1. Introduction
The western equatorial Pacific is the largest rainy region on Earth, with 2–4 m of rainfall per year falling on a region larger than the continent of Australia. The region is warm but rainfall greatly exceeds evaporation (see, e.g., Ando and McPhaden 1997) and, as a result, the near-surface water exists as a large fresh/warm “pool.” Lukas and Lindstrom (1991) pointed out that the heavy rainfall results in a relatively fresh surface mixed layer that is embedded in a deeper isothermal layer (see, e.g., Fig. 1). Lying between the bottom of the surface mixed layer and the bottom of the isothermal layer is a salt and density stratified “barrier” layer that inhibits vertical mixing. Estimates of the surface mixed layer depth (MLD), the isothermal layer depth (ILD), and the barrier layer thickness (BLT) have been given for the tropical Pacific by Ando and McPhaden (1997).
CTD cast showing temperature, salinity, density, and a thick barrier layer from the western equatorial Pacific. The cast was made at 0.01°S, 153.93°E on 29 Apr 1994 at 0427 UTC (1427 LT). Temperature and salinity have been scaled respectively by the coefficients of thermal expansion and saline contraction (computed for 29°C and 35 psu) to emphasize their relative impacts on density. The MLD and ILD are indicated. The layer between these two depths is defined as the barrier layer, whose thickness (BLT) is 36 m in this example (from Ando and McPhaden 1997).
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
Zonal movement of the western equatorial fresh/warm pool of water is fundamental to El Niño–Southern Oscillation (ENSO) dynamics (Picaut et al. 1996; Delcroix and Picaut 1998; Cronin and McPhaden 1998; Picaut et al. 2001; Bosc et al. 2009; Qu et al. 2014). Monthly salinity anomalies as large as 1 psu are common in the western equatorial Pacific as the warm/fresh pool and the barrier layer at its eastern edge move eastward during El Niño and westward during La Niña (see Fig. 2) over distances of thousands of kilometers. This movement is associated with interannual flow, but the strength, spatial structure, and dynamics of the near-surface interannual flow are not known. The existence of near-surface relatively fresh equatorial flow was first documented by Roemmich et al. (1994) when they observed a relatively fresh salinity anomaly (−1 psu) equatorial jet over several months in a surface layer 50 m thick. Beneath this layer was a sharp halocline in isothermal water so that the overall vertical structure of the temperature and salinity was similar to the boundary layer structure. But the Roemmich et al. theory is only valid for about 10 days, and for our study we are interested in interannual flows.
Time–longitude estimate of (a) SST (°C), (b) SSS (psu), and (c) BLT (m) from Argo floats along the equator in the western central Pacific. The white lines are the 29°C, 34.8 psu, and 15-m contours, respectively (from Qu et al. 2014).
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
In this paper, we will use western equatorial Pacific surface and subsurface salinity and temperature data collected by the TRITON array, mostly since the late 1990s, to calculate dynamic height 
The overall structure of the paper is as follows: The data are described in section 2, and major features of the salinity observations in section 3. Monthly salinity variability is mainly due to salinity anomalies (departures from the seasonal cycle) rather than the seasonal cycle itself. Section 4 examines the anomalous dynamic height 
2. Data
a. Upper-ocean salinity and temperature
Monthly in situ temperature and salinity data were downloaded from the TAO Project Office/PMEL/NOAA website (http://www.pmel.noaa.gov/tao/disdelframes/main.html). We mainly used temperature and salinity data along the 137°E, 147°E, and 156°E meridians (Table 1), where the rainfall is enormous (about 2–4 m yr−1), and long surface and subsurface salinity and temperature records are available from the TRITON array deployed by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) after late 1999 (see, e.g., Ando et al. 2005). Long western Pacific salinity records are available at other longitudes (e.g., 165°E), but at these locations subsurface observations are either not available or gappy and shorter.
Western equatorial Pacific TAO/TRITON salinity and temperature measurement periods and parameters. The salinity and temperature data at 0°, 138°E were downloaded from JAMSTEC TRITON stations. At this station there is a data gap from November 2010 to July 2011 for salinity and only 7 months of useful data for temperature, so we did not calculate mean SST, RMS (SST′), and RMS seasonal SST there.
For sea surface temperature (SST), we used the monthly global 1° gridded dataset, NOAA optimum interpolation (OI) SST, version 2 (http://www.esrl.noaa.gov/psd/data/gridded/data.noaa.oisst.v2.html).
In recent years, sea surface salinity (SSS) has been estimated by the Aquarius satellite with 1° resolution. In this paper, monthly SSS data available from the Aquarius website (http://aquarius.nasa.gov/index.html) will be compared with in situ data.
b. Sea level
For sea level we used the monthly ⅓° gridded Archiving, Validation, and Interpretation of Satellite Oceanography (AVISO) dataset (http://www.aviso.oceanobs.com).
c. Currents
Long western Pacific Doppler current records at 137°E, 147°E, and 156°E, either at a fixed depth or from an acoustic Doppler current profiler (ADCP) were downloaded from the TAO Project Office/PMEL/NOAA website (http://www.pmel.noaa.gov/tao/disdelframes/main.html). Monthly estimates of flows nominally averaged over the top 30 m of the ocean from the Ocean Surface Current Analyses–Real Time (OSCAR) dataset (http://www.oscar.noaa.gov/) were also utilized in our analyses. These data are available at ⅓° resolution since October 1992.
d. Wind stress data
To examine the western equatorial Pacific near-surface dynamics, monthly wind stress data were used from European Center for Medium-Range Weather Forecast (ECMWF) dataset (http://apps.ecmwf.int/datasets/data/interim-full-moda), the resolution of which is 0.75°.
e. Outgoing longwave radiation data
In the deep tropics, outgoing longwave radiation (OLR) data can be used as a proxy for rainfall. We used monthly mean OLR data available online (from http://www.esrl.noaa.gov/psd/data/gridded/data.interp_OLR.html). The data have a 2.5° latitude and longitude horizontal resolution and are available since June 1974.
In this paper, we will mainly be concerned with low-frequency departure from the seasonal cycle that is well characterized by monthly anomalous time series. For all the observed data, the monthly anomaly was calculated by removing the average value of each calendar month throughout the record; for example, January anomalies were obtained by subtracting the average January throughout the entire data record. Similar calculations for the other 11 calendar months yield anomalous time series. The anomaly of a specific variable will be denoted by the symbol of that variable with a prime.
3. TAO/TRITON salinity observations
a. SSS
Figure 3 shows monthly SSS TAO/TRITON observations near the equator on the 137°E, 147°E, 156°E, and 165°E meridians. Consistent with previous work discussed in the introduction, monthly salinity variations are large. As expected from Bosc et al. (2009) and Fig. 2, they are very strong at 156° and 165°E between 2°S and 2°N and are largely interannual rather than seasonal. This strong interannual signal is also seen at the equator at 147°E, but much less so at 2°N at 147° and 137°E. Table 1 and Figs. 2 and 3 support the conclusions that interannual variability dominates seasonal variability, that it decreases off the equator at 147°E, 156°E, and 165°E, and that, at least since the late 1990s, at the equator it is largest between about 147°E and 180°. The decrease off the equator at 156° and 165°E is weaker and so slight at 165°E that it may not be real.
Monthly SSS (blue) plotted with the monthly annual cycle (red) from the TAO/TRITON array in the western equatorial Pacific at 2°S, 0°, and 2°N. This figure was constructed from data obtained from the TAO project office PMEL NOAA website (http://www.pmel.noaa.gov/tao/disdel/frames/main.html).
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
b. Relationship between SSS(t) and S(z,t)
Figure 4 shows that, consistent with a coherent surface mixed layer, S′ is equal to SSS′ over the mixed layer depth (about 30–50 m). Beneath this surface mixed layer, the SSS′ signal decreases to a smaller amplitude near the ILD (about 50–80 m).
First EOF structure functions showing the depth dependence of S′ for seven stations near the equator in the TRITON western Pacific array. In each case, the structure function has been normalized by its surface value so that its depth dependence can be easily seen. The % variance described by the first EOF, the station location, and the amplitude (psu) of the SSS′ [S(0)] are marked on each panel. Here and elsewhere in this paper, each principal component is nondimensional and has a variance 0.5 so that the corresponding dimensional EOF structure function is indicative of the amplitude of the variability.
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
4. Estimation of the sea level anomaly due to near-surface fresher water
The near-surface salinity anomalies described in section 3 are so large that they can contribute significantly to the dynamic height above the ILD. In this section, we will examine this contribution. Since a positive temperature anomaly might affect rainfall and hence S′, or a strong shallow barrier layer might affect the surface volume of water heated and hence the temperature anomaly T′, both S′ and T′ will be taken into account in our estimation of density and pressure changes in the isothermal layer.
a. Estimation of the dynamic height anomaly due to density anomalies in the isothermal layer
To determine 
Figure 5 shows the ILD(t) found in this way for the moorings near the equator. The ILD varies considerably, but typically the average ILD is near 60 m. The time-mean isothermal layer depths for all western Pacific moorings are listed in Table 1. Also listed in that table are the mean MLD and barrier layer thickness (BLT = ILD − MLD). Similar to the ILD, the mixed layer depths were determined using the potential density difference method following Bosc et al. (2009), with ΔT = −0.5°C, αT = 3.3 × 10−4 K−1, and values at 10-m depth as the surface level of reference.
Isothermal layer depth along (top to bottom) 137°E (at 2°N), 147°E (at 0° and 2°N), and 156°E (at 2°S, 0°, and 2°N). Depths were estimated from in situ temperature data using the temperature difference method of Sprintall and Tomczak (1992) with temperature threshold ΔT = −0.5°C. Because of diurnal heating, values at 10-m depth were assumed to be at the surface. Average ILD is noted in each panel.
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
b. Comparison of 
Comparison of 
Observed AVISO SSH (cyan) and isothermal layer sea level anomaly 
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
Although SSH′ dominates 
c. Comparison of 
The analysis of Bosc et al. (2009) suggested that S′ may be related to a T′ signal above the ILD. Figure 7 compares 
(a) First EOF structure functions of 
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
5. Estimation of 
a. Establishing equations for 
b. The horizontal structure of 
The centered difference estimates of 
(a) First EOF structure function and (b) corresponding first principal components for three separate EOF analyses of surface 
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
The meridional scale of the jet is comparable to the grid spacing used to calculate the flow, and so in the appendix we consider the likely error. We estimate that near the equator where the signal is large, the error is likely to be about 20%.
c. Comparison of 
Earlier in section 4 we noted that most of 
As for Fig. 8, but with 
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
d. Vertical structure of 
By construction, we expect that T′ will be nearly independent of z over the isothermal layer. Since S′ is nearly uniform over the mixed layer and then decreases and is of one sign until it reaches the bottom of the isothermal layer, we expect from (5.3) that 
(left) First EOF structure function and the (right) corresponding principal component for the upper 74-m monthly anomalous salinity-driven flow 
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
e. Comparison of surface 
The shallow near-surface 
Because the OSCAR “surface” currents are nominally an average over the upper 30 m of the water column, in comparing 
Zonal current monthly anomalies for all three datasets were filtered with a Trenberth (1984), 11-point, symmetric, nonrecursive, interannual filter and then a separate EOF analysis done on each. In all three cases, the first EOF describes over 80% of the variance (Fig. 11). The principal components are highly correlated, and the meridional structures are similar, indicating that, at least at 156°E, much of the interannual surface flow is associated with 
Structure functions for the (a) first EOF and (b) first principal component of 156°E interannually filtered surface u′ for OSCAR (solid circles, black), in situ single-point Doppler (solid squares, cyan), and 
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
We also compared u′ and 
As for Fig. 11, but for 147°E instead of 156°E. The correlation between the principal components of 
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
6. Freshwater jets and ENSO
We have shown that in the western equatorial Pacific, shallow, narrow freshwater jets dominate the interannual flow. Since the zonal interannual flow is a key to the movement of the western equatorial Pacific warm/fresh pool and ENSO dynamics, the freshwater jets are fundamental to the ENSO mechanism. In this section, we first discuss the statistical relationship of 
a. Relationship of 
Zonal equatorial advection by the anomalous zonal flow and associated zonal movement of the western equatorial Pacific warm/fresh pool is central to ENSO dynamics (see, e.g., Gill 1983; McPhaden and Picaut 1990; Picaut and Delcroix 1995; Picaut et al. 2001), with the warm/fresh pool moving eastward during El Niño and westward during La Niña. We checked on this expected relationship by lag–lead correlating monthly unfiltered equatorial 
b. Equatorial wind and rainfall anomalies and the zonal movement of the warm/fresh pool edge
Figure 13a shows zonal wind anomalies and the 29°C proxy for the eastern edge of the warm/fresh pool (thick yellow line). Notice that during an El Niño (westerly wind stress anomalies, red shading) most of the wind forcing is west of the warm/fresh pool edge (yellow line), while during La Niña (easterly wind stress anomalies, blue shading), most of the wind forcing is east of the warm/fresh pool edge. A similar relationship holds for the anomalous freshwater flux. The freshwater flux is dominated by rainfall rather than evaporation (see, e.g., Fig. 4d of Ando and McPhaden 1997), and Fig. 13b shows that during an El Niño (negative OLR anomalies, a proxy for rainfall anomalies, red shading) most of the anomalous rainfall is west of the warm/fresh pool edge, while during La Niña (anomalous drying, blue shading) most of the anomalous freshwater flux is east of the warm/fresh pool edge. Why should this be?
(a) Time–longitude plot of westerly wind stress anomalies (mPa) along the equator in the equatorial Pacific, the thick yellow line denoting the equatorial location of the 29°C isotherm, a proxy for the eastern edge of the warm/fresh pool; (b) as in (a), but for −OLR; and (c) equatorial longitudinal location of the 29°C isotherm (yellow) −40-mPa eastward equatorial wind stress isoline (black) and the 250 W m−2 OLR isoline (red). The break in the red and black curves near the end of 1997 occurs because the −40-mPa and 250 W m−2 values did not occur in the equatorial Pacific then. All data have been filtered with a 5-month running mean. The wind stress was averaged between 2.25°S to 2.25°N, the OLR between 2.5°S and 2.5°N, and the SST between 2°S and 2°N. In (c), the correlation between the 29°C and −40-mPa time series is 0.87 [rcrit(95%) = 0.46], between the 29°C and 250 W m−2 time series is 0.87 [rcrit(95%) = 0.42] and between the −40-mPa and 250 Wm−2 time series is 0.87 [rcrit(95%) = 0.43].
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
Suppose that, to a first approximation, the observed large-scale zonal wind and rainfall anomalies result from the zonal displacement of a fixed mean wind stress and rainfall above the warm/fresh pool. Figures 14a and 14b show, respectively, the mean zonal equatorial wind stress and negative OLR as a function of longitude. In Fig. 14, point P identifies the mean longitudinal location of the 29°C proxy for the eastern edge of the warm/fresh pool, and point A identifies the mean longitudinal location for τx = −40 mPa (Fig. 14a) and −OLR = −250 W m−2 (Fig. 14b). If the wind stress and rainfall did have a mean fixed structure when the warm/fresh pool moved zonally, then we would expect the −40-mPa isoline and −250 W m−2 zonal displacements to be well correlated with the movement of the 29°C proxy for the eastern edge of the warm/fresh pool, and this is the case (see the yellow and black curves in Fig. 13c and the Fig. 13c caption).
(a) Time-mean eastward wind stress τx along the equator in the Pacific. The point P (177.0°E) marks the location of the 29°C equatorial isotherm and point A (179.3°E) marks the location of the −40-mPa wind stress isoline. Both P and A are proxies for the eastern edge of the warm/fresh pool. (b) As in (a), but with −OLR replacing τx. In this case, point A corresponds to the −250 W m−2 isoline.
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
Now consider the relationship between zonal equatorial wind stress anomalies, the rainfall anomalies, and the warm/fresh pool edge. When there is an El Niño and the warm/fresh pool moves eastward, the regions it anomalously covers are wetter with more westerly winds. Thus, west of the displaced warm/fresh pool edge, it is wetter and the winds are anomalously westerly (Figs. 13a,b). Conversely, when there is La Niña and the warm/fresh pool has moved westward, it is anomalously dry and winds are anomalously easterly to the east of the displaced warm/fresh pool edge.
c. Are the freshwater jets forced by the anomalous freshwater flux or anomalous wind stress?
How does anomalous freshwater flux affect the ocean? As noted earlier in section 6b, interannual rainfall dominates the interannual freshwater flux, which in the western equatorial Pacific is about 5 mm day−1 or 1.8 m yr−1 (see, e.g., Fig. 10 of Bosc et al. 2009). If the ocean responded like a large lake, this freshwater flux would result in interannual sea level fluctuations of a few meters per year, much larger than the 5–10 cm yr−1 observed interannual amplitude (see, e.g., Fig. 6). But, in fact, the ocean response is more than an order of magnitude smaller than 5–10 cm yr−1 rather than larger. To understand this, first note that the addition of mass due to the rainfall results in extra weight and therefore extra pressure felt throughout the ocean water column. As a result, the ocean response is barotropic, and, because it is not bounded like a lake, the barotropic signal propagates away rapidly (Huang and Jin 2002).
The above rapid adjustment implies, for example, that even the interannual addition of water over an area comparable to the continent of Australia (as in the western equatorial Pacific) would only result in an effectively instantaneous rise of 1 cm or so in global (and western equatorial Pacific) sea level because the mass added is rapidly spread over the much larger global ocean. In practice, the sea level rise is even smaller because the excess interannual precipitation is compensated almost exactly by reduced interannual precipitation elsewhere in the tropics (Clarke and Kim 2005) so that globally the net freshwater flux is much smaller. Observations suggest that the net effect of this mechanism is only a few millimeters of change in sea level, much smaller than the observed interannual signal in the western equatorial Pacific. Such small interannual observed sea level changes related to El Niño have recently been discussed by Cazenave et al. (2012).
Another possible freshwater flux explanation of 
If 
Dynamic height anomalies (red) relative to the ILD at the equator at 156°E plotted with (a) the time integral of −OLR′ (black) and (b) −OLR′ (black). All data have been filtered with a 5-month running mean. The OLR data were averaged over the 6° (longitude) by 2° (latitude) box centered on 0°, 156°E.
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
Correlation of monthly 
One possibility is that eastward wind stress anomalies (τx)′ generate eastward current anomalies (
Correlation at zero lag with rcrit(95%) in brackets (upper triangle) and maximum correlation with lead in brackets (lower triangle) for the variables 
The 5-month running mean of monthly −OLR′ (blue), (τx)′ (red), 
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
d. Coupled ocean–atmosphere instability
In the previous section, we suggested that anomalous rainfall −OLR′ drives (τx)′ that then generates 
What turns off the instability? Various mechanisms have been proposed [see Clarke (2014) for a review], but a key one is the movement of warm water south of the equator in the Southern Hemisphere summer (December–February). This moves the zonal wind anomalies south of the equator in December–February and typically terminates the El Niño near the beginning of the calendar year (Harrison and Vecchi 1999).
7. Can the anomalous freshwater jet be estimated from SSS′, even Aquarius satellite SSS′?
a. Comparison of Aquarius and in situ SSS
Having a 1° latitude and longitude resolution, the Aquarius satellite estimation of SSS has a far better spatial coverage than the TAO/TRITON moorings. The monthly satellite record is comparatively short, but Fig. 17 shows that the agreement with the in situ monthly SSS is very good.
Time series of satellite-measured (red line) and in situ (blue line) SSS along 138°E (at 0°), 137°E (at 2°N), 147°E (at 0° and 2°N), 156°E (at 2°S, 0°, and 2°N), and 165°E (at 2°S and 2°N).
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
b. Estimation of 
Correlation and regression between the “exact” integral expression for 
The above analysis showed that when the SSS′ signal is strong, 
Structure functions for the (a) first EOF and (b) first principal component of 156°E interannually filtered surface 
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
We also attempted to calculate 
(a) First EOF of 
Citation: Journal of Physical Oceanography 45, 11; 10.1175/JPO-D-14-0245.1
8. Concluding remarks
Analysis of the TAO/TRITON salinity data in the western equatorial Pacific showed that the monthly salinity anomalies were largest at the equator between 156° and 165°E over the period of observation from 1999 to December 2013. Salinity anomalies are usually larger than the seasonal cycle and are largest near the equator; at the equator at 156° and 165°E, they dwarf the seasonal cycle. Subsurface data show that they are shallow, being approximately equal to the SSS′ over the top 50–60 m and then usually decreasing with depth to much smaller amplitudes at 100-m depth.
Although the salinity variations are shallow, they are so strong that they affect the density and dynamic height, especially in the region of maximum salinity variability at the equator between about 156° and 165°E. Over the ILD ~50–70 m, these dynamic height perturbations are generally much smaller than the sea level variability. However, as we have shown, these comparatively small dynamic height perturbations are associated with a shallow equatorial surface jet ~23 cm s−1 within 2°–3° of latitude of the equator that dominates the observed equatorial interannual flow in this region. Our calculations suggest that the jet can be approximately estimated from both in situ and Aquarius satellite SSS′.
Analysis of anomalous monthly OLR data suggests that the interannual surface equatorial jets are not forced by the huge interannual surface freshwater flux. Instead, it is likely that they are generated by anomalous zonal equatorial winds that are part of a coupled ocean–atmosphere involving the zonal movement of the warm/fresh pool of water in the western equatorial Pacific. To a first approximation, mean easterly windstress decreases in strength and rainfall increases in strength westward along the equator in the western equatorial Pacific (see Fig. 14). As explained in section 6, if a small eastward displacement of the warm/fresh pool occurs, the eastward displacement of the wind stress structure will result locally in westerly wind stress anomalies largely west of the warm/fresh pool edge. These generate eastward zonal currents that move the warm/fresh pool farther eastward and the instability grows. The meridional displacement of warm water south of the equator in the Southern Hemisphere summer (December to February) causes the westerly wind anomalies to move south of the equator, typically halting the El Niño growth in December–February (Harrison 1987; Harrison and Vecchi 1999). Similar dynamics of opposite sign occurs during La Niña, the easterly wind anomalies generating the flow being largely east of the warm/fresh pool edge.
Several basic properties of the jets have not been addressed. For example, how exactly does the fresher surface water affect the ocean response to the wind? Specifically, how are the strength and spatial structure of the anomalous zonal surface flow affected? The analysis of Boulanger et al. (2001) considered the ocean response to the strong March 1997 westerly wind event and showed numerically that the presence of the warm/fresh pool had an one-order nonlinear effect on the zonal equatorial surface flow, increasing its strength by a factor of 3. The strong March 1997 westerly wind event lasted only about 2 weeks, a much shorter time scale than the interannual jet flows considered here. But the Boulanger et al. analysis nevertheless highlights the need to understand the effect on the interannual flow of the change in stratification at the warm/fresh pool edge. Brown et al. (2014) have recently shown that many of the state-of-the-art Coupled Model Intercomparison Project phase 5 (CMIP5) models poorly represent the salinity variability at the warm pool edge and so would seem to be missing a basic component of the coupling dynamics.
We gratefully acknowledge funding from the National Aeronautics and Space Administration (grant NNX14AH43G). Dr. Jaci Brown, Dr. Eric Lindstrom, and an anonymous reviewer provided helpful comments on the manuscript, and Dr. Tangdong Qu and Dr. Christophe Maes generously provided a high-resolution version of Fig. 2.
APPENDIX
Instrumental and Analysis Errors
The instrumental error for monthly in situ T is approximately 0.003°C and that for monthly S is 0.005 psu. Based on (4.3), these correspond to errors in 
Of much more concern is the error in estimating 
The above estimate is very crude, and the centered difference approximation may possibly result in random error larger than 20%. But the fact that most of the 
Regarding errors in OSCAR, we note that the OSCAR equatorial interannual currents are likely to have small errors since their time variability and magnitude match quite well with the in situ results (see Fig. 11) and also our own along-track geostrophic calculations from altimeter height (not shown).
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