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    Time series of winds and upper-ocean structure for 0–270 m and May–Dec 1992 (DOY 130–360) at 156° and 157.5°E on the equator: (a) zonal (solid line) and meridional (dashed line) wind components, (b) temperature (°C), (c) salinity, (d) zonal velocity (m s−1), (e) meridional velocity (m s−1), (f) depths of buoyancy frequency maximum (solid), thermocline (dashed), and halocline (dotted), and (g) mixed layer (dashed), EUC core (dotted), and momentum depth (solid). Contour intervals are 4°C for temperature (dashed contour at 29°C), 0.5 for salinity (dashed contour at 35.2), and 0.20 m s−1 for velocity. Shaded curves in (f) and (g) show depth range of pycnocline

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    Terms of the zonal momentum balance for 0–270 m and May–Dec 1992 (DOY 130–360): (a) τx (solid line) and σ | h(Pa) (dashed), (b) ut, (c) ∇ · (uu), (d) Du/Dt, (e) −gη̂x, (f) −ρ−10Px, and (g) ρ−10∇·Ŝ. Contour intervals are 4 × 10−7 m s−2

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    Histograms of the scaling exponent s for (a) ux, s(x) = log10( | ux/UX | )/log10(x/X), (b) (uu)x, s(x) = log10( | (uu)x/(UU)X | )/log10(x/X), and (c) (uu), s(t) = log10( | (uu)/(UU) | )/log10(t/T), where x = 167 km (156°–157.5°E), X = 2000 km (147°–165°E), t = 1 h, and T = 1 day

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    Estimates of the vertical subgrid-scale stress and energy conversions for 0–270 m and May–Dec 1992 (DOY 130–360): (a) eddy stresses [−ρ0()], (b) no-stress method [σ | h = −ρ0() | h], and mean-to-eddy energy conversion through the vertical eddy stress (σUz) estimated using (a) and (b). Contour intervals are 2.5 × 10−2 Pa for the stresses and 0.25 m W m−3 for the energy conversion

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    (a), (f) Average zonal momentum budget separated into locally accelerating and decelerating flows for the (a)–(e) surface and (f)–(j) subsurface; (b), (g) u > 0, ut > 0; (c), (h) u > 0, ut < 0; (d), (i) u < 0, ut > 0; and (e), (j) u < 0, ut < 0. Dashed boxes represent averages for material accelerations: (b), (g) u > 0, Du/Dt > 0; (c), (h) u > 0, Du/Dt < 0; (d), (i) u < 0, Du/Dt > 0; and (e), (j) u < 0, Du/Dt < 0

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    Profiles of momentum balance terms (cm s−1 day−1) for various forcing conditions: (a) WWE decelerates surface westward flow, Hisard jet accelerates westward (DOY = 293); (b) WWE accelerates Yoshida jet, Hisard jet accelerates westward (DOY = 300); (c) westward PGF extends into pycnocline, Yoshida jet decelerates (DOY = 312); (d) eastward acceleration of EUC, strongest WWE (DOY = 316); and (e) westward acceleration of Hisard jet, no WWE (DOY = 323). Terms are ut (shaded curve), Du/Dt (solid), σz/ρ0 (dotted), and −Px/ρ0 (dashed)

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    Profiles of the zonal velocity (solid curve), vertical shear (dotted), and curvature (shaded) for a nondimensional, eastward current given by u(z) = sech(zz0)

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The Effects of Wind Forcing and Pycnocline Stresses on Zonal Currents in the Western Equatorial Pacific

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  • 1 Nova Southeastern University Oceanographic Center, Dania Beach, Florida
  • | 2 Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California
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Abstract

Simultaneous moored temperature, salinity, velocity, and wind measurements from the equator at 157.5°E, during 10 May–21 December 1992, are combined with a no-stress-level boundary condition in the Equatorial Undercurrent core to estimate the total zonal pressure gradient force and subgrid-scale residuals of the momentum balance. Estimates are made of the depth of wind stress penetration, momentum depth, distribution of subgrid-scale stresses, and balance of forcing terms in the surface layer and pycnocline. Westerly winds of greater than 5 m s−1 in September 1992 coincided with the appearance of an eastward surface Yoshida jet and subsurface westward (Hisard) jet on the equator. The momentum depth increased with successive wind events, eroding the shallow halocline until it merged with the permanent thermocline. Wind-induced stresses were not restricted to the depth of density homogenization. The record-length-averaged pressure gradient force was westward and was balanced by downstream accelerations and stress drag. However, time-dependent accelerations were balanced by vertical divergence of the stresses. The pressure gradient dominated decelerations of the surface flows and played a lesser role in accelerating subsurface currents. The force balance was consistent with the concept of wind-driven surface flow above the momentum depth; in the pycnocline it implied forcing of the mean zonal currents via the eddy and turbulent momentum flux divergences. The results indicate that steady-state theories do not explain the existence of subsurface zonal currents on the equator. Time-dependent forcing in the equatorial pycnocline includes significant transfers of zonal momentum by submesoscale processes.

Corresponding author address: S. Kennan, NSU Oceanographic Center, 8000 N. Ocean Dr., Dania Beach, FL 33004. Email: skennan@nova.edu

Abstract

Simultaneous moored temperature, salinity, velocity, and wind measurements from the equator at 157.5°E, during 10 May–21 December 1992, are combined with a no-stress-level boundary condition in the Equatorial Undercurrent core to estimate the total zonal pressure gradient force and subgrid-scale residuals of the momentum balance. Estimates are made of the depth of wind stress penetration, momentum depth, distribution of subgrid-scale stresses, and balance of forcing terms in the surface layer and pycnocline. Westerly winds of greater than 5 m s−1 in September 1992 coincided with the appearance of an eastward surface Yoshida jet and subsurface westward (Hisard) jet on the equator. The momentum depth increased with successive wind events, eroding the shallow halocline until it merged with the permanent thermocline. Wind-induced stresses were not restricted to the depth of density homogenization. The record-length-averaged pressure gradient force was westward and was balanced by downstream accelerations and stress drag. However, time-dependent accelerations were balanced by vertical divergence of the stresses. The pressure gradient dominated decelerations of the surface flows and played a lesser role in accelerating subsurface currents. The force balance was consistent with the concept of wind-driven surface flow above the momentum depth; in the pycnocline it implied forcing of the mean zonal currents via the eddy and turbulent momentum flux divergences. The results indicate that steady-state theories do not explain the existence of subsurface zonal currents on the equator. Time-dependent forcing in the equatorial pycnocline includes significant transfers of zonal momentum by submesoscale processes.

Corresponding author address: S. Kennan, NSU Oceanographic Center, 8000 N. Ocean Dr., Dania Beach, FL 33004. Email: skennan@nova.edu

1. Introduction

Although there exist a variety of conceptual models for the El Niño–Southern Oscillation (ENSO), a common element is the atmospheric forcing of the upper ocean in the western equatorial Pacific Ocean warm-pool region by westerly wind events (WWEs). WWEs occur seasonally when typically weak trade winds reverse, either from the passage of tropical cyclones with westerly flow on their equatorward sides or in association with cross-equatorial winds (Hartten 1996; Harrison and Vecchi 1997). Understanding the causality between WWEs and the initiation of El Niño is fundamental to understanding ENSO.

A missing link in the WWE–ENSO connection is an understanding of the dynamic response of the upper ocean to wind forcing. This subject is addressed in this study by applying a no-stress-level boundary condition for the zonal momentum flux (Kennan and Niiler 2003) to in situ observations of velocity, temperature, and salinity over the upper 270 m, on the equator, in the vicinity of 156°W. The data were obtained from 10 May through 21 December of 1992, encompassing a period during which WWEs were active: winds and ocean temperature and salinity from Tropical Atmosphere–Ocean Array (TAO) Atlas moorings (McPhaden et al. 1998) and ocean currents from moored acoustic Doppler current profilers (ADCP) and satellite-tracked surface drifting buoys.

Subsurface equatorial currents evolve counter to the local winds. The Equatorial Undercurrent (EUC) reaches across the entire Pacific basin, while westward flow—the Hisard jet—appears above the EUC and below the temporary eastward flow during WWEs (Hisard et al. 1970; Delcroix et al. 1993). It has been suggested that the Hisard jet arises from a westward pressure gradient force (PGF) as a result of sea level setup downwind of the wind burst (Hisard et al. 1970). Cronin et al. (2000) reached this conclusion using some of the same observations to be used here (spanning 2 yr and a larger area). Likewise, equatorial circulation theories (Charney 1960; Wyrtki and Bennett 1963; Pedlosky, 1998) and models (Wacongne 1989; McCreary and Yu 1992; Wainer et al. 1999) indicate that downstream acceleration and drag within the EUC balance an average PGF associated with high sea level in the western Pacific.

These zonal jets appear in linear stratified models, but there has been difficulty modeling the deeper jets observed in the Pacific (Firing 1987; Rowe 1996; Firing et al. 1998). These problems may be related to the role of internal gravity waves (IGW) in maintaining the deep-cycle turbulence (Lien et al. 1996; Sun et al. 1998). Sutherland (1996) and Mack and Hebert (1997) have presented evidence that momentum fluxes radiating as internal gravity waves from shear instabilities may diverge at and below the pycnocline and accelerate zonal jets. Muench and Kunze (1999) have developed a more recent model in which the momentum flux divergence associated with waves approaching critical layers accelerates deep jets (Muench and Kunze 2000), and Smyth and Moum (2002) have shown how IGW interactions with critical layers in the EUC depend on the stratification. These studies highlight the importance of IGW and deep-cycle turbulence for understanding the zonal momentum balance of equatorial zonal jets.

This study bridges the conceptual gap between the steady-state and short-term variations of the zonal currents at and above the pycnocline. Kennan and Niiler (2003) have shown that vanishing turbulent stresses at the EUC core can be exploited to obtain accurate estimates of zonal SSH slope. The method is used here to examine the relatively short timescale variations in the momentum balance. The results show that the pressure field adjusted to the zonal flows on timescales of the WWEs. Averaged over the entire study period, the PGF was balanced by downstream acceleration and turbulent stress convergence, in agreement with previous observations (Bryden and Brady 1985; Qiao and Weisberg 1997). However, by focusing on the deviations from this balance, it is shown that subsurface currents arose not from the PGF, but from internal, submesoscale stress convergence. Relatively small scale processes that are not dissipative (i.e., submesoscale but larger than the scales of isotropic turbulence) play crucial roles in the equatorial circulation.

An important issue for modeling the ocean response to wind forcing involves the parameterizations for coupling the boundary, or mixed, layer to the ocean interior. The no-stress-level approach also facilitates an estimation of the depth of penetration of the wind stress: the momentum depth. In agreement with previous observations in the Tropics (Chereskin and Roemmich 1991; Wijffels et al. 1994), it is found that the vertical transfer of stresses often exceeded the scalar mixed layer depth.

Successive wind events caused the surface layer stresses to penetrate progressively deeper, reaching below the halocline to the main pycnocline. The halocline concurrently migrated to the depth of the thermocline so that the multiple pycnocline structure of the warm pool was eroded. The upper-ocean density structure was sensitive to the timing of sequential WWEs. Merging of the halocline with the main thermocline may be related to the ability of strong wind events to force downwelling Kelvin pulses capable of initiating a persistent warming in the eastern Pacific.

2. Data

The datasets used in this study include velocities from four ADCP moorings (0°, 156°E; 0.75°N, 156°E; 0.75°S, 156°E; 0°, 157.5°E) and temperatures, salinities, and winds from five TAO moorings on the equator (154°, 156°, 157.5°, 160.5°, and 165°E). For each dataset, daily averages and standard errors were calculated from hourly observations.

Wind stress was estimated using a typical bulk parameterization (τ = ρairCDu | u | , where ρair = 1.2 kg m−3 is air density, CD = 1.1 × 10−3 is a dimensionless drag coefficient, and u is the wind velocity measured at the mooring; Smith 1988). The resulting time series of wind stress components appears in Fig. 1a.

The baroclinic portion of the PGF was estimated using the density structure of the upper ocean as observed by the TAO array of buoys (McPhaden 1995). Thermistors recorded hourly temperature to 500 m at five moorings (154°, 156°, 157.5°, 160.5°, and 165°E) and Sea-Bird Electronics, Inc., “Seacats” recorded hourly temperature and conductivity measurements at all but the 157.5°E site, at which hourly temperatures were also lacking (Freitag et al. 1999). Salinity observations spanned the main halocline at the 156° and 165°E sites.

Accelerations were estimated from zonal and meridional velocity measured by four downward-looking ADCPs moored at 0°, 156°E; 0°, 157.5°E; 1.5°N, 156°E; and 1.5°S, 156°E from 11 February 1992 to 4 April 1994 (Weisberg et al. 1993, 1994). Profiles for 30–270-m depth were provided on 10-m and hourly intervals. Local acceleration was calculated using centered differencing of daily values at 157.5°E. Spatial gradients were the differences between the eastern and western, and northern and southern moorings. The horizontal divergence was estimated as ∇H · u = ux + υy, and the vertical velocity was calculated by integrating the divergence down from an assumed rigid-lid surface.

Errors were propagated through all calculations using stochastic trials based on the standard errors of the observed variables. The word “significant” is used to refer to signals that exceed the associated standard errors. More details of the data processing and error analyses appear in Kennan and Niiler (2003).

3. Method

On the equator, an equation for the zonal balance of forces on a parcel is
i1520-0485-33-12-2643-e1
where
i1520-0485-33-12-2643-eq1
Here, Π is the baroclinic portion of the pressure field P relative to the surface, η is SSH, S is the vector component of the stress tensor representing subgrid-scale momentum fluxes in the zonal direction, τ is the vertical stress tensor component of the turbulent momentum flux, and other notations are standard. A Reynolds decomposition has been made so that primed quantities are understood to represent the deviations from the unprimed. The subgrid-scale encompasses length scales and timescales shorter than those of the mooring array samplings—O(100 km) horizontal length scale, O(10 m) vertical length scale, and O(1 day) timescale—and longer than those of the turbulence. The turbulence occurs on length scales less than O(1 m) and timescales shorter than the highest-frequency IGW—O(minutes). The horizontal turbulent fluxes of zonal momentum are absorbed in the subgrid-scale stress S, and the vertical flux is explicitly shown in τ.
Kennan and Niiler (2003) have shown that, on a 5-day timescale, the zonal SSH gradient on the equator may be accurately estimated as
i1520-0485-33-12-2643-e2
where τx is the wind stress and σ = −ρ0() is the vertical component of the subgrid scale stress vector S, in analogy with the vertical turbulent flux τ. This diagnosis for SSH slope can be exploited to infer the vertical distribution of vertical subgrid-scale stresses and their effects on the zonal momentum balance.
The integral of the momentum equation is a budget for the vertical flux of zonal momentum as a function of depth. Its residual, the total vertical subgrid-scale zonal stress at depth z, including the turbulent scale (σ + τ) | z, is estimated as
i1520-0485-33-12-2643-e3
and the three-dimensional divergence of the total subgrid-scale stress vector, (S + τk̂), is estimated as the residual of the momentum budget:
i1520-0485-33-12-2643-e4
The subsequent deviations of the estimates from the true values are
i1520-0485-33-12-2643-e5

The discrepancy in estimating SSH gradient [Eq. (5)] is the average convergence of the horizontal subgrid-scale momentum fluxes above the EUC core. The estimated stress error is depth dependent, including the average stress convergence linearly increasing with depth and the surface-to-depth integral of the horizontal stress convergence. At the surface and EUC core all effects cancel because of the known boundary conditions (wind stress and no turbulent stress, respectively). However, the deviation in total stress divergence [Eq. (7)] depends only on the SSH slope error and is thus a depth-independent bias. It follows that estimating the role of the subgrid-scale stresses in the momentum balance is reliable in direct proportion to the accuracy of the SSH slope estimate.

Last, the approximate momentum balance is
i1520-0485-33-12-2643-e8

The accelerations, mean flux convergence, and depth of the EUC core are estimated from the moored ADCP data. The baroclinic PGF is derived from the moored thermistor and Seacat observations, and the wind stress comes from wind measurements on the TAO moorings. The vertical subgrid-scale stress at the EUC core is estimated using hourly correlations between the ADCP velocity and thermistor isotherm displacements at 156°E.

4. Results

a. Upper-ocean structure

During 10 May–21 December 1992, winds were either weak [<10 kt (1 kt = 0.5144 m s−1)], or bursting to the east on approximately weekly timescales (3–21 days; Fig. 1a). During the strongest wind events from September onward, the wind stress exceeded 0.05 Pa for periods of approximately 1–7 days; hourly winds sometimes exceeded 0.1 Pa, or 30 kt. There were also cross-equatorial winds of similar magnitudes and timescales.

Prior to September of 1992, water warmer than 29°C and fresher than 34.5 resided above approximately 40–50 m (Figs. 1b,c). The halocline coincided with a shallow pycnocline above the deeper, main thermocline. The pycnocline therefore spanned from the halocline through the thermocline. The main pycnocline was taken as the depth of maximum buoyancy frequency; the top and bottom of the pycnocline were defined as the depths at which the frequency dropped below 80% of the maximum (Fig. 1f). These depths often corresponded to distinct buoyancy frequency maxima, representing multiple pycnoclines. The mixed layer depth (MLD) was estimated as the depth at which the buoyancy frequency first exceeded 5.67 cph, corresponding to 1 kg m−4, similar to the criterion of Lukas and Lindstrom (1991).

The halocline and shallow pycnocline were usually shallower than 50 m prior to yearday (DOY) 300, followed by a shift in the entire thermohaline structure: the MLD doubled, and the halocline and thermocline merged into one pycnocline (Figs. 1b,c,f,g). This event coincided with the first consistent succession of wind events of magnitude greater than 0.05 Pa and duration longer than a few days (Fig. 2a).

During moderate WWEs in July and August there was eastward flow at the surface—the Yoshida jet—greater than 0.20 m s−1, which was connected in the vertical direction with the eastward flow found at and below the main pycnocline—the EUC (Figs. 1a,d). After the first significant burst (greater than 0.05 Pa, 15 kt) occurred around mid-September, a westward flow sandwiched between the surface and subpycnocline eastward flows—the Hisard jet—appeared.

Also conspicuous were meridional flows above the pycnocline (Figure 1e), often independent of the wind, propagating toward the surface. Their cause is beyond the scope of this study, but McCreary (1985) has reviewed various nonzonal, wind-forcing situations that may be relevant.

The surface flow was in direct response to the westerly winds—it has been described in previous observations (McPhaden et al. 1992; Ralph et al. 1997) and modeled by theory (Yoshida 1959; Matsuno 1966; Moore and Philander 1978). The correlation between ut at the surface and zonal wind speed was 0.64. The reversing, or Hisard, jet has also previously been identified as a response to WWEs along the equator (Hisard et al. 1970; McPhaden et al. 1992). Local accelerations dominated at the surface, and vertical flux divergence was largest at depth (Fig. 2). Local accelerations (Fig. 2b) were of order 10−7 m s−2 during all the wind events prior to DOY 320. The flux divergence (Fig. 2c) had a vertical structure of order 50 m set by the vertical scale of the zonal currents.

The sea surface height (SSH) gradient was estimated using the no-stress method according to Eq. (2). Five-day averages of this slope were correlated with altimetry estimates at 0.77 (Kennan and Niiler 2003). Here, 3-day averages are shown (Fig. 2e). For May–December 1992, the PGF resulting from SSH slope was mostly westward. When combined with the baroclinic PGF estimated from the TAO moorings, the total PGF was still mostly westward, but with significant eastward events. The dominant vertical scales of the PGF, which extended through the thermocline, were much larger than for the accelerations—order 50 m. The PGF magnitudes were also smaller than for the accelerations (Fig. 2f).

The total subgrid-scale stress divergence (∇·Ŝ) was estimated as the residual from the momentum balance [Eq. (4); see Fig. 2g]. The dominant magnitudes and scales were clearly associated with flux divergence and local acceleration imbalances, indicating a qualitative short-term balance between zonal accelerations and subgrid-scale stress divergence.

b. Subgrid-scale fluxes

The vertical and temporal scales of the stress divergence (∇·Ŝ) were similar to those of the acceleration, not the PGF, which was nearly coherent in the vertical direction (Fig. 2). Moreover, below the surface the imbalance was predominantly with flux divergence. This result is consistent with previous observations that divergence and vorticity scale with decreasing horizontal length scale (Kennan and Flament 2000; Flament and Armi 2000).

Although it is known that IGW and eddies can interact with mean flows, it is not evident what the role of the subgrid scale was in the observations. The spatial scaling of zonal velocity gradient and zonal flux divergence were tested by comparing estimates of ux and (uu)x from the COARE ADCP array with a larger-scale estimate. The small-scale zonal velocity gradient was calculated from the 156° and 157.5°E moorings. The large-scale gradients were determined by linear regression to the mooring data from 147°, 156°, 157.5°, and 165°E. A normalized spatial scaling parameter s(x) was constructed to quantify the dependence on length scale; s = 0 indicated scale independence (ux independent of length scale), s = 1 indicated direct scaling (ux increased with increasing length scale), and s = −1 indicated inverse scaling (ux increased with decreasing length scale):
i1520-0485-33-12-2643-eq2
where x = 167 km, X = 2000 km, and ux and UX were zonal velocity gradients estimated on the small and large scales, respectively. Zonal flux divergence (uu)x was treated similarly. The results were plotted as histograms of s (Figs. 3a,b). For ux the average was s = −0.82; (uu)x gave s = −1.0. Both the zonal velocity gradient and zonal momentum flux divergence scaled with inverse length scale (the latter more so). As a consequence, these terms probably increased in relative importance as the length scale decreased beyond the resolution of the ADCP array.
Temporal scaling was checked by estimating
i1520-0485-33-12-2643-eq3
where UU was the squared daily zonal velocity component and uu was the daily average of the hourly squared velocity (t = 1 h, T = 1 day).

The results gave s(t) = 1.0 (Fig. 3c), implying a direct scaling with decreasing timescale. Combined with the inverse scaling with space scale, it seems reasonable that the subgrid-scale flux divergence should have been of the same magnitude on smaller length scales and timescales as the overall mean. It was therefore not surprising to find that the flux divergence of Fig. 2g was of the same magnitude as the mean flux divergence terms. Moreover, observations of the material acceleration following drifters that passed by the ADCP array showed that at least one-half of the energy was not resolved by the mooring array (Kennan and Niiler 2003).

c. Stress distribution

The subgrid-scale vertical stress is σ = −ρ0(). At the high frequencies where this stress is expected, its magnitude may be estimated by assuming a linear, adiabatic temperature equation and expressing the vertical velocity as a function of the isotherm displacements: w′ = −TtT−1z, where T is the mean temperature and T′ is the fluctuating part. The fluctuating zonal current u′ and temperature T′ were obtained by subtracting daily values from hourly values. The mean correlation () was calculated as the average daily product at thermistor depths and was subsequently interpolated in the vertical direction.

Using this proxy to estimate the vertical subgrid-scale stress at the EUC core improved the results of the no-stress method slightly (Kennan and Niiler 2003). The full distribution with depth appears in Fig. 4a. The vertical subgrid-scale stress (σ̂) was also estimated by integrating the momentum budget from the surface wind stress to the EUC core boundary condition, according to Eq. (3) (Fig. 4b). The stresses throughout the pycnocline (equivalent to the hourly proxy at the EUC core by design) were all significant, with magnitudes of 0.01–0.1 Pa and signal-to-noise ratios of greater than 1. The wind stress could be seen penetrating the shallow pycnocline during strong WWEs—note the stress in the upper 50–100 m on DOY 175–185, 210–215, and 290–320.

The two estimates of the stress showed features of the same magnitude and temporal and vertical scales (Figs. 4a,b). The exact timing and positioning of the features was not consistent. The estimate made using hourly data suffered from several limitations, including inadequate vertical sampling by thermistors and possible aliasing of internal gravity waves with periods shorter than 1 h. Nevertheless, both results showed the high-frequency currents acting in concert to produce significant stresses in the pycnocline—this supports the interpretation of the momentum residual as including the vertical stress divergence.

Note that the stress was the most poorly estimated quantity based on the no-stress method, because any error in SSH slope contributed an error that increased with depth to the subgrid-scale stress estimate [Eq. (6)]. An error of 2 × 10−8 in SSH slope (typical according to the error analyses) corresponded to a σ̂ bias of 0.02 Pa at 100-m depth, a significant fraction of the 0.02–0.04-Pa values found there. Meanwhile, the error in ∇·Ŝ was a depth-independent 2 × 10−7 m s−2, relatively small when compared with the order 10−6 m s−2 accelerations.

To determine the depth of penetration of the wind stress—the momentum depth—individual vertical profiles were examined to find the depth at which the stress first reached zero. In instances in which profiles did not change sign above the EUC core, the momentum depth was taken as the depth at which the stress reached a local minimum (27 days). In instances in which the stress increased in magnitude with depth, a momentum depth could not be determined, and it was set to the MLD (25 days). The MLD was also used as a proxy for the momentum depth whenever the winds were less than 5 m s−1 (83 days). In the end, there were 99 days on which the stress distribution passed cleanly through zero or reached a minimum; 108 days were defaulted to the MLD.

Under weak winds, salinity stratification was associated with a shallow pycnocline, and the momentum depth was generally near 50 m (Fig. 1g). Under the influence of the October WWEs, the halocline and momentum depth both migrated to about 100 m, until eventually the halocline and thermocline merged into one pycnocline (Fig. 1f). During the stronger winds, the momentum depth exceeded the MLD and the shallow pycnocline depths, even reaching below the deep pycnocline during the November WWE. Thus, the mixing of momentum by the wind exceeded the MLD during wind events and was associated with the deepening of the shallow pycnocline. Subgrid-scale mixing of scalars and momentum was not equivalent.

The gradual erosion of the double pycnocline structure occurred through the succession of WWEs. From May of 1992, no WWE succeeded in eroding the barrier layer until November, when it was accomplished by a series of events that began in October. Even though wind events occurred periodically over the 6-month period that began in May, the double pycnocline structure persisted, never disappearing for more than a week. Not until the close succession of events that began in October was a single strong pycnocline formed. It thus seems likely that not only the amplitude of wind forcing, but also the timing of events, is responsible for setting the density structure of the upper ocean in this region. Single wind events, or events separated by a week or so, appear to be unable to effect a lasting impact on the pycnocline.

The subgrid-scale stress multiplied by the large-scale vertical shear gives the transfer of kinetic energy from the mean to eddy flows (large to subgrid scales) owing to vertical stresses: −ρ0()Uz. These stresses are likely associated with some combination of IGW and submesoscale eddies, the former being well documented in the equatorial Pacific. The kinetic energy transfer was calculated using both estimates of the mean subgrid-scale stresses (Figs. 4c,d). The two estimates showed some agreement, although features were stronger in the estimate made directly from the hourly data: positive values near the surface and throughout the pycnocline during May–September and frequent negative values at and below the EUC and progressively shallower after October of 1992. Positive values indicated large-scale-to-small-scale energy cascades such as would be expected in the presence of shear (Kelvin–Helmholtz) instabilities. The negative values, however, implied that the mean flow gained kinetic energy from the subgrid-scale stresses. Negative values coincided with accelerations of the Hisard jet and EUC (cf. with Fig. 1d). A subgrid-scale-to-mean-flow conversion of kinetic energy was consistent with the time-dependent forcing by the subgrid-scale stress divergence, which will be shown below.

d. Zonal momentum balance

The upper 250 m were separated into the wind-driven surface layer and the subsurface pycnocline. The surface layer was defined by the upper pycnocline depth, except that it was never shallower than 50 m. The pycnocline zone extended from the bottom of the wind-driven layer to 250 m. Each term in the momentum balance [Eq. (8)] was averaged over the layers and the record length. Bar graphs that represent each term as an acceleration appear in Fig. 5. For ease of interpreting the dynamics, the advection terms are shown instead of momentum fluxes. (Formulation of the no-stress method to include the σ | h term required using the flux divergence, but numerically the total flux divergence and advection were equivalent.) The material acceleration (Du/Dt) and the barotropic and baroclinic components of the PGF were included. The standard errors on the average terms were consistently 10% or less.

The flow fields were steady on average from May to December (Figs. 5a,f). However, both the surface and subsurface experienced net westward PGF and eastward stress divergence. Zonal advection indicated a net downstream deceleration throughout the water column. SSH gradient dominated the PGF, from the net effect of the setup downwind of WWEs, whereas the baroclinic portion was smaller and eastward from an average eastward decrease in temperature above 150 m. Within the the warm pool, during periods of westerly winds, cold water is advected eastward in the mixed layer (Ralph et al. 1997).

The momentum balance was next separated into four regimes (Figs. 5b–e,g–j): locally accelerating eastward flow (u > 0, ut > 0; Figs. 5b,g), locally decelerating eastward flow (u > 0, ut < 0; Figs. 5c,h), locally decelerating westward flow (u < 0, ut > 0; Figs. 5d,i), and locally accelerating westward flow (u < 0, ut < 0; Figs. 5e,j).

In the surface layer, accelerations were consistently balanced by σz, except during decelerating eastward flow. This was the wind stress penetrating throughout the surface layer to force the west wind drift during weak easterlies, and the Yoshida jet during WWEs. The case of the decelerating eastward flow indicated that the Yoshida jet fell back against the SSH gradient when westerly winds relaxed (Fig. 5c). There were also some significant zonal and vertical advections of momentum in the surface layer of 1–2 × 10−7 m s−2.

Below the wind-driven layer, under all conditions, the accelerations were again balanced by the subgrid-scale stress divergence (Figs. 5g–j). The exceptions were some westward accelerations (the Hisard jet) where the westward PGF was indistinguishable from the stress convergence (Figs. 5h,j). However, in these instances the vertical advection was significant and in the same sense as the stress convergence. Because σz represents the effects of subgrid-scale advection, the results indicated advection dominated slightly over the PGF in balancing local accelerations.

The westward PGF persisted throughout the pycnocline except during decelerating westward flow (decelerating Hisard jet), although it was reduced by the contribution from the thermohaline structure.

The separation of the subsurface flow field by accelerations was also done using the total accelerations on parcels, which confirmed that accelerations were always balanced by σz (dashed boxes in Figs. 5g–j). The Lagrangian view shows clearly the balance of forces on parcels of the array scale. In both the local and material view, eastward accelerations of EUC were dominated by the subgrid-scale stress divergence. In the Eulerian view, subgrid-scale convergence and the westward PGF were equally important in accelerating the Hisard jet. However, if the stress convergences had been resolved as advection terms, the dominant balance on local accelerations would have been by advection.

These results are in contrast to the model for subsurface equatorial flow in which the PGF balances accelerations below the wind-driven layer (Pedlosky 1998; Cronin et al. 2000). Although this balance held for the steady state, it did not explain the existence of the reversing jets in the pycnocline. Separating the forcings of the flow into the different acceleration directions revealed that forcing was accomplished by the subgrid-scale stress divergence.

Example profiles of Du/Dt, ut, PGF, and σz for 5 days, representing varying forcing and flow-response conditions, are shown in Fig. 6: a WWE decelerated the westward surface flow, and stress divergence established the Hisard jet in the upper pycnocline (19 October—DOY 293; Fig. 6a) (see Figs. 1a,e); a WWE accelerated the Yoshida jet while the Hisard jet intensified (DOY 300; Fig. 6b); WWEs ceased and the Yoshida jet relaxed against the westward PGF, which also dominated the Hisard jet (DOY 312; Fig. 6c); during the largest WWE, the momentum depth exceeded 150 m and the Yoshida jet was nearly 100 m deep—the upper EUC accelerated via σz at almost 0.1 m s−1 day−1 (DOY 316; Fig. 6d); and on 18 November (DOY 323) stress divergence in the upper pycnocline accelerated the Hisard jet in the absence of a WWE (Fig. 6e).

Thus, during May–December of 1992, the only exception to wind-driven surface flow through subgrid-scale stress divergence was the deceleration of the Yoshida jet against a westward PGF after WWEs. The overall averages showed eastward (westward)-flowing parcels decelerating (accelerating) downstream of a westward PGF with an eastward stress divergence. Because the stress divergence alternated with the advection terms on relatively short timescales while the PGF was nearly constantly westward, the PGF dominated the steady state.

By examining time periods of consistent accelerations, the role of the subgrid scale became apparent. In the pycnocline, the vertical stress divergence was responsible for accelerating both the westward Hisard jet and the eastward EUC, whereas the PGF was largely a westward offset (Figs. 2, 5). There was no obvious correlation with the wind, except that the Hisard jet first seemed to appear during a WWE.

The approximate steady state and time-dependent momentum balances were
i1520-0485-33-12-2643-eq4
or downstream deceleration of the EUC against an average westward PGF (or downstream acceleration of the Hisard jet), and local accelerations in the directions of instantaneous, subgrid-scale, momentum flux divergences.

5. Discussion

a. Dynamics of the Hisard jet and EUC

Some equatorial theories have demonstrated that subsurface currents may be derived without large stresses in the pycnocline (Veronis 1960; Stommel 1960). The models require only that wind-forced equatorial trapped wave modes project onto the stratification (Moore and Philander 1978), giving a wavelike force balance on short timescales (Zhang and Rothstein 1998; Richardson et al. 1999) and a steady-state balance between the zonal PGF and viscous drag on long timescales (McCreary 1981; Yu and Schopf 1997). Including advection leads to an inertial balance with the PGF (Charney 1960; Pedlosky 1998). Gill (1971) was able to formulate a linear model for the EUC in which no PGF was required, but horizontal eddy viscosity dominated over vertical eddy viscosity.

The results here showed that subgrid-scale stresses were more variable than the PGF in depth and time, however. Their effect appeared to vanish in the averaging process even though they dominated the time-dependent accelerations. Bryden and Brady (1985) and Johnson and Luther (1994) also found large residuals in the zonal momentum budget on the equator. In addition, Hebert et al. (1991) showed that, although the wind-stress-to-PGF balance holds for the vertically averaged circulation on seasonal and longer timescales, the vertical structure of the currents shows variability in the momentum flux divergences on shorter timescales.

In a previous analysis of some of the same data used here, Cronin et al. (2000) concluded that the PGF dominated the forcing of the upper equatorial ocean. However, the results were obtained by assuming no PGF at 500 m, which Kennan and Niiler (2003) have shown is inappropriate on the equator.

Large stresses from IGW and turbulent fluxes exist on all timescales in the equatorial pycnocline and are due to the shear of the zonal currents and interactions with the currents (Moum et al. 1989; Hebert et al. 1991; Lien et al. 1995; Peters et al. 1995; Sutherland 1996; Mack and Hebert 1997; Sun et al. 1998). When models parameterize subgrid-scale momentum flux divergences as viscous, they eliminate the possibility of a reverse cascade of energy from the small to large scales [unless the scales are explicitly resolved, as in large eddy simulations (Wang et al. 1998; Skyllingstad et al. 1999.) Dillon et al. (1989) found that the large turbulence observed during the Tropic Heat Experiment did not balance the momentum budget for the central Pacific, suggesting that the dissipation method may be flawed. The dissipation method does not allow for the advection or storage of turbulent energy, ignoring all accelerating stress divergences.

b. Eddy viscosity parameterizations

Acceleration of subsurface jets by subgrid-scale momentum flux convergences implies that subgrid-scale processes cannot be represented in numerical models by parameterizations that require positive eddy viscosity coefficients. In analogy with viscous stresses, the Reynolds parameterization for stresses assumes proportionality to the mean shear: σ = −ρ0() ∼ ρ0AUz, where A is an eddy viscosity. In the surface layer the subgrid-scale stresses were usually the same sign as the shear, implying a positive coefficient (Fig. 4). However, the stress and shear were often of opposite signs in the pycnocline, requiring a negative coefficient (A was calculated, but the results were highly unstable, varying from order 0.001 to 10 m2 s−1).

The eddy-to-mean-kinetic-energy transfer term (Fig. 4f) is parameterized as −ρ0()Uz = ρ0A | Uz | 2. Because the squared shear is positive definite, the reverse energy cascade requires a negative eddy viscosity coefficient. This requirement is true even if the stress divergence is parameterized as ρ−10σzAUzz + AzUz. Consider an idealized eastward current centered at depth −z0, with a nondimensional vertical speed profile given by u(z) = sech(zz0), and a curvature of uzz(z) = u0[1 − 2 sech(zz0)2] (Fig. 7). Because uz = 0 and uzz < 0 at the current core, A must be negative for a local eastward acceleration; positive viscosity weakens the core because uzz > 0 on the flanks. In the term (AzUz), the shear is negative (positive) above (below) the core, and so a positive acceleration can only be achieved away from the core by a negative (positive) viscosity gradient above (below). This requirement implies a viscosity profile peaking at the flow maximum, where microstructure measurements show a minimum in dissipation.

Other geophysical flow phenomena that are inconsistent with positive eddy viscosities include the midlatitude jet stream of the earth's atmosphere (e.g., Lindzen 1981; Holton 1979, chapter 10) and evidence for eddy-to-mean-flow transfers in the Gulf Stream recirculation and Kuroshio extension (Bryden 1982; Hall 1991). On Jupiter, banded zonal jets gain their mean energy and momentum from smaller-scale convective eddies (Ingersoll et al. 1981, 2000).

To summarize the scenario being suggested: the existence of subsurface, zonal currents along the equator must be attributed to divergence of the subgrid-scale momentum fluxes. These fluxes likely include the effects of IGW interacting with the shear flow and deep-cycle turbulence. A PGF is not required for the direction of a zonal equatorial current; instead, the steady state of a flow balance that has a net downstream acceleration sets up an appropriate downstream pressure gradient. If a “pure” water parcel could be followed, the concept of a Reynolds decomposition would be moot, with material acceleration exactly balanced by the PGF and molecular dissipation. Alternatively, from the perspective of the IGW field, the “eddies” are the isotropic turbulence, which is to some order represented well by the Reynolds decomposition and can be described using established parameterizations. The need to understand the dynamics of currents on scales larger than those of the microscale and IGW field gives rise to concepts such as negative viscosity and the forcing of currents by momentum flux divergences.

c. Implications for El Niño

Although it is known that the history of WWE forcing is important for the ocean response away from the equator (Smyth et al. 1996), the importance of wind-burst timing on the equator, in the absence of a Coriolis force, has not been addressed. The results presented here have shown that during a succession of wind events on the equator the wind stress penetrated progressively deeper, exceeding the halocline depth and even reaching the main pycnocline. The halocline migrated to the depth of the thermocline so that the multiple pycnocline structure of the warm pool was pushed to 100-m depth and partially merged into one intense pycnocline. Other isolated WWEs failed to push the halocline below about 50-m depth or to erode the multiple pycnocline structure. Thus, the upper-ocean density structure was sensitive to both the magnitude and sequence of WWEs.

The merger of the shallow halocline with the thermocline coincided with the formation of major downwelling events that were observed to propagate as Kelvin waves across the Pacific in late 1992 to early 1993 by satellite and the TAO (Boulanger and Menkes 1995) and were probably responsible for the reinitiation of the ongoing ENSO event at that time (Goddard and Graham 1997). Thus, the onset of El Niño may depend on the local occurrence, in the warm pool, of sequential wind events that erode the barrier layer. The merging of the halocline with the main thermocline may be related to the ability of strong wind events to force downwelling Kelvin pulses capable of initiating a persistent warming in the eastern Pacific.

6. Conclusions

The depth of penetration of the wind stress—momentum depth—and the zonal momentum balance over the upper 270 m on the equator at 156°E in the western equatorial Pacific warm pool have been estimated for the time period of May–December of 1992. Submeso scale stress divergence was estimated using a no-turbulent-stress condition for the zonal momentum flux at the EUC core.

The momentum depth deepened during successive wind events, often exceeding the MLD and reaching through the pycnocline. Thus momentum transfer from the wind was not limited to the depth of density homogenization. The shallow halocline deepened along with the momentum depth during successive WWEs, whereas it remained fairly constant during isolated events. In support of the hypothesis that multiple, shallow pycnoclines in the warm pool form a barrier layer to mixing by the wind (Lukas and Lindstrom 1991), successive events were needed before the shallow pycnocline was eroded and vertical momentum transfer reached below 50-m depth. As a consequence, it is possible that the timing of WWEs and the subsequent response of the upper-ocean thermal structure play crucial roles in the ability of the atmosphere to initiate El Niño events.

The momentum balance revealed that local, time-dependent accelerations of the zonal currents were driven by the vertical stress divergence at all depths. In the surface layer, these were consistent with the vertical turbulent transfer of the zonal momentum input by the wind. In the pycnocline, the implied eddy viscosity was negative, with a momentum transfer cascade from small scales to large scales. The acceleration of subsurface jets by momentum flux divergences may be related to the rectification of wave events such as Kelvin pulses forced by wind events or internal gravity waves radiating from shear instabilities.

The current paradigm for subsurface equatorial circulation is incomplete. Whereas the long-term, steady-state balance for the subsurface flows involves balances among downstream acceleration, turbulent drag, and the PGF, the time-dependent forcing occurs on the submesoscale—scales smaller than the deformation radius and subgrid from the perspective of the present observations. The pressure field continually adjusts to balance the total acceleration and momentum flux divergence patterns, and the flow direction is the result of the net effect of the transient forcings. The steady-state drag on the currents is the small residual of large, instantaneous accelerations.

A complete predictive theory for the response of equatorial currents to wind forcing will need to account for the history of wind forcing, the barrier-layer response to this forcing, the deepening of the momentum depth beyond the depth of the scalar mixed layer, and the occurrence of negative eddy viscosity phenomena in the pycnocline forcing localized zonal currents. The latter likely include the interactions between the IGW field and deep-cycle turbulence, as well as submesoscale processes that have yet to be described.

Acknowledgments

This work was supported by National Science Foundation Grant OCE-9613771. Data were generously provided by R. Weisberg, TAO Project Office (M. McPhaden, director), R. Lukas, and AVISO. Preliminary results were presented at the COARE98 meeting in Boulder, Colorado, in July of 1998. Thanks are given to E. Kunze, A. Yankovsky, and two anonymous reviewers for detailed comments on the manuscript; G. Veronis, B. Saltzman, and a reviewer provided insights concerning IGW and dissipative mechanisms.

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Fig. 1.
Fig. 1.

Time series of winds and upper-ocean structure for 0–270 m and May–Dec 1992 (DOY 130–360) at 156° and 157.5°E on the equator: (a) zonal (solid line) and meridional (dashed line) wind components, (b) temperature (°C), (c) salinity, (d) zonal velocity (m s−1), (e) meridional velocity (m s−1), (f) depths of buoyancy frequency maximum (solid), thermocline (dashed), and halocline (dotted), and (g) mixed layer (dashed), EUC core (dotted), and momentum depth (solid). Contour intervals are 4°C for temperature (dashed contour at 29°C), 0.5 for salinity (dashed contour at 35.2), and 0.20 m s−1 for velocity. Shaded curves in (f) and (g) show depth range of pycnocline

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2643:TEOWFA>2.0.CO;2

Fig. 2.
Fig. 2.

Terms of the zonal momentum balance for 0–270 m and May–Dec 1992 (DOY 130–360): (a) τx (solid line) and σ | h(Pa) (dashed), (b) ut, (c) ∇ · (uu), (d) Du/Dt, (e) −gη̂x, (f) −ρ−10Px, and (g) ρ−10∇·Ŝ. Contour intervals are 4 × 10−7 m s−2

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2643:TEOWFA>2.0.CO;2

Fig. 3.
Fig. 3.

Histograms of the scaling exponent s for (a) ux, s(x) = log10( | ux/UX | )/log10(x/X), (b) (uu)x, s(x) = log10( | (uu)x/(UU)X | )/log10(x/X), and (c) (uu), s(t) = log10( | (uu)/(UU) | )/log10(t/T), where x = 167 km (156°–157.5°E), X = 2000 km (147°–165°E), t = 1 h, and T = 1 day

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2643:TEOWFA>2.0.CO;2

Fig. 4.
Fig. 4.

Estimates of the vertical subgrid-scale stress and energy conversions for 0–270 m and May–Dec 1992 (DOY 130–360): (a) eddy stresses [−ρ0()], (b) no-stress method [σ | h = −ρ0() | h], and mean-to-eddy energy conversion through the vertical eddy stress (σUz) estimated using (a) and (b). Contour intervals are 2.5 × 10−2 Pa for the stresses and 0.25 m W m−3 for the energy conversion

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2643:TEOWFA>2.0.CO;2

Fig. 5.
Fig. 5.

(a), (f) Average zonal momentum budget separated into locally accelerating and decelerating flows for the (a)–(e) surface and (f)–(j) subsurface; (b), (g) u > 0, ut > 0; (c), (h) u > 0, ut < 0; (d), (i) u < 0, ut > 0; and (e), (j) u < 0, ut < 0. Dashed boxes represent averages for material accelerations: (b), (g) u > 0, Du/Dt > 0; (c), (h) u > 0, Du/Dt < 0; (d), (i) u < 0, Du/Dt > 0; and (e), (j) u < 0, Du/Dt < 0

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2643:TEOWFA>2.0.CO;2

Fig. 6.
Fig. 6.

Profiles of momentum balance terms (cm s−1 day−1) for various forcing conditions: (a) WWE decelerates surface westward flow, Hisard jet accelerates westward (DOY = 293); (b) WWE accelerates Yoshida jet, Hisard jet accelerates westward (DOY = 300); (c) westward PGF extends into pycnocline, Yoshida jet decelerates (DOY = 312); (d) eastward acceleration of EUC, strongest WWE (DOY = 316); and (e) westward acceleration of Hisard jet, no WWE (DOY = 323). Terms are ut (shaded curve), Du/Dt (solid), σz/ρ0 (dotted), and −Px/ρ0 (dashed)

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2643:TEOWFA>2.0.CO;2

Fig. 7.
Fig. 7.

Profiles of the zonal velocity (solid curve), vertical shear (dotted), and curvature (shaded) for a nondimensional, eastward current given by u(z) = sech(zz0)

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2643:TEOWFA>2.0.CO;2

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