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    The time-mean sections of ADCP velocity and CTD density from an MLR spanning longitudes 170°–110°W. The regression simultaneously fit a time mean and a zonal trend at each depth–latitude. Negative contours in this and subsequent figures are dashed

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    The time location of equatorial ADCP sections used in the present study as a function of year and time within the year. Symbol color corresponds to the approximate longitude of each section

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    Variance-preserving spectra of meridional and zonal velocities from equatorial MCMs at four longitudes

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    The 13–30-day-period bandpassed meridional velocity at 25-m depth from equatorial MCMs. Superimposed are the covariances of bandpassed meridional velocity with bandpassed zonal velocity and temperature (green and red, respectively), further smoothed to 62-day period for clarity. Yellow crosses denote the equatorial crossing times (as in Fig. 2) of ADCP sections within 17° longitude of each MCM location

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    The satellite-derived surface currents of BL02 sampled at the equator and plotted as a function of longitude and time. Superimposed are the time/longitude locations of the ADCP sections

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    Monthly sections of seasonally averaged zonal velocity composited from the residuals of the MLR of Fig. 1 and smoothed cyclically around the year to suppress periods shorter than 120 days

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    (Continued )

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    Seasonal ADCP velocities as in Fig. 6, but for the equator at various depths. Superimposed dashes are the equivalent seasonal analyses of MCM velocities trapezoidally averaged between longitudes 170°–110°W

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    Seasonal ADCP velocities as in Fig. 6 but plotted at 20-m depth as a function of time and latitude. Shown are velocities (top) with and (middle) without the time mean added in, and (bottom) bootstrap-derived rms errors

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    Seasonal velocities in Fig. 8 but for the satellite-derived surface currents of BL02, composited from 6 Oct 1992 through 26 Dec 2001

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    The SOI calculated traditionally as the normalized difference in standardized sea level pressures at (top) Tahiti and Darwin and (bottom) using pressures within 5° latitude of the equator in the eastern Pacific and Indonesia

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    Equatorial SOI from Jul 1990 to Jun 2001 plotted as a function of season, with the 170°–110°W ADCP section times marked on each year trace as crosses. Colors denote the ENSO phase assigned to each section, determined by 1.0-sigma thresholds of the equatorial SOI

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    (a) The composited ADCP velocities (cm s−1) for ENSO warm phase, smoothed from Jul through Jun to suppress periods shorter than 180 days. The time mean (Fig. 1), zonal trend, and seasonal composite (Fig. 6) of all ADCP data were previously removed. (b) The rms errors of the warm-phase composite [(a)]

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    (Continued )

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    As in Fig. 12a, but for the ENSO cold phase. (b) The rms errors of the cold-phase composite [(a)]

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    (Continued )

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    ENSO warm- and cold-phase composited velocities as in Figs. 12 and 13, but plotted at 20-m depth as a function of time and latitude. Shown are velocities (top) with and (middle) without the time mean and seasonal cycle added in

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    The 25-m zonal velocities from equatorial MCMs spanning the period Jul 1979–Jun 2002. Data are anomalies after removal of the time mean and seasonal cycle (Fig. 7) at each longitude and are plotted as a function of season with ENSO phase color coded as in Fig. 11. The average for each ENSO phase is superimposed in heavy lines

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    The covariance of nearby ADCP zonal velocities with de-meaned, normalized instability indices constructed from 13-30-day meridional velocities at the 110°, 140°, and 170°W moorings (i.e., Fig. 4; see text). Contour intervals are 5 cm s−1 for covariance velocity and 2 cm s−1 for the bootstrap-derived rms errors. Zero contours are suppressed for clarity

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    As in Fig. 16, but for covariance of ADCP meridional velocities with MCM instability indices

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    As in Fig. 16, but for covariance of squared ADCP meridional velocities with MCM instability indices. Contour intervals are 200 cm2 s−2 for both covariance and rms errors

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    As in Fig. 16, but for covariance of the product of ADCP zonal and meridional velocities with MCM instability indices. Contour intervals are 100 cm2 s−2

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    As in Fig. 16, but for covariance of the product of ADCP meridional velocity and CTD densities with MCM instability indices. Contour intervals are 2 cm s−1 (kg m−3)

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    Typical eddy energy production values estimated by multiplying the covariances of Figs. 19 and 20 by gradients of background flow fields constructed by summing the mean flow (Fig. 1) with the instability-correlated flow (e.g., Fig. 16). Contour intervals are 200 × 10−6 ergs (cm3 s)−1, or 2 × 10−3 W m−3

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    Composited ADCP meridional and zonal velocity means for high- and low-instability periods, defined as periods in which the instability index has a magnitude greater than 0.5. Also shown are the covariances between the residual meridional and zonal velocities and between residual meridional velocity and CTD density for each composite period. Error bars are rms errors derived from bootstrap calculations

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    Monthly zonal flow anomalies from BL02's satellite-derived surface currents averaged over 10° longitude around 110° and 140°W, selected for periods having instability indices greater than 1.6. Also shown are the 6 Oct 1992 through 7 Jul 2001 time mean flows for comparison

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    Two individual ADCP sections from times/locations corresponding to unstable monthly profiles in Fig. 23. The 110°W section corresponds to the atypical monthly profile at 110°W in Fig. 23 having westward anomalous flow at 5°N; the 140°W section shows a more typical current structure during strong instabilities

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Tropical Instability Wave Variability in the Pacific and Its Relation to Large-Scale Currents

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  • 1 Earth and Space Research, Seattle, Washington
  • | 2 Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire
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Abstract

Shipboard acoustic Doppler current profiler (ADCP)-derived zonal currents from 170° to 110°W are assembled into composite seasonal and ENSO cycles to produce detailed representations of large-scale ocean flow regimes that favor tropical instability waves (TIWs). The instability-favorable portion of these cycles, namely, the August– October period of the seasonal cycle and the pre-December period of the ENSO cold phase, both have intense westward flow in the South Equatorial Current, most particularly the branch north of the equator (SECN), and strengthened eastward flows in the North Equatorial Countercurrent (NECC) and the Equatorial Undercurrent (EUC). Taken together these flows enhance current shear in the two regions generally associated with TIW activity, namely, the cyclonic and anticyclonic shear regions located to the south and north of the SECN, respectively. Direct correlation of ADCP currents and CTD densities to an instability index derived from equatorial 13–30-day meridional velocities confirms the importance of the strengths of the SECN and NECC in determining the timing of TIW events. Very little correlation was found in the EUC, implying that its strength is not a determining factor in such timing. Reynolds stress and density flux calculations indicate that in a time-averaged sense TIWs derive energy from both the cyclonic and anticyclonic flanks of the SECN, and from both sides of the equatorial cold tongue. During low-instability periods these Reynolds stresses and fluxes substantially vanish, indicating that eddy energy production ceases. This is in marked contrast to Baturin and Niller's study, which indicated that eddy energy production was relatively continuous at 110°W. The current structures of individual months associated with TIW activity show substantial variability among themselves. Combined with previous findings of multiple modes of instabilities, this indicates that caution is required when attempting to model instabilities from averages of observed background flows such as those presented here.

Corresponding author address: Eric S. Johnson, Earth and Space Research, 1910 Fairview Ave. E., Suite 210, Seattle, WA 98102. Email: ejohnson@esr.org

Abstract

Shipboard acoustic Doppler current profiler (ADCP)-derived zonal currents from 170° to 110°W are assembled into composite seasonal and ENSO cycles to produce detailed representations of large-scale ocean flow regimes that favor tropical instability waves (TIWs). The instability-favorable portion of these cycles, namely, the August– October period of the seasonal cycle and the pre-December period of the ENSO cold phase, both have intense westward flow in the South Equatorial Current, most particularly the branch north of the equator (SECN), and strengthened eastward flows in the North Equatorial Countercurrent (NECC) and the Equatorial Undercurrent (EUC). Taken together these flows enhance current shear in the two regions generally associated with TIW activity, namely, the cyclonic and anticyclonic shear regions located to the south and north of the SECN, respectively. Direct correlation of ADCP currents and CTD densities to an instability index derived from equatorial 13–30-day meridional velocities confirms the importance of the strengths of the SECN and NECC in determining the timing of TIW events. Very little correlation was found in the EUC, implying that its strength is not a determining factor in such timing. Reynolds stress and density flux calculations indicate that in a time-averaged sense TIWs derive energy from both the cyclonic and anticyclonic flanks of the SECN, and from both sides of the equatorial cold tongue. During low-instability periods these Reynolds stresses and fluxes substantially vanish, indicating that eddy energy production ceases. This is in marked contrast to Baturin and Niller's study, which indicated that eddy energy production was relatively continuous at 110°W. The current structures of individual months associated with TIW activity show substantial variability among themselves. Combined with previous findings of multiple modes of instabilities, this indicates that caution is required when attempting to model instabilities from averages of observed background flows such as those presented here.

Corresponding author address: Eric S. Johnson, Earth and Space Research, 1910 Fairview Ave. E., Suite 210, Seattle, WA 98102. Email: ejohnson@esr.org

1. Introduction

a. Background

Since Duing et al.'s (1975) discovery that the large-scale current systems of the tropical oceans supported wavelike instabilities [hereinafter Tropical Instability Waves (TIWs)], substantial research has focused on the energetics of these waves as a key to understanding their dynamics, their intermittency in time and space, and their effects on the larger flow. Such understanding requires reliable knowledge of both the wave motions themselves and the slower, larger-scale flow on which they grow, and it has been approached through both observations and model simulations.

Philander (1976, 1978) provided the first simple model of instabilities on a shear flow resembling surface currents in the equatorial mid-Atlantic Ocean and found barotropic instabilities that resembled early observations in form and period. Cox (1980) described comparable shear instabilities generated in a general circulation model (GCM) of the Pacific Ocean driven by average seasonal-cycle winds. Hansen and Paul (1984) used drifter observations to provide the first detailed observation of the waves' eddy fluxes and energetics and noted that the wave-induced fluxes had a large effect on the local heat budget. Philander et al.'s (1986) GCM simulation emphasizes that the model TIWs are highly inhomogeneous in both space and time. Weisberg and Weingartner (1988) using moored current-meter (MCM) observations in the Atlantic showed that TIWs act to reduce both the shear of the larger currents and their thermal structure, thus deriving energy from several source mechanisms.

While it was generally agreed that current shear (i.e., barotropic generation) was the larger source of eddy energy, controversy arose over where exactly in the highly structured tropical current system this generation arose. The modeled instabilities of Philander (1978) and Cox (1980) and the observed instability of Flament et al. (1996) derived energy from the anticyclonic shear between the westward-flowing South Equatorial Current (SEC) spanning the equator and the eastward-flowing North Equatorial Countercurrent (NECC) around 7°N (Fig. 1). Hansen and Paul (1984), Philander et al. (1986), and Weisberg and Weingartner (1988) found larger eddy energy generation in the cyclonic shear region nearer the equator, between the Northern Hemisphere part of the SEC (SECN) and the intruding eastward flow of the Equatorial Undercurrent (EUC). The Tropical Instability Wave Experiment (TIWE; Qiao and Weisberg 1995), was intended to be the definitive experiment, but unfortunately mooring failures limited it to sampling only the near-equatorial, cyclonic shear region. Luther and Johnson (1990, henceforward LJ90) further complicated the picture by finding evidence of three different instabilities, distinct in frequency, time, and location, within a single year of data collected by the North Pacific Experiment (NORPAX) around 150°–158°W. McCreary and Yu (1992) also found three instabilities in a 2.5-layer model, two of which appeared similar to those observed by LJ90. In an effort to identify the large-scale flow structures associated with instability waves, Baturin and Niiler (1997, henceforward BN97) divided 15 yr of surface drifter data into instability-on and instability-off periods using 15–30-day meridional velocity variability from equatorial MCMs as a metric of instability activity. They found that the instability-on periods at 110° and 140°W were characterized by stronger flow in both the SEC and NECC, with eddy energy production occurring on both sides of SECN. The subsurface flow, however, was not sampled.

Further exploring the relationship between TIWs and the background flow, Proehl (1996) imposed two of LJ90's observed background flows on an equatorial channel model and succeeded in reproducing the associated instabilities and their wave-mean flow energetics. He interpreted his results in terms of one-dimensional overreflection theory [see Lindzen (1988) for an overview], which views an instability as a growing oscillation trapped between two turning latitudes, one of which shields a nearby critical layer. The shielded critical layer is the source of unstable growth; a wave is able to approach the critical region and amplify by drawing energy from the larger flow, yet reflect from the turning latitude and emerge again within finite time. This understanding makes clear the need for accurate, closely sampled background flow information, both to fully demonstrate the physics associated with instability and to distinguish between multiple modes of instability in situations that afford multiple turning latitudes and critical layers.

b. Present approach

This paper is the first of two intended to assemble closely sampled observations of tropical background flow under various conditions and to model the associated instability waves. The overall focus is to provide an analysis of wave dynamics sufficiently detailed that theoretical interpretations such as overreflection can elucidate not only the effects of wave-mean flow interaction (such as eddy fluxes and mean to eddy energy conversion), but link them to the actual structures of background flow that engender instability and hence determine the instabilities' wavelength, period, growth rate, etc.

This present paper focuses on producing the detailed observations of background flows associated with instability. While data are insufficient to provide exact background flows associated with specific instability wave modes, we will be able to characterize in general which flow features are important to the time variability of TIW processes. Subsequent modeling efforts will require close sampling in latitude and depth; thus we rely on equator-crossing sections of shipboard acoustic Doppler current profiler (ADCP) and CTD data to determine the structure of background flows, with satellite-derived surface currents and equatorial MCMs providing broader content through their comprehensive sampling. The substantial high-frequency variability in the equatorial oceans, due in part to TIWs themselves, prevents the sparse, discretely sampled shipboard data (Fig. 2) from resolving the background currents in time with a fidelity sufficient for the present purposes. For example, attempts to smooth the ADCP data in time and longitude to define an approximate background flow throughout the study period were unable to convincingly track low-frequency variability more reliably measured by the continuously sampled MCMs. Thus our requirement for close resolution in latitude and depth forces us to relinquish time resolution and consider composited current structures from flow regimes known to favor TIW activity.

Both the boreal autumn portion of the seasonal cycle and the cold phase of the El Niño–Southern Oscillation (ENSO) are known to engender strong TIW activity (Philander et al. 1985); thus we begin by compositing these structures. Since TIWs are sporadic even within such instability-favorable periods (e.g., Philander et al. 1986), we then utilize directly calculated covariances between local TIW amplitudes and broader-scale currents to define more precisely the relevant current features. Last, we emphasize that even flows believed to harbor strong TIW activity exhibit a certain amount of variability among themselves, apparently because of the multiple modes of instability found previously and the possible propagation of energy from other regions. Nevertheless, at the cost of blurring together all such unstable flows, our composite structures can at least identify those features common to all or most such flows.

2. Data

a. ADCP

The ADCP data used here consist of roughly meridional sections spanning the tropical Pacific from 8°S to 15°N. Data were extracted from cruises of the U.S. Joint Global Ocean Flux Study (JGOFS) Equatorial Pacific Process Study (Murray et al. 1995), the World Ocean Circulation Experiment (WOCE; Firing et al. 1998), the Tropical Atmosphere–Ocean (TAO) mooring maintenance cruises [years 1991–95 from Johnson and Plimpton (1999); last 6 yr provided by E. Firing (2002, personal communication)], and the Tropical Ocean Climate Study (TOCS; Kashino et al. 2001). The JGOFS data and early TAO data were processed as in Johnson and Plimpton (1999); the remaining data were acquired from the National Oceanographic Data Center (NODC) shipboard ADCP archive and were processed by various investigators as referenced in the individual data metafiles. Here we have gridded the 1–5-min time-averaged data into 0.5°-latitude bins, substantially reducing instrument noise while retaining good meridional resolution of the large-scale currents. The sections are scattered across the Pacific Ocean with generally no more than two or three sections per year available at an individual longitude (Fig. 2). Occasional gaps of up to 1.5° latitude were interpolated using a combination of beam and Laplace's equations, which gave smooth interpolations without overshoot.

b. CTD

The CTD data were collected and prepared by the TAO project as reported in Johnson et al. (2000) and the JGOFS Equatorial Pacific Process Study (Murray et al. 1995). They are available generally at 1°-latitude intervals along the shipboard sections and were interpolated to the 0.5°-latitude grid using beam/Laplace interpolation as above. Data coverage is sparse before 1993, and also poleward of 10°N. CTD salinities, temperatures, and pressures are combined here into σθ-relative 0 dbar as our measure of density.

c. MCM

Daily averaged MCM data were available continuously from TAO moorings on the equator at 110°, 140°, and 170°W and 165°E. We use the mechanical current-meter data where available, generally before 1999 at 110°W, 140°W, and 165°E, and moored ADCP data otherwise. Occasional data gaps were filled from the two nearest instrument depths using a least-mean-square error estimator constructed using historical data correlations, then adjusted in amplitude to preserve the target depth's historical variance. Only estimators demonstrating a historical correlation to the target data of 0.85 or better were used. These estimated time series were substituted directly into data gaps in the case of meridional velocity, but for zonal velocity were faired into the adjoining data by adding a linear trend to make the estimate match the three days of observations at either end of the gap. This allows for long-term time changes of zonal velocity's vertical shear, which can be substantial and are important to the present research. The same process was used to extrapolate moored ADCP data upward to 25-m depths; generally only 5–10-m extrapolations were required.

Near-surface meridional velocity is dominated by TIW activity at approximately a 20-day period (Fig. 3), while zonal velocity contains additional variability at lower frequencies, including various equatorial waves, the seasonal cycle, ENSO, and so on. We isolate TIW activity from extraneous frequencies by bandpassing to retain periods between 13 and 30 days (Fig. 4). TIW momentum and heat fluxes are estimated by simply multiplying together the appropriate bandpassed time series and smoothing the result to suppress periods shorter than 63 days to half-amplitude or less; such smoothing is required to give meaningful estimates of variance or covariance, which by definition are time-averaged quantities. The resulting time series have 30-day resolution, or 2 degrees of freedom per half-amplitude period. As in BN97 we use a normalized time series of meridional velocity amplitude to measure TIW activity. We complex demodulate (e.g., Tsai et al. 1992) meridional velocity in the 13–30-day band to form time series of amplitude and phase relative to its center frequency. We further smooth the amplitude series of 63-day periods as above. Complex demodulation gives amplitudes very similar to those obtained by simply squaring the bandpassed time series and smoothing (as for the covariance calculations above). Nevertheless it has the added advantage of also estimating the wave's local phase, and hence through a time derivative its local frequency. Because this will be pertinent to the follow-on paper, we introduce the analysis now for consistency.

d. Satellite-derived surface currents

The satellite-derived surface currents of Bonjean and Lagerloef (2002, henceforward BL02) are used to evaluate changing background flows on time scales relevant to individual instability wave packets, thus providing a context for the discretely sampled ADCP data (Fig. 5). As in Lagerloef et al. (1999, henceforward LMLN99) these are surface layer velocities calculated from satellite vector winds and altimeter sea surface height using algorithms tuned to reproduce the motion of 15-m drogued drifters. The mean pressure gradient, unavailable from altimeter data because of uncertainties in the geoid, is adjusted to match Levitus and Boyer's (1994) climatology. BL02 improved LMLN99's treatment of geostrophy near the equator, where the Coriolis parameter goes to zero. They also developed a more realistic model for vertical shear including the effects of both wind stress and horizontal density gradients, the latter inferred from gradients of sea surface temperature (SST). The resulting currents compare well to large-scale currents measured by MCMs and drifters but do not resolve variability at TIW time and space scales. Thus we use them only for estimates of large-scale background flows.

3. Composite current structures

a. Motivation

Both the seasonal and ENSO cycles compose substantial portions of the large-scale, low-frequency tropical current variability (Fig. 5), which allows robust estimation of their structure and time progression. Our work here extends and modifies the efforts of Johnson et al. (2002, henceforward JSKM02), who provided comparable analyses using substantially the same data. We allow for more realistic time variability in both the seasonal and ENSO cycles (see discussion section) and choose the longitude range 170°–110°W to focus on the eastern Pacific where TIWs are prevalent. This results in seasonal and ENSO cycles reasonably representative of local conditions while still minimizing the occurrence of poorly sampled months (Fig. 2).

b. Multiple linear regression

Prior to analyzing the time variability we use a multiple linear regression (MLR) to fit a mean and zonal trend to the ADCP data at each depth and latitude (Fig. 1; see Johnson and Luther 1994). The zonal trend accounts to first order for the longitudinal variability of the data. Following removal of the mean and trend we are able to analyze the residual currents with less concern for zonal variability. Nevertheless when averaging over the full longitude range some vertical smearing of time-dependent processes results, since in general these have vertical scale following thermocline depth, which increases from east to west. For processes that vary strongly in longitude (e.g., TIW statistics) we average over shorter longitude ranges.

c. Seasonal composite

Following removal of the MLR mean and zonal trend (Fig. 1) we form a seasonal composite from the residual currents. The data are arranged in a series by time of year, then are smoothed cyclically around the year with a Gaussian-shaped filter that suppresses periods shorter than 120 days to half-amplitude or less, giving a time resolution of 60 days. The resulting seasonal anomalies of zonal currents are strongly surface trapped (Fig. 6). The strongest anomalies in April–July are characterized by anomalous eastward flow at and north of the equator (strengthening the EUC while weakening the overlying SEC; see Fig. 1). Paired with the near-equatorial eastward anomalies are westward (weakening) anomalies farther north in the NECC. The remainder of the year has anomalies of approximately opposite sign and weaker magnitude. Above 150-m depth this seasonal composite captures 23% of the total current variance, with the remainder distributed among lower (e.g., ENSO) and higher (intraseasonal oscillations and other equatorial waves, TIWS, etc.) frequencies. Despite the ADCP data's scattered time sampling its seasonal composite compares well at most depths to equivalent seasonal cycles extracted from equatorial MCM data (Fig. 7). The ADCP composite's spring surge extends slightly deeper (e.g., at 116-m depth during June–July) probably because the ADCP data available during these months are strongly biased toward the west Pacific (Fig. 2), where both the thermocline and the penetration of seasonal variability are deeper. Comparison is relatively poor during December–January because of the paucity of ADCP data there.

Since the seasonal composite is surface trapped and strongly coherent in the vertical direction, the preponderance of its variability can be represented by 20-m-depth velocities (Fig. 8). Such a view makes clear that seasonal variations are comparable in magnitude to the near-surface mean flow, and again that velocities around the equator are paired in time with oppositely signed velocities in the NECC. Note that the positive and negative velocity extremes at a given latitude are separated by only 3–4 months in time, not the 6 months of a pure sinusoidal signal. Standard errors, constructed at each time from the filter-weighted variance of the composited data about the composite mean, indicate that in general the seasonal composite is statistically significant at two standard errors or more, though the paucity of data through December and January make the calculation there largely an extrapolation with potentially large errors. The latitude and time structure of the composited ADCP currents compare very well to an equivalent seasonal composite of BL02's surface currents (Fig. 9), though BL02's amplitudes are somewhat smaller because of their heavy smoothing in latitude. Similar agreement is found with the GCM seasonal cycle of Harrison et al. (2001b) at 140°W, the only substantive difference being the somewhat deeper penetration of the ADCP seasonal variability at the equator (also noted in Fig. 7) and a weaker EUC probably attributable to our zonal averaging. All these satisfactory comparisons indicate that the sporadic ADCP sampling has not unduly compromised this analysis, and that the December–January data gap has been adequately bridged.

The instability-favorable period of August–October is characterized by increasing strength in both the SECN and the NECC, with correspondingly stronger shears between (Fig. 8). Shear between the SECN and the EUC also strengthens in this period (Fig. 6), though not as much. Thus the structure of the seasonal cycle supports increased shear (and presumably increased eddy energy conversion) in both regions identified as potential sources for TIWs, that is, in the cyclonic and anticyclonic shear regions south and north of the SECN, respectively.

d. ENSO composite

The Southern Oscillation index (SOI) traditionally is used to characterize the basinwide state of ENSO (Fig. 10). For our purposes we use an equatorial version of the index (EQSOI) that more closely reflects variability across the equatorial Pacific. (EQSOI is the standardized difference between near-equatorial pressure anomalies in the eastern Pacific and Indonesia; see Kousky 2004.) As above we select ADCP sections between 170° and 110°W and remove the previously fitted MLR mean and zonal trend. For each section we use then-current values of EQSOI to determine the approximate ENSO state (Fig. 11). We then average warm, normal, and cold sections together into composites of the respective ENSO phases. How one constructs such a composite is a matter of legitimate debate. The simple assumption that currents vary linearly with SOI (e.g., JSKM02) turns out to neglect lowest-order time variation of currents within each ENSO event. Since ENSO events are known to be largely phase locked to the seasonal cycle, and have extremes occurring around December–January (Fig. 11), one can with some justification simply form a composite year for each of the cold, normal, and warm ENSO phases (e.g., Rasmusson and Carpenter 1982). Objections have been raised to such analyses (e.g., Wallace et al. 1998), not least in that it obscures real differences between the sampled events. Additional concerns arise here, where sporadic sampling results in different parts of the ENSO composite being contributed by entirely different events (Fig. 11), most notably in the warm composite. Nevertheless, in Rasmusson and Carpenter's (1982) words, “When used with care, compositing can serve as a powerful tool for uncovering features common to a number of individual cases.”

ENSO events peak around December–January (Fig. 11); hence we composite the warm, normal, and cold data into separate years running from July through June, using an SOI magnitude of 1.0 (one standard deviation as defined by the base period) to define the ENSO phases. Compositing proceeds exactly as for the seasonal cycle, except the time smoothing is not cyclical through the June–July boundary (since ENSO is not a yearly repeating process), and the data are smoothed more heavily to suppress periods shorter than 180 days; thus time scales of 3 months and longer are retained. Bimonthly sections of warm-phase anomalous zonal velocity (Fig. 12a; dropouts due to paucity of data) begin around September with weakened SECN and EUC flow and a weakened or southward shifted NECC. Around the peak of the composite, event anomalies transform into a slight strengthening of the SECN and NECC, with the EUC still weak. The cold-phase composite (Fig. 13a), interestingly enough, begins as a negative version of the warm phase, with strengthened EUC, SEC, and NECC. Again through the peak of the event the velocities change sign, resulting in weakened flow in the SECN, the surface NECC, and this time the EUC as well. The standard errors of the warm and cold composites are large; for example, the transition period currents around January are not well observed. Nevertheless the composites' strong velocity maxima before and after the transition period are robustly observed.

The antisymmetry between the warm and cold composites is strongest in the surface layer (Fig. 14). The warm/cold anomalies are time correlated at values ranging from −0.8 to −0.96 in the SECN between 1°S and 5°N. The oppositely signed flow anomalies in the NECC are also visually antisymmetric between the two phases, though slight variations in latitudinal location of the patterns render the pointwise correlations variable. We emphasize that this antisymmetry between the two composites is inherent in the data and does not exist by statistical construction as it would for, say, an EOF analysis in which a single function models all variability. Our analysis allows a third (normal) state that is not constrained to have zero mean but that nevertheless is characterized by weak currents at the analysis noise level (10 cm s−1) except for a May–June strengthening of the EUC by ∼20 cm s−1 (not shown). Thus the data suggest that ocean currents have similar but oppositely signed dynamical responses to the two forcing regimes. Similarly, Larkin and Harrison (2002) found that tropical Pacific SST and wind stress anomalies associated with warm and cold ENSO phases are substantially inverses of one another. Their suggestion of stronger zonal wind forcing up through December in the warm phase is consistent with our stronger warm-phase currents, though the statistical significance of the difference in current strength is slight.

More relevant to the present work, when combined with the mean and seasonal cycle flows, the cold-phase anomalies during August–November produce unusually intense anticyclonic shear between the SECN and the NECC, and to a lesser extent cyclonic shear between the SECN and the EUC's eastward influence near the equator. As with the seasonal cycle this can be expected to enhance TIW activity in both shear zones. In contrast, the warm-phase anomalies weaken the otherwise instability-favorable shear regions during August–November, actually extinguishing the near-equatorial cyclonic shear entirely in September.

Establishing ENSO velocity composites' representativeness of other time periods is problematic, given the relative paucity of both data and ENSO events. MCM velocities over the past 20 yr provide a somewhat longer and certainly more closely sampled view of ENSO variability along the equator itself (Fig. 15). As Wallace et al. (1998) cautioned, individual events do vary substantially, and variation with longitude is also readily apparent, especially over the full 110°W–165°E range; yet within the region 170°–110°W it is clear that warm- and cold-phase events tend to have opposite near-surface velocities, that each phase's velocities tend to change sign around the turn of the year, and that the sign and magnitude of these velocities match those of the ADCP composites. Thus we are encouraged to accept the ADCP composites as representative at least of average ENSO characteristics throughout recent decades. This is of course sufficient for the present work, since it is precisely these events that have been observed to affect instability wave variability; thus their composite affords us an example of a flow regime favorable to TIW activity regardless of whether it is representative of future ENSO cycles.

4. Instability-correlated current structures

While the August–October portions of the seasonal cycle and the ENSO cold phase generally coincide with increased instability activity, not all their current structures are necessarily relevant to TIWs. Further, even within such favorable flow regimes, instabilities are episodic (Fig. 4). Thus we turn to a covariance analysis to identify flow features that are directly associated with instability activity.

a. Covariance analysis

Following BN97 in concept we use for an index of local TIW activity the amplitudes of complex demodulated 13–30-day meridional velocity fluctuations at equatorial moorings. The derivation of this index is detailed in the MCM data section above. While BN97 used their index to sort drifter data into high- and low-instability periods and averaged each, we form a direct covariance between our comparable index and nearby ADCP currents. This makes more efficient use of the relatively scarce ADCP data, at the cost of focusing the analysis on differences between high- and low-instability states rather than their actual values. We form a time covariance between each mooring time series and all ADCP data located within 17° longitude; since the moorings are at 110°, 140°, and 170°W this results in some overlap of the three averages. This is a reasonable accommodation to the fact that TAO cruises result in a large amount of data exactly midway between moorings. Since differences between longitudes are of the essence here we do not de-mean the entire dataset before analysis as in the seasonal and ENSO composites above; rather in the course of each longitude's calculation we de-mean the relevant set of ADCP sections, and further de-mean and normalize the instability index as subsampled to those section times:
i1520-0485-34-10-2121-eq1
where U and V are zonal and meridional ADCP velocities, Vamp is the amplitude of 13–30-day meridional velocity variations produced by complex demodulation of MCM data at each longitude (see section 2), and I is the resulting instability index. Angle brackets indicate an average over the available data, and primed quantities are the subsequent residuals. Thus the covariances UI and VI resulting from the calculation have units of velocity and represent the local current anomalies associated with one-standard-deviation departures of TIW amplitude from locally average conditions as sampled by the available ADCP data. Reynolds stresses are calculated after first removing the instability-correlated flow in order to remove the presumably slowly varying background flow from the higher-frequency stresses directly involved in TIW energetics:
i1520-0485-34-10-2121-eq2
Errors for the analysis are constructed using bootstrap techniques (e.g., Johnson and Luther 1994; Efron 1979), essentially through finding the standard deviation of our results over 200 otherwise identical calculations performed on randomized subsamples of the available data. This method is particularly appropriate here since the distribution of the instability index does not conform with any standard probability distribution as would be required in a parametric error analysis.

b. Flow structure

The strengths of the westward-flowing SECN and the eastward NECC (see Fig. 1) both have positive covariances with TIW activity at all three longitudes (Fig. 16). The covariance signal in the SECN extends surprisingly deep, well beyond the usual range associated instability activity (e.g., LJ90). This does not necessarily imply that deeper flow is relevant to instability activity, since TIW velocities and fluxes at those depths are small and any eddy energy generation very slight. Rather, the deeper flows may simply be correlated to shallower flows that are themselves directly relevant. Interestingly enough instability-correlated variability in the EUC is conspicuous in its absence: only at 170°W does EUC strength have much positive covariance with instability activity. This suggests that while the presence of the EUC may be important to instability dynamics, its strength is not a controlling factor determining their occurrence. All the observed zonal flow signals exhibit strong statistical significance in that they differ from zero by at least two rms errors. Bear in mind that the difference between typical high- and low-instability states will be 2 times the covariance signals shown, or about 50 cm s−1 for the SECN and 40 cm s−1 for the NECC.

Meridional velocity covariance with instability activity produces the typical equatorial pattern of wind-driven, meridional divergence near the surface (Fig. 17). These covariances are less significant than for zonal velocity, but again are consistent at all three longitudes.

Density covariance with TIWs (not shown) is essentially in geostrophic balance with the zonal velocity covariance, and as such includes a steepening of the meridionally sloping isopycnals. Stratification of the surface layer also decreases, especially above the thermocline trough between the SECN and the NECC where the equatorial front is located.

c. Reynolds fluxes

Meridional velocity variance is also correlated to instability activity (Fig. 18), as might be expected since our index of instability activity is itself a measure of meridional velocity variance at the equator. The instability signal is strongest off the equator, in the region from 2° to 6°N and to a lesser extent from 0° to 3°S. It is not clear from the present data whether this represents the structure of a single instability mode or variance patches contributed by several modes.

The Reynolds stress, 〈U*V*〉, is a useful diagnostic of TIW interaction with the meridionally sheared mean currents and has been found to be the largest near-equatorial mechanism of mean flow to eddy energy conversion (e.g., Hansen and Paul 1984; LJ90; Qiao and Weisberg 1998). The Reynolds stress we find associated with TIW activity (Fig. 19) is positive south of the SECN core (at about 2°–3°N; see Fig. 1) and negative to the north, in both cases moving eastward momentum into the SECN core and slowing its westward flow. While the observed values are of marginal statistical significance they are consistent at all three longitudes, and in fact deepen westward with the deepening above-thermocline layer. Around 5°N there is an intriguing hint of positive momentum flux at all three longitudes, implying that some TIW energy generated at lower latitudes may be reabsorbed into the eastward flow of NECC.

Similarly, the Reynolds density flux 〈V*σ*〉 diagnoses TIW interaction with background meridional density gradients. We find oppositely directed instability-correlated fluxes bracketing the equator of such sign as to move dense water poleward (downgradient) away from the cold tongue (Fig. 20). Again the fluxes deepen westward with the deepening thermocline; also, fluxes south of the equator are strongest to the east. Fluxes near the NECC's thermocline ridge at 10°N are confusing, with large noise levels as data quantity diminishes to the north and with inconsistent patterns among the three longitudes.

5. Discussion

a. Eddy energy production

The rate of energy conversion from mean flow to eddies by the TIWs can be estimated from the observed Reynolds fluxes and background flow gradients (e.g., LJ90). Intuitively this conversion is simply the work done against the mean flow by the eddy stresses. We calculate eddy energy production by first estimating the background flow present during TIW activity as the sum of the mean flow (similar to Fig. 1) at each longitude plus the instability-correlated flow (Fig. 16). Then we multiply the gradients of this background flow by the appropriate Reynolds flux (Figs. 19, 20) to get energy production. Bear in mind that this calculation is not strictly correct: energy production is a nonlinear quantity whose average value cannot be found by multiplying the average values of its constituent quantities. Nevertheless since the present data does not simultaneously measure both eddy fluxes and background flow no better estimate can be found. Again, because we are working with covariances the total difference between high- and low-instability states will be 2 times the correlated energy production patterns shown. The estimated barotropic energy production from meridionally sheared zonal currents is strongest to the east and large in both the cyclonic and anticyclonic shear regions flanking the SECN (Fig. 21), thus accommodating both hypotheses advanced in the literature. Baroclinic conversion from sloping isopycnals is also positive on both sides of the cold tongue where density fluxes are downgradient, though as one proceeds westward the southern region of eddy energy production diminishes and the northern region becomes dominant and larger in extent. Barotopic energy production from meridionally sheared meridional currents is relatively small and is not shown.

It cannot be demonstrated from the present data whether these various regions of eddy energy production are associated with distinct instabilities, or whether instabilities exist that derive energy from multiple regions simultaneously. The fact that baroclinic energy conversion north of the cold tongue has opposite east–west dependence from the others suggests that it at least is a distinct instability. The various regions correspond poorly to the three instabilities observed by LJ90; LJ90's period “A” instability identifies well with the barotropic conversion found here in the cyclonic EUC–SECN shear, but they did not observe much barotropic energy conversion in the anticyclonic SECN–NECC shear region as found here, and their baroclinic period “C” involved equatorward-directed density fluxes flattening the NECC slope around 6°–8°N rather than poleward-directed fluxes crossing the cold tongue boundaries as found here. The present baroclinic energy conversion around 2°–6°N is more consistent with the frontal instabilities documented in models by McCreary and Yu (1992) and later authors. The fact that this source is more energetic at the western longitudes and is time correlated with deeper, more uniform surface layers is consistent with Masina's (2002) finding that baroclinic instability of the equatorial front is intensified by increased mixed layer depth. There is some additional baroclinic eddy energy production within the NECC slope at 110°W, but it is difficult to put much confidence in it. The baroclinic energy conversion south of the equator in the more eastern sections can be tentatively associated with the hitherto neglected equatorial squirts, filaments of cold water seen occasionally advecting southward from the equatorial cold tongue in SST images. A baroclinic energy source for these features would be consistent with previous studies (e.g., Fukamachi et al. 1995) that find coastal squirts to be instabilities of density fronts.

b. Comparison to Baturin and Niiler

Our calculation of instability-associated currents and Reynolds stresses parallels that of BN97 but focuses only on the differences between high- and low-instability states. Thus to facilitate comparison we recast our calculation in their form, sacrificing some statistical confidence in order to estimate the actual structures of each state. As above we de-mean and normalize the instability index over all available ADCP sections within 17° longitude of 110° and 140°W. As in BN97 we choose sections with associated instability indices different from zero by more than 0.5 and group them into high- and low-instability ensembles. The resulting numbers of (high/low) sections at 110°W are (11/8), respectively, and at 140°W (22/17). Choosing the shallowest ADCP data (20 m) to compare with BN97's 15-m drogued drifters, we see as above that high-instability periods are characterized by stronger westward flow in the SECN and significantly enhanced eastward flow in the NECC (Fig. 22). Our high-instability SECN is marginally stronger than BN97's at both longitudes, though not significantly so; our low-instability speeds are slower as well, significantly so at 140°W. Variation of the NECC is also roughly comparable between the two studies. Our meridional circulation, on the other hand, differs markedly from BN97. We find the meridional divergence around the equator to be substantially stronger during high-instability periods at both longitudes, especially at 110°W. This is consistent with expectations of stronger divergence during those parts of the seasonal and ENSO cycles that favor instabilities, since both are linked dynamically to stronger eastward trade winds and their associated Ekman divergence. It is also consistent with results from the yearlong TIWE (Qiao and Weisberg 1998; Weisberg and Qiao 2000). BN97, in contrast, found just the opposite tendency, that is, diminished meridional divergence during high-instability periods, again most markedly at 110°W. In addition, their divergences are about half as strong overall as ours, possibly indicating disparities between the two sampling periods.

The Reynolds stress during high-instability periods has strong downgradient flux on both sides of SECN at both longitudes, implying conversion of mean flow to eddy energy in both shear zones. Similarly, density fluxes are poleward out of the equatorial cold tongue, again converting mean flow energy to eddy energy. During low-instability periods the Reynolds stress and density fluxes reduce essentially to zero. The estimated stress at 110°W actually reverses sign, but the statistical significance of this is poor. Independently sampled MCM time series at 0°N, 110°W (Fig. 4) do not show comparably negative Reynolds stresses during periods of low-instability activity. Subsampling the MCM data to ADCP section times at 110°W produces negative stresses comparable to the ADCP results; thus we conclude that at least on the equator the negative Reynolds stresses during low-instability periods are most likely sampling errors, with the true value probably closer to zero. While the substantial uncertainties in both the mean flow and Reynolds stress averages make pointwise calculations of eddy energy conversion problematic, our results nevertheless directly contradict BN97's finding of a mere reduction in eddy stress magnitude going from high- to low-instability periods at 110°W, with commensurate reduction in mean flow to eddy energy conversion. TIWE was unfortunately limited to 140°W and is consistent with both studies in that Reynolds stress and energy flux there diminish substantially to zero during the low-instability season (Qiao and Weisberg 1998).

The systematic differences between the two analyses demand fundamental explanations. BN97's sampling period of 1980–94 only partially overlaps ours from 1991 to 2000; probably our inclusion of several strong cold-phase ENSO years toward the end of the decade produced the stronger zonal currents we find associated with TIW activity (Fig. 16). Yet it is difficult to see why the inclusion of such strong events would also produce oppositely signed meridional divergences (Fig. 17), or why with such TIW-favorable periods included we would see even less production of eddy energy during low-instability periods than did BN97. Apparently BN97 did not remove the seasonal cycles or de-mean the velocities in each of their composite periods before taking the 〈UV′〉 product, thus confusing the product of instability-correlated, low-frequency flow variations with higher-frequency, TIW-induced Reynolds stresses. Yet the magnitudes of their background flow variations do not seem large enough to produce all of the low-instability 〈UV′〉 they calculate. Perhaps TIW processes are sufficiently variable in time and space that the two datasets harbor real dynamical differences.

c. Comparision with GCM integrations

Masina and Philander's (1999) numerical model run under perpetual August climatological winds found two modes of TIW in the equatorial Pacific. The first was a mixed baroclinic–barotropic mode in the east that extracted energy simultaneously from the northern temperature front of the equatorial cold tongue and from the cyclonic, EUC–SECN shear north of the equator. These features are also seen in our 110°/140°W results, though additional eddy energy generation observed in the SECN–NECC shear and across the southern cold tongue boundary indicates that the ocean supports further modes of instability not present in the model. This may be due to the model's rather weak reproduction of the NECC and SEC. Interestingly, their east Pacific mode does replicate the paired local maxima of meridional velocity variance seen here (Fig. 18) and by BN97. In the model the southern maxima arises from pressure fluxes transporting eddy energy southward, though this cannot be confirmed with the present data. Their model's second mode of instability in the central Pacific, comprising barotropic conversion on both sides of the EUC and baroclinic conversion at the southern cold tongue boundary, does not appear in our data. Further, the model fails entirely to reproduce our observed Northern Hemisphere baroclinic conversion in the central Pacific, indicating that the model misses appreciable heat fluxes in this region.

Harrison et al.'s (2001a) GCM integration forced with a climatological seasonal cycle produces eddy variances and stresses similar to those reported here at 140°W. Their model TIWs do produce significant Reynolds stresses across the SECN–NECC anticyclonic shear region, but unpublished results show that very little eddy energy conversion results because of weakness of the NECC shear. This reinforces the suggestion that models with more robust NECC and SEC flows would be able to produce a more realistic suite of TIWs.

d. Time–space inhomogeneity of instability activity

It is clear that instability wave packets are sporadic in both time and space (Fig. 4), implying a sensitive dependence on small or rapidly varying changes in the background flow. Further, as detailed in the introduction, both previous observations and model results indicate the existence of multiple modes of instability; we cannot assume that TIWs are a single process occurring uniformly throughout each instability-favorable period/location. Thus it is important to examine individual unstable flows for uniformity among themselves and for consistency with the averaged TIW-favorable flows found above.

BL02's satellite-derived surface currents are sampled with sufficient time and space resolution that we can extract snapshots of near-surface zonal flow at arbitrary times. From monthly averaged flows spanning 6 October 1992 through 7 July 2001 we select meridional sections along 140° and 110°W that supported intense instability activity as evidenced by an instability index greater than 1.6. At 110°W most of the selected anomalous flow profiles (Fig. 23) are similar in structure and magnitude, corresponding well to the averaged unstable anomalous flow structures found previously (Fig. 16, and Figs. 6b and 13a for September). Several notable exceptions stand out. The essentially reversed flow anomaly profile at 110°W (westward at 5°N and eastward nearer the equator) is from February 1998 and will be discussed further below. At 140°W a somewhat broader assemblage of flows is evident, though still following the general form of the averaged structures. At both longitudes westward flow anomalies in the SECN appear to be more consistently represented than eastward anomalies in the NECC. This suggests (though does not prove) that SECN strength is the more important determining factor of instability wave activity.

Though identified here as a high-instability period, the February 1998 flow anomalies at 110°W were extremely atypical of unstable periods. In fact, an ADCP section along 110°W from the end of that period shows very weak flow throughout the equatorial region, rather than the more intense flows typical of high-instability periods such as September 1998 at 140°W (Fig. 24). Similarly the 13–30-day equatorial heat and momentum fluxes in February 1998 had opposite sign to what is usually associated with TIW activity (Fig. 4). Though the source of this unusual activity is difficult to identify without more extensive data, an ADCP section along 95°W 10 days earlier shows strong meridional velocities (up to 80 cm s−1) around 8°–10°N. Similar features appear in other sections early in 1999 and 2000 (not shown), raising the possibility that instabilities located in or around the NECC (e.g., LJ90; McPhaden 1996) can propagate instability-band energy toward the equator even though currents there are stable. Zonal propagation is also possible (e.g., D. B. Chelton et al. 1999, unpublished manuscript), as is local generation from purely baroclinic sources. We conclude only that caution is required when using local wave energy levels as the sole basis for assessing the stability of background flow structures, and most especially when using the average of many such background flows.

e. Background flows' relation to wave dynamics

While the observations show that the interannual variation in the strength of the mean flow is correlated to the tropical instability wave activity, one must still consider what aspect of the flow field is essential for wave growth. The important issues for the onset of instability are that perturbations have a mechanism by which they can extract momentum from the background flow field and that they are geometrically constrained. Ripa (1983, 1987) generalized the classic Rayleigh–Kuo criterion for a rotating fluid to show that one necessary condition for instability is that the meridional gradient of the potential vorticity (PV) along isopycnals must change sign. The appropriate level-coordinate expression near the equator for this meridional PV gradient is
QyβUyyβyU2zN2y
with the last term being the contribution to the flow curvature due to isopycnal slope. The importance of the Qy = 0 surface is that it represents a turning surface for Rossby waves (where the group velocity reverses direction). A second necessary condition for instability comes from the semicircle theorem (Howard and Drazin 1964; Ripa 1983, 1987), which assures that a critical surface (where the waves phase speed matches the flow speed) exists. These two conditions relate to instability in that the presence of the critical surface allows the wave perturbations to interact with the background flow and exchange momentum. The presence of the turning surface allows these wave signals to approach the critical surface, interact, and escape again in finite time. The importance of these two surfaces acting in this way was shown by Lindzen and coworkers (see Lindzen 1988) to be essential for shear-driven instabilities. Consequently, the onset of instability is tied to times when the flow curvature (along isopycnals) is strong enough to overcome beta, and the net shear across the unstable region is sufficient to create a critical layer. The strength of the instability is tied to the flow geometry of the SEC and EUC as was discussed for the TIWs by Proehl (1996, 1998).

f. Previous ADCP seasonal and ENSO composites

Although they rely on essentially the same dataset, our seasonal and ENSO analyses differ substantially from those of JSKM02. They approximate the seasonal cycle by a 1-cpy sinusoid, yet it is clear from other data (Figs. 7 and 9) and model simulations (e.g., Harrison et al. 2001b) that other frequencies contribute. Specifically, the eastward surge along the equator around May is not matched by an equal but opposite westward surge around November. The ADCP sampling in December– January is very sparse (Fig. 11); thus JSKM02's fitted sinusoid is poorly constrained through that period and tends to overshoot the data in order to match the rest of the year more closely. Our time-smoothed seasonal cycle, while equally poorly constrained through December–January, at least does not import errors from other parts of the year. It results in a seasonal cycle that matches the independent datasets reasonably well.

Similarly, JSKM02 assumed that ENSO-related currents vary directly in proportion to SOI. It is clear from the present analysis that such currents in fact vary throughout a cold/warm event, with their dominant feature being a December–January sign reversal at the peak of the event (Fig. 15). This midevent flow reversal is attributed to reflections of ENSO-forced Kelvin and Rossby waves off the ocean boundaries by Shu and Clark (2002), who discuss it further in terms of delayed oscillator theory. We emphasize that our unconstrained composites capture true ocean variability and thus present a valid challenge to theory and models. Nevertheless the presence of longitudinal variability in ENSO-associated currents (e.g., Fig. 15) dictates caution in the use of our (or any) ENSO composite. Ideally, with more data one could further focus the analysis into western and eastern basin composites, as well as test their representativeness over a broader period of time (e.g., Larkin and Harrison 2002, and references therein).

6. Conclusions and summary

To summarize our study, we have assembled meridional sections of ADCP-derived zonal currents from 170° to 110°W into composite seasonal and ENSO cycles in order to produce detailed representations of the large-scale ocean flow regimes that favor tropical instability waves. The seasonal cycle is dominated by an April–July (boreal spring) surge of eastward current anomaly around the equator paired with westward velocity in the NECC. In July these flows reverse and are oppositely directed during August–September, diminishing to weaker flows through the rest of the year. The ENSO composites show a remarkable degree of antisymmetry between the warm and cold years, with the time evolution of warm-phase currents being to a large degree the opposite of cold-phase currents. Taking the case of the cold phase, through the first half of the composite year (August–December) the current anomalies are westward around the equator and eastward in the NECC. At the height of the ENSO event (around January) these currents reverse, and for the remainder of the composite year (through May) flow in the opposite directions. The seasonal cycle is observed with very high statistical confidence; the ENSO cycles are less robust, but appear to be reasonable representations of ENSO variability at least through the last two decades.

The instability-favorable portion of these cycles are the August–October period of the seasonal cycle and the pre-December period of the ENSO cold phase. Both flow regimes have intense westward flow in the SEC, most particularly the SECN, and strengthened eastward flows in the NECC and the EUC. Taken together these flows enhance the two shear regions generally associated with TIW activity, namely, the cyclonic and anticyclonic shear regions located to the south and north of the SECN, respectively. Direct correlation of ADCP currents and CTD densities to an instability index derived from the amplitude of 13–30-day-band meridional velocities confirms the importance of the SECN and NECC to the timing of instability wave events. The EUC is assigned a very small role, implying that while its existence may be important to TIW dynamics and energetics, its strength is not a controlling factor determining their timing. Calculations of Reynolds stresses and density fluxes indicate that TIWs, at least in a time-averaged sense, derive energy barotropically from both the cyclonic and anticyclonic flanks of the SECN, and baroclinically from both sides of the equatorial cold tongue. During low-instability periods these Reynolds stresses and density fluxes substantially vanish, indicating that eddy energy production ceases. This is in marked contrast to the drifter results of BN97, who found relatively continuous eddy energy production at 110°W. Barotropic energy production is strongest in the eastern region at 110°W, as is baroclinic production south of the cold tongue; baroclinic production north of the cold tongue is strongest toward the west at 170°W.

The sporadic nature of instability waves makes it difficult to sample the background flow associated with an individual wave or packet of waves; further, their previously demonstrated variation in dynamics compromise the relevance of even long-term statistical averages to any given mode of instability. Monthly averaged flows from apparently unstable periods do in fact show substantial variability among themselves. Propagation of instability-band wave energy either zonally or meridionally is also possible; thus the presence of TIW-band energy does not guarantee that the local background flows are dynamically unstable. All these findings counsel the use of caution when modeling instabilities from averages of observed background flows. Ultimately the fullest understanding of TIW processes is likely to result from a combination of statistical approaches (such as the present) and process-oriented studies that examine individual instability events more thoroughly.

Acknowledgments

Support from National Science Foundation Grant OCE97-30553 is gratefully acknowledged. We also thank Sean Kennan, Ed Harrison, Gary Lagerloef, and John Lyman for enjoyable discussions that contributed significantly to this paper. We are also indebted to other investigators who made have their data available; equatorial current data were downloaded from the TOGA–TAO Web site, satellite-derived surface currents were kindly provided by Fabrice Bonjean and Gary Lagerloef, and ADCP data were provided by Eric Firing. Insightful comments from two anonymous reviews spurred significant improvements in the paper.

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Fig. 1.
Fig. 1.

The time-mean sections of ADCP velocity and CTD density from an MLR spanning longitudes 170°–110°W. The regression simultaneously fit a time mean and a zonal trend at each depth–latitude. Negative contours in this and subsequent figures are dashed

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

 Fig. 2.
Fig. 2.

The time location of equatorial ADCP sections used in the present study as a function of year and time within the year. Symbol color corresponds to the approximate longitude of each section

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 3.
Fig. 3.

Variance-preserving spectra of meridional and zonal velocities from equatorial MCMs at four longitudes

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

 Fig. 4.
Fig. 4.

The 13–30-day-period bandpassed meridional velocity at 25-m depth from equatorial MCMs. Superimposed are the covariances of bandpassed meridional velocity with bandpassed zonal velocity and temperature (green and red, respectively), further smoothed to 62-day period for clarity. Yellow crosses denote the equatorial crossing times (as in Fig. 2) of ADCP sections within 17° longitude of each MCM location

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 5.
Fig. 5.

The satellite-derived surface currents of BL02 sampled at the equator and plotted as a function of longitude and time. Superimposed are the time/longitude locations of the ADCP sections

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 6.
Fig. 6.

Monthly sections of seasonally averaged zonal velocity composited from the residuals of the MLR of Fig. 1 and smoothed cyclically around the year to suppress periods shorter than 120 days

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 6.
Fig. 6.

(Continued )

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

 Fig. 7.
Fig. 7.

Seasonal ADCP velocities as in Fig. 6, but for the equator at various depths. Superimposed dashes are the equivalent seasonal analyses of MCM velocities trapezoidally averaged between longitudes 170°–110°W

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 8.
Fig. 8.

Seasonal ADCP velocities as in Fig. 6 but plotted at 20-m depth as a function of time and latitude. Shown are velocities (top) with and (middle) without the time mean added in, and (bottom) bootstrap-derived rms errors

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 9.
Fig. 9.

Seasonal velocities in Fig. 8 but for the satellite-derived surface currents of BL02, composited from 6 Oct 1992 through 26 Dec 2001

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 10.
Fig. 10.

The SOI calculated traditionally as the normalized difference in standardized sea level pressures at (top) Tahiti and Darwin and (bottom) using pressures within 5° latitude of the equator in the eastern Pacific and Indonesia

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

 Fig. 11.
Fig. 11.

Equatorial SOI from Jul 1990 to Jun 2001 plotted as a function of season, with the 170°–110°W ADCP section times marked on each year trace as crosses. Colors denote the ENSO phase assigned to each section, determined by 1.0-sigma thresholds of the equatorial SOI

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 12.
Fig. 12.

(a) The composited ADCP velocities (cm s−1) for ENSO warm phase, smoothed from Jul through Jun to suppress periods shorter than 180 days. The time mean (Fig. 1), zonal trend, and seasonal composite (Fig. 6) of all ADCP data were previously removed. (b) The rms errors of the warm-phase composite [(a)]

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 12.
Fig. 12.

(Continued )

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 13.
Fig. 13.

As in Fig. 12a, but for the ENSO cold phase. (b) The rms errors of the cold-phase composite [(a)]

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 13.
Fig. 13.

(Continued )

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 14.
Fig. 14.

ENSO warm- and cold-phase composited velocities as in Figs. 12 and 13, but plotted at 20-m depth as a function of time and latitude. Shown are velocities (top) with and (middle) without the time mean and seasonal cycle added in

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

 Fig. 15.
Fig. 15.

The 25-m zonal velocities from equatorial MCMs spanning the period Jul 1979–Jun 2002. Data are anomalies after removal of the time mean and seasonal cycle (Fig. 7) at each longitude and are plotted as a function of season with ENSO phase color coded as in Fig. 11. The average for each ENSO phase is superimposed in heavy lines

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 16.
Fig. 16.

The covariance of nearby ADCP zonal velocities with de-meaned, normalized instability indices constructed from 13-30-day meridional velocities at the 110°, 140°, and 170°W moorings (i.e., Fig. 4; see text). Contour intervals are 5 cm s−1 for covariance velocity and 2 cm s−1 for the bootstrap-derived rms errors. Zero contours are suppressed for clarity

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 17.
Fig. 17.

As in Fig. 16, but for covariance of ADCP meridional velocities with MCM instability indices

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 18.
Fig. 18.

As in Fig. 16, but for covariance of squared ADCP meridional velocities with MCM instability indices. Contour intervals are 200 cm2 s−2 for both covariance and rms errors

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 19.
Fig. 19.

As in Fig. 16, but for covariance of the product of ADCP zonal and meridional velocities with MCM instability indices. Contour intervals are 100 cm2 s−2

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 20.
Fig. 20.

As in Fig. 16, but for covariance of the product of ADCP meridional velocity and CTD densities with MCM instability indices. Contour intervals are 2 cm s−1 (kg m−3)

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 21.
Fig. 21.

Typical eddy energy production values estimated by multiplying the covariances of Figs. 19 and 20 by gradients of background flow fields constructed by summing the mean flow (Fig. 1) with the instability-correlated flow (e.g., Fig. 16). Contour intervals are 200 × 10−6 ergs (cm3 s)−1, or 2 × 10−3 W m−3

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 22.
Fig. 22.

Composited ADCP meridional and zonal velocity means for high- and low-instability periods, defined as periods in which the instability index has a magnitude greater than 0.5. Also shown are the covariances between the residual meridional and zonal velocities and between residual meridional velocity and CTD density for each composite period. Error bars are rms errors derived from bootstrap calculations

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 23.
Fig. 23.

Monthly zonal flow anomalies from BL02's satellite-derived surface currents averaged over 10° longitude around 110° and 140°W, selected for periods having instability indices greater than 1.6. Also shown are the 6 Oct 1992 through 7 Jul 2001 time mean flows for comparison

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

Fig. 24.
Fig. 24.

Two individual ADCP sections from times/locations corresponding to unstable monthly profiles in Fig. 23. The 110°W section corresponds to the atypical monthly profile at 110°W in Fig. 23 having westward anomalous flow at 5°N; the 140°W section shows a more typical current structure during strong instabilities

Citation: Journal of Physical Oceanography 34, 10; 10.1175/1520-0485(2004)034<2121:TIWVIT>2.0.CO;2

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