The Pacific Subsurface Countercurrents and an Inertial

2448 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27

The Paci®c Subsurface Countercurrents and an Inertial Model*

GREGORY C. JOHNSON AND DENNIS W. M OORE NOAA/Paci®c Marine Environmental Laboratory, Seattle, Washington (Manuscript received 5 December 1996, in ®nal form 21 April 1997)

ABSTRACT The Tsuchiya jets, or subsurface countercurrents, extend across the Paci®c Ocean carrying 7 (Ϯ2) ϫ 106 m3 sϪ1 eastward on each side of the equator. Mean meridional sections of potential temperature, salinity, neutral density anomaly, and the square of buoyancy frequency are presented for the western, central, and eastern tropical Paci®c Ocean. These sections are used together with maps of depth and salinity on isopycnals, as well as thickness between isopycnals, to describe the evolution of the Tsuchiya jets as they ¯ow from west to east. An inertial-jet model is formulated in which conservation of the Bernoulli function and potential vorticity combine with the eastward shoaling of the tropical pycnocline to dictate the jet structure. This model jet is consistent with a number of features of the Tsuchiya jets: their roughly constant volume transports, their advection of properties such as salinity and oxygen over long zonal distances, their rapidity and narrowness, their poleward shift from west to east, the large potential vorticity gradients across them, and the pycnostad between them that builds in size and strength from west to east. However, an observed decrease in density carried by the Tsuchiya jets from west to east, not included in the model jet, suggests that diffusive or advective interaction with the surrounding ocean also may be important in subsurface countercurrent dynamics.

1. Introduction both SSCCs and a strong gradient in salinity across the north SSCC, suggesting that the SSCCs are a barrier to The subsurface countercurrents (SSCCs) in the Pa- meridional ¯ow, but that between them water properties ci®c Ocean (Tsuchiya 1972, 1975), or Tsuchiya jets, are may be homogenized in gyres composed of the eastward persistent eastward subsurface currents found on either ¯owing SSCCs and the westward ¯owing Equatorial side of the equator with a pycnostad between them. The Intermediate Current (EIC). SSCCs are remarkably steady and extend across the In the central Paci®c, the Tsuchiya jets are distinctly entire Paci®c Ocean. A recent study of mean hydro- visible in an annual mean hydrographic section nomi- graphic sections from CTD data averaged on potential nally along 155ЊW from CTD data averaged on pressure density anomaly surfaces in the western Paci®c quan- surfaces (Wyrtki and Kilonsky 1984). As in the western ti®es the SSCC locations, velocities, and transports be- Paci®c, the north SSCC is stronger with a transport of tween 137Њ and 165ЊE (Gouriou and Toole 1993). For 9 ϫ 106 m3 sϪ1 and a mean velocity of 0.07 m sϪ1,as the north SSCC they suggest that a velocity core, distinct compared to the south SSCC with a 4 ϫ 106 m3 sϪ1 from the Equatorial Undercurrent (EUC) and the North transport and a mean velocity of 0.05 m sϪ1. Peak ve- Equatorial Countercurrent (NECC), develops between locity values are not reported but a zonal velocity section 137Њ and 142ЊE. At 165ЊE Gouriou and Toole estimate shows peak speeds Ͻ0.15 m sϪ1 in the north SSCC and 6 3 Ϫ1 a north SSCC volume transport of 11 ϫ 10 m s with Ͻ0.10 m sϪ1 in the south SSCC near 240-m depth at Ϫ1 a peak velocity of 0.27 m s occurring at 2.5ЊN near Ϯ4Њ from the equator. These peaks are 40 m shallower 280-m depth. For the south SSCC, they surmise an or- and 1.5Њ poleward of the maxima at 165ЊE. These peaks igin between 142Њ and 165ЊE. At 165ЊE they estimate are also much weaker than those at 165ЊE and 110ЊW 6 3 Ϫ1 a transport of 7 ϫ 10 m s with a peak velocity of (see below), but without commensurate changes in Ϫ1 0.22 m s at 2.5ЊS near 280-m depth. They also note transports. This seeming discrepancy arises because the strong gradients in potential vorticity across the axes of cross-sectional areas of the SSCCs are larger at 155ЊW than at 165ЊE and 110ЊW. These differences are at least partially artifacts of a shift in longitude of the mean * PMEL Contribution Number 1806. station positions near the south SSCC that increases station spacing there. A salinity section suggests the gradient observed across the north SSCC in the western Corresponding author address: Dr. Gregory C. Johnson, NOAA/ Paci®c Marine Environmental Laboratory, 7600 Sand Point Way N.E., Paci®c also exists in the central Paci®c at 4ЊN. In ad- Bldg. 3, Seattle, WA 98115-0070. dition, dissolved oxygen and nutrient concentration sec- E-mail: [email protected] tions show that both SSCCs are associated with oxygen-

Unauthenticated | Downloaded 09/26/21 06:16 PM UTC NOVEMBER 1997 JOHNSON AND MOORE 2449 rich, nutrient-poor water near Ϯ4Њ latitude (Wyrtki and (Pedlosky 1987, 1988, 1991), but until now no inertial Kilonsky 1984), properties advected from the west (Tsu- model has been proposed for the SSCCs. chiya 1975). In this paper we use historical CTD data to create The Tsuchiya jets in the eastern Paci®c are very well mean hydrographic pro®les averaged on neutral density studied. East of 119ЊW, they have been described ex- anomaly surfaces (Jackett and McDougall 1997) for se- tensively by Tsuchiya (1972, 1975) through analysis of lect areal bins in the tropical Paci®c Ocean, reducing many synoptic hydrographic sections. He notes that the the data across the entire ocean in a uniform manner SSCCs exist between 3Њ and 6ЊN and 4Њ and 8ЊS, and designed to preserve the small meridional and vertical shift poleward to the east. The north SSCC mean trans- scales of hydrographic features found in the Tropics. port is estimated at 8 ϫ 106 m3 sϪ1 with an average peak We present mean meridional sections of properties at velocity of 0.27 m sϪ1 at depths from 30 to 200 m; the 165ЊE, 155ЊW, and 110ЊW together with maps of prop- south SSCC transport is estimated at 5 ϫ 106 m3 sϪ1 erties on and between appropriate isopycnals. These data with an average peak velocity of 0.15 m sϪ1 at depths are used in a trans-Paci®c analysis to emphasize several from 80 to 250 m (Tsuchiya 1975). A similar, but more points about the Tsuchiya jets. First, the SSCCs are recent study of the north SSCC also using analysis of separate from the EUC, at least in the central and eastern several synoptic CTD sections along 110ЊW suggests a Paci®c. Second, the SSCCs start near the equator in the mean transport of 14 ϫ 106 m3 sϪ1 with a mean peak west and shift poleward toward the east. Third, this velocity of 0.40 m sϪ1 at 4.6ЊN near 120-m depth (Hayes poleward shift is correlated with a shoaling of the pyc- et al. 1983). The discrepancy between these two trans- nocline and the building pycnostad between the SSCCs. port estimates for the north SSCC near 110ЊW may arise We also present a simple inertial model of the SSCCs. from differences in the de®nition of its upper boundary. This inertial model accounts for the roughly constant The higher peak velocity estimate in the second study volume transports of the SSCCs, their advection of prop- probably results from ®ner horizontal resolution of the erties over long zonal distances, their persistent narrow- synoptic sections. In any case, the SSCCs in the eastern ness and rapidity, their poleward shift from west to east, Paci®c are again shallower and poleward of their lo- the pycnostad between them that builds in size and cations in the central Paci®c with transports and veloc- strength from west to east, and the associated potential ities roughly consistent with those reported to the west. vorticity gradients across them. The poleward shift as the SSCCs ¯ow eastward from 155Њ to 110ЊW has also been noted in a diagnostic cal- 2. Data and data reduction culation of the upper-ocean circulation (Bryden and Bra- dy 1985). For this study, CTD stations within different areal Finally, the water in the equatorial pycnostad in the bins in the tropical Paci®c are averaged to make a mean eastern Paci®c has been traced westward along the south hydrographic pro®le for each bin (Fig. 3: the dots in- Tsuchiya jet and then along a counterclockwise route dicate the locations of mean hydrographic pro®les near in the subtropical gyre to a surface origin near Tasmania the bin centers). In latitude, the bins are centered on by Tsuchiya (1981). This work demonstrates that the every 1Њ from 20ЊSto20ЊN. Bin widths are 1Њ in latitude, properties of water on a germane isanosteric surface are and hence include CTD stations halfway between in- modi®ed relatively little by mixing as it is advected over teger latitudes. In longitude, the bins are centered on great distances around the South Paci®c Ocean. It is the TAO array mooring longitudes (McPhaden 1993), argued that vertical mixing is dominant in in¯uencing with 85ЊW and 126ЊE added as central longitudes for the water properties near their surface origin, but that the far eastern and western Paci®c. Bin widths ranging lateral mixing plays the stronger role farther along the from 9Њ to 15Њ of longitude result from bin edges located subsurface ¯ow path. midway between these nominal longitudes. This strat- We are aware of only one theory for the dynamics of egy yields 13 mean meridional hydrographic sections, the Tsuchiya jets (McPhaden 1984). A linear, vertically some better sampled than others, which are used to make diffusive model simulates the SSCCs as lobes of the maps of properties on and between neutral density

EUC, formed at the poleward edge of a broad diffusive anomaly, ␥n, surfaces, and meridional property sections equatorial boundary layer. Within the boundary layer, at 165ЊE, 155ЊW, and 110ЊW, the three best-sampled downward vertical diffusion of cyclonic relative vortic- longitudes. CTD stations include all high-resolution data ity is balanced by poleward advection of planetary vor- available from the NODC archives, as well as those in ticity. Outside the boundary layer, the planetary vorticity the PMEL database from PMEL and some other cruises advection is balanced by vortex stretching, creating a not yet available from NODC. Nearly 14 000 individual pycnostad. In this model, the SSCCs are the result of CTD stations are used, located between 20.5ЊS and geostrophic balance across the pycnostad. However, in 20.5ЊN latitude and between 120ЊE and 80ЊW longitude, the central and eastern Paci®c Ocean, the SSCCs are taken from 1967 through 1996. separated from the EUC, suggesting nonlinear dynamics The CTD station data within each bin, consisting of may be important there (McPhaden 1984). More re- salinity S and temperature T as a function of pressure cently, the EUC has been modeled as an inertial jet P are averaged as a function of ␥n to create mean hy-

Unauthenticated | Downloaded 09/26/21 06:16 PM UTC 2450 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 drographic pro®les. Averaging S, T, and P as functions centered near the 20ЊC isotherm) shoals and strengthens of ␥n is more involved than the conventional approach from west to east (Fig. 1). This feature is deep (120± of averaging S, T, and ␥n as functions of P, but the 200 m) and relatively weak at 165ЊE, intermediate in technique better preserves water properties in the sharp depth (80±200 m) and strength at 155ЊW, and shallow tropical pycnocline (Gouriou and Toole 1993). First, to (50±120 m) and strong at 110ЊW. The poleward deep- reduce small-scale noise, individual CTD station S and ening of the thermocline south of the equator, and north T pro®les are ®ltered in P with a 10-dbar half-width of the equator to 4Њ±5ЊN, is associated with the southern Hanning ®lter and subsampled at 10-dbar intervals. and northern components of the westward-¯owing

Then ␥n is computed for these subsampled data and South Equatorial Current (SEC), respectively. The pole- averaged as a function of P to obtain a mean ␥n(P) ward shoaling of the thermocline north of 4Њ±5ЊNis pro®le at 10-dbar resolution. Following this step, the associated with the eastward-¯owing NECC. The individually ®ltered and sampled pro®les of S, T, and spreading of the thermocline around the equator marks P are linearly interpolated to each ␥n(P) pro®le value the eastward ¯owing EUC. This spreading is discernable to allow averaging of the individual CTD station data at 165ЊE and stronger at 155ЊW. At 110ЊW the EUC is as a function of ␥n at roughly 10-dbar resolution. Mean shallow and south of the equator, where isotherms dip pro®les for S(␥n), T(␥n), and P(␥n) are then calculated. near 1ЊS. This southern displacement from the equator Finally the mean P(␥n) pro®le is used to put the mean has been shown to be the result of meridional wind pro®les of S(␥n) and T(␥n) onto an even 10-dbar grid forcing (Philander and Delecluse 1983). Most relevant and construct a ®nal mean ␥n pro®le. to this study is a poleward shoaling of isotherms below Depth and properties of the surface mixed layer, in- the thermocline centered near Ϯ2.5Њ latitude at 165ЊE, cluding ␥n, vary over time. To construct a mixed layer Ϯ3.5Њ at 155ЊW, and Ϯ4.5Њ±5.5Њ at 110ЊW. This shoaling for the mean pro®les of S(␥n), T(␥n), and ␥n, the fol- shifts poleward and upward to the east under the ther- lowing procedure is used. First, the mixed-layer P for mocline, marking the Tsuchiya jets. By 110ЊW, the ther- each CTD station is de®ned as the P above which ␥n is mostad near 13ЊC between the SSCCs is very pro- Ϫ3 less than 0.1 kg m denser than the mean ␥n of the top nounced. 10 dbar. Mean S and T from the surface to the mixed- Mean meridional S sections show a subsurface con- layer P are calculated for each CTD station. Then these vergence of tongues toward the EUC (Fig. 1). The south- S and T values are averaged, weighted by the individual ern subsurface S maximum, water subducted in the mixed-layer P's so that deeper mixed-layer values get southern subtropics where evaporation dominates over more weight, to ®nd mean mixed-layer values for S and precipitation, is prominent in all three sections and T. These values are used with the mean mixed-layer P strongest at 155ЊW. North of the equator, surface S de- to calculate a mean mixed-layer ␥n. In order to avoid creases to the east under the intertropical convergence ␥n inversions in the mean pro®les, the pressure of the zone, a region of high precipitation (Ando and Mc- mean mixed-layer ␥n in the ®nal mean ␥n pro®le is used Phaden 1997). Salinity distributions on isopycnal sur- to de®ne a ®nal mean mixed-layer P. To ®nish, the mean Ϫ3 faces around ␥n ϭ 25.5 kg m , the core density of the mixed-layer S, T, and ␥n values are substituted into the EUC, suggest that the subsurface S minimum is almost mean S(␥n), T(␥n), and ␥n pro®les from the mean mixed- certainly a remnant of the North Paci®c Intermediate layer P to the surface. Water (Talley 1993). This fresh tongue appears to be The resulting 10-dbar mean hydrographic pro®les are converging along isopycnals toward the EUC, especially used exclusively in the analysis. The only further at 155ЊW, but almost certainly takes an indirect route smoothing performed for the mean meridional sections involving the nearly zonal interior currents and nearly presented is on the square of the buoyancy frequency, meridional western boundary currents. At 110 W the 2 Њ N , which is calculated from the mean hydrographic core of the EUC is marked by an isolated S maximum pro®les and then smoothed with a 30-dbar half-width advected from the west (Hayes et al. 1983; Lukas 1986), Hanning ®lter before use. Isopycnal maps are made by here found at 1ЊS, 65 m. Most relevant to this study, linearly interpolating the 10-dbar values of each mean isohalines are nearly vertical in the region of the north hydrographic pro®le to the appropriate . These values ␥n SSCC. The resulting strong deep S gradient near 2Њ± are then objectively mapped assuming a Gaussian co- 3ЊNat165ЊE, 2Њ±4ЊN at 155ЊW, and 4Њ±5ЊN at 110ЊW variance with correlation length scales of 1.5 lat and Њ suggests a front there and reinforces the assertion that 18 long and an error energy of 0.04. These correlation Њ the Tsuchiya jets are a barrier to meridional ¯ow (Gou- length scales are roughly 1.5 times the data separation, riou and Toole 1993). In addition, there is a well-de®ned with anisotropy appropriate for the interior of the Trop- S minimum just north of the front, just hinted at in the ics, where zonal scales greatly exceed meridional scales. sections by a pinching of isohalines at 4ЊN, 5ЊN, and 6ЊN going from 165ЊE to 155ЊW to 110ЊW, but very 3. Mean meridional sections of properties and apparent in an isopycnal map discussed in the next sec- transports tion (Fig. 3, top panel). Since S increases from west to Mean meridional potential temperature, ␪, sections east, this feature is probably fresher water being ad- show that the thermocline (roughly from 15Њ to 25ЊC, vected eastward on the northern edge of the north SSCC.

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FIG. 1. Mean meridional ␪ and S sections in the top 500 m of the ocean from 10ЊSto10ЊN along 165ЊE, 155ЊW, and 110ЊW. Contour intervals are 1ЊC (thick lines 5ЊC) for ␪ and 0.1 PSS-78 (thick lines 0.5 PSS-78) for S. Vertical exaggeration is 4000:1.

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Mean meridional ␥n sections (Fig. 2) are similar in SSCC peak velocity is weak, mostly owing to a shift appearance to those of ␪ (Fig. 1) and are shown pri- in longitude of the mean station positions (Fig. 3, solid marily for reference to the isopycnal maps and the mod- dots). At any rate, peak velocities from the mean sec- el. The previous discussion of the thermocline and ther- tions are most likely lower than those in synoptic sec- mostad applies equally to the pycnocline and pycnostad, tions because of the relatively large latitudinal bin with S modifying the structure slightly. However, the widths and temporal variability of the SSCCs core lat- mean meridional N 2 sections (Fig. 2) are worthy of more itudes. The volume transport estimates and peak veloc- discussion. The surface mixed layer is characterized by ity statistics are in rough accord with the studies dis- very low N 2 and shoals from 165ЊE to 110ЊW. The pyc- cussed in the introduction. However, the estimates pre- nocline, a vertical maximum in N 2, is relatively thick, sented here are improved by uniform analysis of an deep, and weak at 165ЊE. By 110ЊW it has thinned, expanded dataset. nearly doubled in strength, and shoaled. Below the pycnocline, N 2 generally weakens with increasing depth, 4. Isopycnal maps but a very distinct equatorial pycnostad associated with Ϫ3 the SSCCs develops, here described as it strengthens Salinity on ␥n ϭ 26.5 kg m , an isopycnal near the from west to east. At 165ЊE, the 20 and 25 ϫ 10Ϫ6 sϪ2 pycnostad and within the Tsuchiya jet cores, as de®ned contours rise up at Ϯ2Њ from the equator, marking a by the transport-weighted ␥n just discussed, reveals a Ϫ3 weak pycnostad centered near ␥n ϭ 26.74 kg m at great deal about the SSCCs sources and structure (Fig. these latitudes. By 155ЊW a well-developed stability 3). The strong S front starting just north of the equator minimum is evident on both sides of the equator, with in the western Paci®c shifts poleward and weakens to Ϫ6 Ϫ2 Ϫ3 values near 12 ϫ 10 s at ␥n ϭ 26.62 kg m , again the east. This S front suggests that the SSCCs are a most extreme Ϯ2Њ from the equator, but broader in the barrier to meridional ¯ow (Gouriou and Toole 1993), at horizontal. By 110ЊW the minimum is less than 10 ϫ least in the western Paci®c where the front is sharp. The Ϫ6 Ϫ2 Ϫ3 10 s near ␥n ϭ 26.47 kg m . The latitudinal dis- meridional S minimum just north of the front is the result tribution shows a slight increase in stability on the equa- of advection in the north SSCC. The only strong S con- tor, but the pycnostad extends from 5ЊSto4ЊN. Thus, trast is near the northern edge of the north SSCC, sug- as the pycnostad builds in strength and expands in area gesting that the source waters for both SSCCs are pri- to the east, it also shoals and its core ␥n value decreases marily from the southwestern Paci®c (Tsuchiya 1981), by 0.27 kg mϪ3. similar to but slightly denser than the waters feeding Geostrophic volume transport and velocity calcula- the EUC (Tsuchiya et al. 1989). Salinity may also be tions are made using a reference surface of 700 dbar, an advective tracer for the south SSCC, showing a faint Ϫ3 near ␥n ϭ 27.3 kg m . This surface is deep enough to maximum, but dissolved oxygen concentration (not an- capture the Tsuchiya jets and is the mean of those used alyzed here) easily reveals both SSCCs through advec- in three previous quantitative works in the region: 600 tively formed isolated maxima on isopycnals (Tsuchiya dbar at 165ЊE (Gouriou and Toole 1993), 1000 dbar at 1975; Wyrtki and Kilonsky 1984). Ϫ3 155ЊW (Wyrtki and Kilonsky 1984), and 500 dbar at The isopycnal ␥n ϭ 26.0 kg m (Fig. 3) is near the 110ЊW (Tsuchiya 1975). Table 1 lists the volume trans- base of the pycnocline, above the pycnostad associated port estimates of eastward ¯ow between ␥n ϭ 25.5 and with the SSCCs (Fig. 2). The poleward deepening south 27.3 kg mϪ3. The lower limit is near the reference sur- of the equator, the deep values near the equator, and face and the upper limit is imposed to isolate the north those from 4Њ to 6ЊN are expressions of the southern SSCC from the eastward-¯owing NECC. Only eastward component of the SEC, the EUC, and the axis between ¯ow between the bounding latitudes contributes to the the northern component of the SEC and the NECC, transports in Table 1; these horizontal limits are based respectively. However, most germane to the dynamics on a subjective examination of the mean meridional ␥n of the SSCCs, the surface rises steadily to the east as and N 2 sections so as to capture the eastward ¯ow just does the pycnocline just above it. Ϫ3 poleward of the equatorial pycnostad. These horizontal In contrast, ␥n ϭ 26.8 kg m (Fig. 3) is below the limits are also well de®ned in that there is westward pycnostad associated with the Tsuchiya jets, except in ¯ow to either side. The SSCCs volume transports are the far western Paci®c (Fig. 2). However, while this relatively constant, except at 165ЊE where the north surface is below the pycnostad, it is not so deep that it SSCC value may be high because some NECC ¯ow is escapes the in¯uence of the SSCCs. In fact, it is at the included in the estimate. The transport-weighted ␥n of zone of maximum vertical shear of the SSCCs in the the SSCCs (Table 1) are near the pycnostad core values central Paci®c, slightly above it in the western Paci®c, discussed above, since the SSCCs reside in the pyc- and slightly below it in the eastern Paci®c. The strong Ϫ3 nostad, but show only an 0.09 kg m decrease in ␥n to shoaling poleward of Ϯ2Њ latitude in the western Paci®c, the east, a third of the decrease in those core values. shifting to poleward of Ϯ4Њ latitude in the eastern Pa- The peak velocities shift poleward and shoal in both ci®c, is the expression of the eastward-¯owing SSCCs hemispheres (Table 1). Peak velocities remain strong in each hemisphere. The weaker gradient in the Southern across the Paci®c except at 155ЊW, where the south Hemisphere is consistent with the lower velocity and

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2 Ϫ3 FIG. 2. As in Fig. 1 but for ␥n and N . Contour intervals vary for both quantities, but thick lines are at 1.0 kg m Ϫ6 Ϫ2 2 intervals for ␥n and 200 ϫ 10 s intervals for N .

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TABLE 1. Geostrophic volume transport and velocity calculations made for the Paci®c SSCCs using the mean meridional sections at each Ϫ3 longitude, referenced to 700-dbar pressure. Only eastward ¯ow between ␥n ϭ 25.5 and 27.3 kg m within the latitude bounds given is used in the transport calculations. Volume transport and transport-weighted ␥n remain roughly constant from west to east. Peak velocity latitudes, depths, and magnitudes show the Tsuchiya jet cores shifting poleward, shoaling, and maintaining speed from west to east. Transport calculations Peak velocities Volume Transport-

Section Latitude transport weighted ␥n Peak Peak depth Peak magnitude (long) bounds (106 m3 sϪ1) (kg mϪ3) latitude (m) (m sϪ1) South SSCC 165ЊE 5Њ±2ЊS 6.6 26.62 2.5ЊS 250 0.17 155ЊW 8Њ±3ЊS 4.1 26.67 3.5ЊS 250 0.07 110ЊW 6Њ±3ЊS 6.2 26.57 5.5ЊS 160 0.16 North SSCC 165ЊE 2Њ±5ЊN 10.3 26.58 2.5ЊN 240 0.26 155ЊW 2Њ±5ЊN 7.0 26.63 3.5ЊN 220 0.21 110ЊW 3Њ±6ЊN 7.4 26.45 4.5ЊN 130 0.21 transport estimates for the SSCC there. The slight shoal- ity. Near the equator, the pycnocline in the Paci®c shoals ing at the equator is a shallow signature of the EIC. to the east as a result of the near-balance in the layer The most evocative map in terms of the Tsuchiya jet above, between zonal pressure gradient and wind stress dynamics is that of thickness between the surfaces just (McPhaden and Taft 1988). Off the equator, the pyc- Ϫ3 discussed, ␥n ϭ 26.0 and 26.8 kg m (Fig. 3), which nocline shoals to the east as a result of the near-balance bound the pycnostad core values. In the model presented of the wind stress curl and the product of poleward mass Ϫ3 below, ␥n ϭ 26.0 kg m can be thought of as repre- transport and ␤ (Sverdrup 1947). However, the dynam- senting the pycnocline between the surface layer and ics of the surface layer, here termed layer 0, have been Ϫ3 the active layer, and ␥n ϭ 26.8 kg m the interface studied extensively elsewhere. Only the observed east- between the active layer and the quiescent abyssal layer. ward shoaling of the pycnocline is vital to the evolution Hence the thickness between these surfaces is that of of the model jet, found in layer 1, so the pycnocline the active layer. This thickness map dramatically illus- depth D, which is the interface between layer 0 and trates the poleward shift of the SSCCs from west to east. layer 1, is simply set to shoal eastward. The abyss, here It also shows the pycnostad between the SSCCs as it termed layer 2, is assumed to be quiescent, allowing builds and spreads poleward from west to east. Finally, reduced-gravity dynamics to hold in layer 1. Since layer the poleward thinning of this layer across the axes of 1 has a positive thickness, h, the depth of the interface the SSCCs is indicative of the strong potential vorticity between layers 1 and 2 is ␩ ϭ D Ϫ h. Here D and ␩ gradients across them. The slight decrease in thickness are negative relative to the ocean surface. With the focus on the equator is the result of a constructive combination on layer 1, between the prescribed pycnocline and the of the deep expression of the eastward-¯owing EUC at quiescent abyss, the dynamics reduce to a nonlinear the upper isopycnal and the shallow expression of the model with 1½ layers. The model works with any spec- westward-¯owing EIC at the lower isopycnal. i®ed D(x) that is a function of the zonal direction, x, with no meridional, y, dependence. The inviscid momentum equations for the active layer 5. An inertial model 1 are The simple model inertial jet presented below repro- ␤yu ϭ gЈ␩ ϭϪgЈh , (1) duces many of the properties of the Tsuchiya jets. At yy this point, the Tsuchiya jets have been shown to be uuxyϩ ␷u Ϫ ␤y␷ ϭ gЈ␩ xϭ gЈD xϪ gЈh x. (2) features of the equatorial circulation that extend across These equations are formulated assuming u k ␷, so that much of the Paci®c Ocean. Observational characteristics the meridional momentum balance is purely geostrophic of the SSCCs that are reproduced by the model are their but the zonal momentum balance retains the inertial terms. constant volume transports, their advection of properties The reduced gravity gЈϭ2g(␳ Ϫ ␳ )/(␳ ϩ ␳ ) is deter- over long zonal distances, their rapidity and narrowness, 2 1 2 1 mined by the density difference between the quiescent their poleward shift from west to east, the large potential abyssal layer 2 and the active layer 1 (Fig. 4), where ␳ ϭ vorticity gradients across them, and the pycnostad be- ␥ ϩ 1000 kg mϪ3. The continuity equation is tween them which builds from west to east. n

The essential properties of the model are illustrated (uh)x ϩ (␷h)y ϭ 0, (3) in a schematic (Fig. 4). Since the basic dynamics is the so a transport streamfunction, ␺(x, y), can be de®ned as same on either side of the equator, only the north SSCC will be modeled here in the interest of clarity and brev- uh ϭϪ␺y, ␷h ϭ ␺x, (4a, 4b)

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Ϫ3 FIG. 3. Salinity on ␥n ϭ 26.5 kg m , with contour intervals of 0.05 PSS-78 and saltier values Ϫ3 increasingly shaded (top panel). Depth of ␥n ϭ 26.0 kg m , with contour intervals of 25 m Ϫ3 and deeper values increasingly shaded (second panel from top). Depth of ␥n ϭ 26.8 kg m , with contour intervals of 25 m and deeper values increasingly shaded (third panel from top). Ϫ3 Thickness between ␥n ϭ 26.0 and 26.8 kg m , with contour intervals of 25 m and thicker values increasingly shaded (bottom panel). All panels are objectively mapped from the values at each mean hydrographic pro®le location as described in the text. The mapping uses the Peters projection. satisfying (3). From (1) and (2) the Bernoulli function, spect to streamfunction, is also conserved on streamlines. The potential vorticity includes relative vorticity uu22 B(␺) ϭϪgЈ␩ ϭϪgЈ(D Ϫ h), (5) from meridional variations in zonal velocity as a result 22 of retaining inertial terms in (2). which includes the zonal kinetic energy as a result of The model boundary conditions are set as follows. retaining inertial terms in (2), is conserved following At the western edge of the model domain, longitude x ϭ x (140ЊE), an in¯ow pro®le u (y) is speci®ed in the ¯uid parcels, and therefore must be a function of ␺ 0 0 active layer, bounded by quiescent ¯uid at both the equa- alone. Furthermore, the potential vorticity, torward, ye, and poleward, yp, edges. Specifying an dB ␤y Ϫ uy equatorward interface depth, ␩e,aty ϭ ye and inte- Q(␺) ϭϭ , (6) d␺ h grating (1) with respect to y gives the corresponding layer interface depth, ␩0(y). After integrating (4a) to ®nd being the derivative of the Bernoulli function with re- ␺ at x ϭ x0, (5) and (6) are used to ®nd B(␺) and Q(␺).

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FIG. 4. Perspective view of the model jet from 30ЊW of south at 30Њ elevation (solid lines for visible jet boundaries, dashed lines for hidden boundaries). The surface layer is not discussed. The pycnocline depth, D, is the interface between layer 0 and layer 1. This interface is constant in latitude but slopes linearly up to the east (upper plane of dotted lines). Since layer 0 is ignored, D can be thought of as inverted topography at the top of layer 1. The interface depth between the active layer 1 and the quiescent abyssal layer 2 is ␩. This deeper interface is constant on either side of the jet (lower sets of dotted lines), but slopes up within it, where the velocity, u, is ®nite. The interface depths D and ␩ are both negative values referenced to the surface, but their difference, the layer 1 thickness, h, is a positive quantity. The reduced gravity, gЈ,at␩ is

related to the neutral density anomalies, ␥n, as discussed in section 5. As the pycnocline shoals

to the east, the jet edges ye and yp shift poleward as the jet thickens, conserving Bernoulli function and potential vorticity on streamlines. Vertical±meridional exaggeration is 167 000:1 and meridional±zonal exaggeration is 124:1.

It follows from (1) that, since the ¯uid is quiescent 0.05 m sϪ1, a peak velocity of 0.25 m sϪ1 at 2.26ЊN, a outside the model jet, the interface depths at its edges, decay scale of 0.72Њ lat, and edges at 0.09Њ and 4.61ЊN. Ϫ3 Ϫ2 ␩e and ␩p, are both constants. The jet edges are stream- The reduced gravity gЈϭ5 ϫ 10 ms , a value lines, ␺e and ␺p, so applying (5) shows that zonal speeds characteristic of the density difference between the at the edges, ue and up, are also constants. abyss and the pycnostad. Setting ␩e ϭϪ375 m and

Equations (4a), (5), and (6) can be recast as a set of integrating to yp gives ␩0(y) and ␩p ϭϪ300 m. The net coupled ®rst-order differential equations: transport is 7.0 ϫ 106 m3 sϪ1, close to values of the observed SSCC (Table 1). B(␺) u2 ␺ ϭϪu ϪϩD(x) , (7) For these initial conditions, when (7) and (8) are in- y gЈ 2gЈ []tegrated at xc, three solutions are found. The existence of multiple solutions should not be too much of a sur- B(␺) u2 u ϭ ␤y Ϫ Q(␺) ϪϩD(x) . (8) prise since the dynamical system is nonlinear and the y []gЈ 2gЈ model jet edges are free to vary their position. The ®rst solution is the original Gaussian. A second solution is At each longitude, we guess the location of ye, integrate (7) and (8) until ␺ ϭ ␺ , check to see if u ϭ u there, slightly narrower, with edges shifted poleward to 0.48Њ p p and 4.86ЊN, a peak velocity of 0.27 m sϪ1 at 2.20ЊN, and if not, repeat the process, adjusting ye until this condition is met. This solution algorithm has been used and an interior velocity minimum near the north edge. before for similar problems (Pedlosky 1987). A mono- The third solution is the narrowest, a blunted triangular tonic potential vorticity pro®le across the model jet velocity pro®le extending from 0.68Њ to 3.77ЊN with a maintains suf®cient conditions for stability of the basic maximum value of 0.30 m sϪ1 at 2.25ЊN (Figs. 4 and state (Pedlosky 1979). 5). The ®rst two solutions get broader, slower, and quick- A number of integrations were carried out, but only ly develop interior zonal ¯ow minima and then reversals one is presented here. The model pycnocline depth is as the pycnocline shoals to the east. Flow reversals make chosen as D(x) ϭ Do ϩ sx, and shoals linearly with s it impossible to calculate a solution with the simple ϭ 1.1305 ϫ 10Ϫ5 from Ϫ237.5 m at 140ЊE, the western procedure outlined here, so we cannot follow these so- edge of the model domain, to Ϫ62.5 m at 80ЊW, the lutions across the entire domain. The third solution nar- eastern edge of the domain. Here u0(y) at x0 ϭ 140ЊE rows, accelerates, and does not develop interior ¯ow Ϫ1 is chosen as a Gaussian with ue ϭ 0.05 m s , up ϭ minima or reversals as the pycnocline shoals to the east.

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FIG. 5. Active layer thickness within the model jet plotted against latitude from 140ЊEto80ЊWat20Њ intervals (top left panel) and velocity plotted against latitude from 140ЊEto80ЊWat20Њ intervals (top right panel). Jet edges (thick dashed Ϫ3 lines in bottom panel) are plotted over thickness between ␥n ϭ 26.0 and 26.8 kg m as in the bottom panel of Fig. 3. The jet shifts poleward, narrows in the meridional, thickens in the vertical, and accelerates to the east as a consequence of conservation of potential vorticity and Bernoulli function under the shoaling pycnocline.

This third jetlike solution can be found across the entire ␩0(y), so it is substituted as the initial condition at lon- domain and is chosen as the preferable one. E. Firing gitude x0 and carried eastward. (1995, personal communication) has also pointed out The solution dynamics are simple. The model is in- that the narrowest, fastest jet has the lowest total energy viscid, so the boundary values at the western edge of for a given B(␺) and transport, making it plausibly the the model jet and the zonal slope of the pycnocline most stable ¯ow. This solution does not match u0(y) and determine its evolution across the basin. As the jet

Unauthenticated | Downloaded 09/26/21 06:16 PM UTC 2458 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 moves eastward, it is stretched vertically by the shoaling edge the tendency of the relative vorticity is to reduce pycnocline over the quiescent abyss, hence it shifts pole- the magnitude of the potential vorticity, while at the ward to conserve Q. As the jet becomes thicker in the poleward edge the tendency is to increase it. This growth vertical to the east it accelerates and narrows in the of relative vorticity near the edges is accomplished horizontal to conserve transport. Retention of the in- through the narrowing of the jet and an increase in the ertial terms in (2) allows the jet to narrow and accelerate, peak velocity from 0.30 to 0.47 m sϪ1 from west to east making relative vorticity important in Q conservation (Figs. 4 and 5). near the jet edges. A totally different behavior is predicted if the model is formulated using the dynamics of 6. Discussion the ventilated thermocline theory (Luyten et al. 1983), where the geostrophic balance holds for both momen- The model does not consider the origin of the Tsu- tum equations but the continuity equation remains non- chiya jets. One possibility is that in the western Paci®c linear. In this case, the interface depth alone gives the the Tsuchiya jets are generated as lobes of the EUC Bernoulli function and the potential vorticity contains under the diffusive dynamics discussed by McPhaden only the planetary term. Streamlines follow ␤y/h con- (1984). These lobes could separate from the EUC in the tours, so they originate on the equator and shift poleward east due to the poleward shift forced by the shoaling to the east in direct proportion to the increase in active thermocline, as discussed here, and propagate nearly layer thickness caused by the shoaling pycnocline. The inertially. However, vertical friction suf®ciently strong streamlines under the ventilated thermocline dynamics to spin up the SSCCs in the western Paci®c would likely diverge to the east whereas those of the chosen inertial damp them out in the central Paci®c. Another possibility solution converge. Hence, the inclusion of inertial terms, for their origin is a current at the western boundary retaining relative vorticity and kinetic energy in the dy- turning east, similar to the way in which the EUC ap- namics, is central to the character of the model jet pre- pears to be fed in observations and models (Tsuchiya sented here. et al. 1989; Pedlosky 1991). While observations suggest We derive a simple measure of the poleward shift as the south SSCC is fed by water from the south (Tsuchiya the model jet moves eastward. The streamfunction- 1981), the north SSCC appears to have contributions weighted latitude of the jet, ͗y͘, written in streamfunc- from both hemispheres (Bingham and Lukas 1995). tion coordinates, is In the eastern Paci®c another interesting problem aris- ␺ es: the termination of the Tsuchiya jets. In an inertial 1 p ͗y͘ϭ yd␺. (9) model of the EUC, the right strength of diffusive up- ␺peϪ ␺ ͵ ␺e welling at the equator can remove mass from the EUC Some manipulation leads to an expression for ͗y͘ as as it ¯ows eastward, terminating it at the eastern bound- proportional to the means and differences of various ary (Pedlosky 1988). It seems likely that vertical dif- quantities at the jet edges fusive processes, at or away from the equator, could be included in a more complex model of the SSCCs to model their termination. It is possible that vertical dif- gЈ hppϪ hee␩ ϩ ␩ ͗y͘ϭ D Ϫ . (10) fusive processes could take place within the SSCCs. ␤␺p Ϫ ␺ 2 ΂΃e []Alternatively, the pycnostad between the SSCCs does The term inside the square brackets can also be written intersect the equator, and might allow strong vertical as (hp ϩ he)/2. Thus ͗y͘ shifts poleward more quickly processes there to be connected to the SSCCs. We know if the reduced gravity is large, the difference in interface of no observational study describing the fate of the north depths at the jet edges is large, the net transport is small, SSCC. However, observations suggest that the EUC and or the pycnocline slope to the east is large. the south SSCC turn south at the eastern boundary to The model jet shifts poleward just as predicted by the feed the Peru±Chile undercurrent and countercurrent ͗y͘ expression (Figs. 4 and 5). The model parameters (Lukas 1986). This observational work seems to pre- give a ͗y͘ that starts at 2.1ЊN at 140ЊE and reaches 5.8ЊN clude the total dominance of vertical processes in de- by 80ЊW. Mean layer thicknesses within the jet increase termining the fate of the EUC and the SSCCs. steadily from 106 to 278 m from west to east, a factor One interesting feature of the observations not ex- of 2.62. The jet narrows from 3.09Њ to 0.72Њ latitude by plained by the model is the decrease of transport-weight- a factor of 0.233. The jet accelerates from a mean ve- ed ␥n in the Tsuchiya jets from west to east. This de- locity of 0.19 to 0.31 m sϪ1 from west to east, a factor crease, if it is signi®cant in the face of the many un- of 1.63. Multiplication of these factors to obtain unity certainties present in the transport calculations, suggests illustrates how transport is conserved within the jet. As that mixing processes in the ocean may play some role the jet narrows and thickens, the thickness increase is in the SSCCs dynamics. These mixing processes pre- offset by a poleward shift in latitude to conserve po- sumably do work to diffuse the SSCCs, altering the tential vorticity overall (Figs. 4 and 5). The relative potential vorticity distribution within them by decreas- vorticity becomes very large at the edges of the jet to ing the magnitude of the relative vorticity on their edges. conserve potential vorticity there. At the equatorward The model results suggest that the tendency toward po-

Unauthenticated | Downloaded 09/26/21 06:16 PM UTC NOVEMBER 1997 JOHNSON AND MOORE 2459 tential vorticity conservation in the ocean overcomes Lukas, R., 1986: The termination of the equatorial undercurrent in the effects of mixing to keep the Tsuchiya jets focused the eastern Paci®c. Progress in Oceanography, Vol. 16, Per- gamon Press, 63±90. and shifting poleward by vortex stretching under the Luyten, J. R., J. Pedlosky, and H. Stommel, 1983: The ventilated shoaling pycnocline. thermocline. J. Phys. Oceanogr., 13, 292±309. McPhaden, M. J., 1984: On the dynamics of equatorial subsurface Acknowledgments. This work was funded by the Cli- countercurrents. J. Phys. Oceanogr., 14, 1216±1225. mate and Global Change Program through the NOAA , 1993: TOGA-TAO and the 1991±1993 El NinÄo±Southern Os- cillation event. Oceanography, 6, 36±44. Of®ce of Global Programs and by the NOAA Paci®c , and B. A. Taft, 1988: Dynamics of seasonal and intraseasonal Marine Environmental Laboratory. LuAnne Thompson variability in the eastern equatorial Paci®c. J. Phys. Oceanogr., provided insightful advice on model formulation and 18, 1713±1732. integration. Julian McCreary and Eric Firing made nu- Pedlosky, J., 1979: Geophysical Fluid Dynamics. Springer-Verlag, 624 pp. merous helpful suggestions to improve the manuscript. , 1987: An inertial theory of the Equatorial Undercurrent. J. Nancy Soriede, Marie Schall, Dal McClurg, and Stephan Phys. Oceanogr., 17, 1978±1985. Zube all helped with programming and database man- , 1988: Entrainment and the termination of the Equatorial Un- agement. Kristene McTaggart calibrated a great deal of dercurrent. J. Phys. Oceanogr., 18, 880±886. the PMEL CTD data used in this work. , 1991: The link between western boundary currents and equatorial undercurrents. J. Phys. Oceanogr., 21, 1553±1558. Philander, S. G. H., and P. Delecluse, 1983: Coastal currents in low REFERENCES latitudes (with application to the Somali and El NinÄo currents). Deep-Sea Res., 30, 887±902. Ando, K., and M. J. McPhaden, 1997: Variability of surface layer Sverdrup, H. U., 1947: Wind-driven currents in a baroclinic ocean hydrography in the tropical Paci®c Ocean. J. Geophys. Res., in with application to the equatorial currents of the eastern Paci®c. press. Proc. Nat. Acad. Sci., 33, 318±326. Bingham, F. M., and R. Lukas, 1995: The distribution of intermediate Talley, L. D., 1993: Distribution and formation of North Paci®c In- water in the western equatorial Paci®c during January±February termediate Water. J. Phys. Oceanogr., 23, 517±537. 1986. Deep-Sea Res. II, 42, 1545±1573. Tsuchiya, M., 1972: A subsurface north equatorial countercurrent in Bryden, H. L., and E. C. Brady, 1985: Diagnostic model of the three- the eastern Paci®c Ocean. J. Geophys. Res., 77, 5981±5986. dimensional circulation in the upper equatorial Paci®c Ocean. J. , 1975: Subsurface countercurrents in the eastern equatorial Pa- Phys. Oceanogr., 15, 1255±1273. ci®c Ocean. J. Mar. Res., 33(Suppl.), 145±175. Gouriou, Y., and J. Toole, 1993: Mean circulation of the upper layers , 1981: The origin of the Paci®c equatorial 13ЊC water. J. Phys. of the western equatorial Paci®c Ocean. J. Geophys. Res., 98, Oceanogr., 11, 794±812. 22 495±22 520. , R. Lukas, R. A. Fine, E. Firing, and E. Lindstrom, 1989: Source Hayes, S. P., J. M. Toole, and L. J. Mangum, 1983: Water-mass and waters of the Paci®c Equatorial Undercurrent. Progress in transport variability at 110ЊW in the equatorial Paci®c. J. Phys. Oceanography, Vol. 23, Pergamon Press, 101±147. Oceanogr., 13, 153±168. Wyrtki, K., and B. Kilonsky, 1984: Mean water and current structure Jackett, D., and T. J. McDougall, 1997: A neutral density variable during the Hawaii-to-Tahiti shuttle experiment. J. Phys. Ocean- for the world's ocean. J. Phys. Oceanogr., 27, 237±263. ogr., 14, 242±254.

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