and |sin␣| ϭ 0.035. Thus, uЈϭu and ␷ЈϭϪu sin␣ ϩ ␷. The u component is unaffected, whereas the ␷ component may be affected in the event of large u. FIG. A1. Comparisons between horizontal divergence and vertical velocity pro®les when calculated using unscaled (as in the text) or Since the EUC presents such a scenario it is important x. The solid lines are for the centered difference to calculate what this potential source of error might beץ/u͗͘ץ scaled values of x estimated on the equator and the dashed lines are for the calculation of the meridional divergence andץ/u͗͘ץ values of .x where the factor of 0.8 approximates the average hence wץ/u͗͘ץ for 0.8 times of ͗u͘ between the equator and 1ЊN and S. Consider a worst case for which there are oppositely directed compass offsets to the north and south of the equator on the TIW5 and TIW2 moorings. This would x effectively result in an additive 4Њ error on meridionalץ/u͗͘ץ b. Systematic error in Figure A2 compares vertical pro®les for the record divergence. The maximum bias will ocur at the EUC y and ͗w͘ the errorsץ/␷͗͘ץ length averaged horizontal divergence and vertical ve- core where u is largest. For Ϫ1 Ϫ1 (x evaluated on the are [|uЈns | ϩ |uЈ |](2⌬y) sin2Њ and {[|uЈ ns | ϩ |uЈ |](2⌬yץ/u͗͘ץ locity calculated using either x (dashed line). sin2Њ]} dz, respectively. These worst case errors areץ/u͗͘ץ equator (solid line) or 0.8 times The rationale for scaling down the centered difference shown in Fig. A1. The reversal in sign with depth of -x follows from the symmetry of ͗u͘ about the the meridional divergence error results in a partial canץ/u͗͘ץ equator (Fig. 3). The factor of 0.8 approximates the cellation of the w error upon vertical integration. Nev- average of ͗u͘ between the equator and 1ЊN and S. Either ertheless, at 250-m depth some two-thirds of the down- x welling could be attributed to such error (although weץ/u͗͘ץ formulation gives nearly the same result since y in the horizontal di- note that, if the compass errors pointed the oppositeץ/␷͗͘ץ plays a secondary role to x are therefore incon- direction, then the downwelling would be substantiallyץ/u͗͘ץ vergence. Small changes in sequential. For consistency with other w determinations higher). As noted, the compasses were checked and such we use the unscaled formulation in the text. constant offsets were not found. Such error would also

y, and ͗w͘ assuming systematic and oppositely directed 2Њ compassץ/␷͗͘ץ ,FIG. A2. Error pro®les for ͗␷͘ errors on each of the two off-equator moorings.

Unauthenticated | Downloaded 10/01/21 09:37 AM UTC JANUARY 2000 WEISBERG AND QIAO 123 cause an inconsistency with the ZPG calculated merid- lation during northern winter as inferred from outgoing long ional divergence at the EUC core, which is not observed. wave radiation. Mon. Wea. Rev., 113, 1889±1909. Levitus, S., 1988: Ekman volume ¯uxes for the World Ocean and individual ocean basins. J. Phys. Oceanogr., 18, 271±279. Mangum, L. J., and S. P. Hayes, 1984: The vertical structure of the REFERENCES zonal pressure gradient in the eastern Equatorial Paci®c. J. Geo- phys. Res., 89, 10 441±10 450. Bjerknes, J., 1966: A possible response of the atmospheric Hadley Matsuno, T., 1966: Quasi-geostrophic motions in the equatorial area. circulation to equatorial anomalies of ocean temperature. Tellus, J. Meteor. Soc. Japan, 2, 25±43. 18, 820±829. McPhaden, M. J., and B. A. Taft, 1988: Dynamics of seasonal and Broecker, W., T.-H. Peng, and M. Stuiver, 1978: An estimate of the intraseasonal variability in the eastern equatorial Paci®c. J. Phys. upwelling rate in the equatorial Atlantic based on the distribution Oceanogr., 18, 1713±1732. of bomb radiocarbon. J. Geophys. Res., 83, 6179±6186. Meyers, G., 1979: Annual variation in the slope of the 14ЊC isotherm Bryden, H. L., and E. C. Brady, 1985: diagnostic model of three- along the equator in the Paci®c Ocean. J. Phys. Oceanogr., 9, dimensional circulation in the upper equatorial Paci®c Ocean. J. 885±891. Phys. Oceanogr., 5, 1255±1273. Mitchell, T. P., and J. M. Wallace, 1992: The annual cycle in equatorial Charney, J. G., 1960: Non-linear theory of a wind-driven homoge- convection and sea surface temperature. J. Climate, 5, 1140± neous layer near the equator. Deep-Sea Res., 6, 303±310. 1156. , and S. Spiegel, 1971: Structure of wind-driven equatorial cur- Oberhuber, J. M., 1988: An Atlas Based an the `COADS' Data Set: rents in homogeneous oceans. J. Phys. Oceanogr., 1, 149±160. The Budgets of Heat, Buoyancy, and Turbulent Kinetic Energy Cromwell, T., 1953: Circulation in a meridional plane in the central at the Surface of the Global Ocean. Max-Planck Institut fuÈr equatorial Paci®c. J. Mar. Res., 12, 196±213. Meteorologie Rep. 15, Max-Planck-Institut fuÈr Meteorologie, Defant, A., 1981: The Troposphere. W. J. Emery, Transl. Ed., Am- Hamburg, Germany, 199 pp. erind, 113 pp. Philander, S. G. H., 1973: The equatorial thermocline. Deep-Sea Res., Esbensen, S. K., and V. Kushnir, 1981: The heat budget of the global 20, 69±86. ocean: An atlas based on estimates from surface marine obser- , 1990: El NinÄo,LaNinÄa, and the Southern Oscillation. Aca- vations. Climate Research Institute Rep. 29, Oregon State Uni- demic Press, 289 pp. versity, Corvallis, OR, 27 pp and 188 ®gures. , W. J. Hurlin, and R. C. Pacanowski, 1986: Properties of long Fine, R. A., W. H. Peterson, C. G. H. Rooth, and H. G. Ostlund, equatorial waves in models of the seasonal cycle in the tropical 1983: Cross equatorial tracer transport in the upper waters of Atlantic and Paci®c Oceans. J. Geophys. Res., 91, 14 207± the Paci®c Ocean. J. Geophys. Res., 88, 763±769. 14 211. Fofonoff, N. P., and R. B. Montgomery, 1955: The Equatorial Un- , , and A. D. Siegel, 1987: Simulation of the seasonal cycle dercurrent in the light of the vorticity equation. Tellus, 7, 518± of the tropical Paci®c Ocean. J. Phys. Oceanogr., 17, 1986± 521. 2002. Gouriou, Y., and G. Reverdin, 1992: Isopycnal and diapycnal cir- Poulain, P. M., 1993: Estimates of horizontal divergence and vertical culation of the upper equatorial Atlantic Ocean in 1983±1984. velocity in the equatorial Paci®c. J. Phys. Oceanogr., 23, 601± J. Geophys. Res., 97, 3543±3572. 607. Gregg, M. C., 1987: Diapycnal mixing in the thermocline: A review. Qiao, L., and R. H. Weisberg, 1995: Tropical instability wave ki- J. Geophys. Res., 92, 5249±5286. nematics: Observations from the Tropical Instability Wave Ex- Halpern, D., and P. H. Freitag, 1987: Vertical motion in the upper periment. J. Geophys. Res., 100, 8677±8693. ocean of the equatorial eastern Paci®c. Oceanol. Acta., Proc. , and , 1997: The zonal momentum balance of the Equatorial Int. Symp. on Equatorial Vertical Motion, SP, 19±26. Undercurrent in the central Paci®c. J. Phys. Oceanogr., 27, , and R. H. Weisberg, 1989: Upper ocean thermal and ¯ow ®elds 1094±1119. at 0Њ,28ЊW (Atlantic) and 0Њ, 140ЊW (Paci®c) during 1983± , and , 1998: Tropical instability wave energetics: Obser- 1985. Deep-Sea Res., 36, 407±418. vations from the Tropical Instability Wave Experiment. J. Phys. , R. A. Knox, D. S. Luther, and S. G. H. Philander, 1989: Es- Oceanogr., 28, 345±360. timates of equatorial upwelling between 140ЊW and 110ЊW dur- Quay, P. D., M. Stuiver, and W. S. Broecker, 1983: Upwelling rates ing 1984. J. Geophys. Res., 94, 8018±8020. for the equatorial Paci®c Ocean derived from the bomb 14C dis- Hansen, D., and C. Paul, 1984: Genesis and effects of long waves tribution. J. Mar. Res., 41, 769±792. in the equatorial Paci®c. J. Geophys. Res., 89, 10 431±10 440. Reynolds, R. W., and T. M. Smith, 1994: Improved global sea surface , and , 1987: Vertical motion in the eastern equatorial Paci®c temperature analysis using optimum interpolation. J. Climate, 7, inferred from drifting buoys. Oceanol. Acta., Proc. Int. Symp. 929±948. on Equatorial Vertical Motion, SP, 27±32. Robinson, A. R., 1966: An investigation into the wind as the cause Harrison, D. E., 1996: Vertical velocity in the central tropical Paci®c: of the Equatorial Undercurrent. J. Mar. Res., 24, 179±204. a circulation model perspective for JGOFS. Deep-Sea Res. II, Roemmich, D., 1983: The balance of geostrophic and Ekman trans- 43, 687±705. ports in the tropical Atlantic Ocean. J. Phys. Oceanogr., 13, Hastenrath, S., and P. J. Lamb, 1978: Heat Budget Atlas of the Trop- 1534±1539. ical Atlantic and Eastern Paci®c Oceans. University of Wis- Seager, R., and R. Murtugudde, 1997: Ocean dynamics, thermocline consin Press, 104 pp. adjustment, and regulation of tropical SST. J. Climate, 10, 521± Johnson, E. S., and D. S. Luther, 1994: Mean zonal momentum bal- 534. ance in the upper and central equatorial Paci®c Ocean. J. Geo- Stommel, H., 1960: Wind-drift near the Equator. Deep-Sea Res., 6, phys. Res., 99, 7689±7705. 298±302. Kessler, W. S., M. J. McPhaden, and K. M. Weickmann, 1995: Forcing Tennekes, H., and J. L. Lumley, 1972: A First Course in Turbulence. of intraseasonal Kelvin waves in the equatorial Paci®c. J. Geo- The MIT Press, 300 pp. phys. Res., 100, 10 613±10 632. Weingartner, T. J., and R. H. Weisberg, 1991a: On the annual cycle Knauss, J. A., 1966: Further measurements and observations of the of equatorial upwelling in the central Atlantic Ocean. J. Phys. Cromwell Current. J. Mar. Res., 24, 205±240. Oceanogr., 21, 68±82. Knox, R. A., and D. Halpern, 1982: Long range Kelvin wave prop- , and , 1991b: A description of the annual cycle in sea agation of transport variations in Paci®c Ocean equatorial cur- surface temperature and upper ocean heat in the equatorial At- rents. J. Mar. Res., 40 (Suppl), 329±339. lantic. J. Phys. Oceanogr., 21, 83±96. Lau, K. M., and P. H. Chan, 1985: Aspects of the 40±50 day oscil- Weisberg, R. H., J. C. Donovan, and R. D. Cole, 1991: The Tropical

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Instability Wave Experiment (TIWE) Equatorial Array: a report Wyrtki, K., 1981: An estimate of equatorial upwelling in the Paci®c. on data collected using subsurface moored acoustic Doppler cur- J. Phys. Oceanogr., 11, 1205±1214. rent pro®lers, May 1990±June 1991. Department of Marine Sci- , and G. Eldin, 1982: Equatorial upwelling events in the central ence, University of South Florida, 84 pp. Paci®c. J. Phys. Oceanogr., 12, 984±988. Wunsch, C., 1984a: An eclectic Atlantic Ocean circulation model. , and B. Kilonsky, 1984: Mean water and current structure during Part I: The meridional heat ¯ux. J. Phys. Oceanogr., 14, 1712± the Hawaii-to-Tahiti Shuttle Experiment. J. Phys. Oceanogr., 14, 1733. , 1984b: An estimate of the upwelling rate in the equatorial 242±254. Atlantic Ocean based on the distribution of bomb radiocarbon Yang, Y. J., T. Y. Tang, and R. H. Weisberg, 1997: Basin-wide zonal and quasigeostrophic dynamics. J. Geophys. Res., 89, 7971± wind stress and ocean thermal variations in the equatorial Paci®c. 7978. J. Geophys. Res., 102, 911±927.

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