Interaction between an Island and the Ventilated Thermocline: Implications for the Hawaiian Lee Countercurrent

Transcription

1 3408 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 3 Interaction between an Island and the Ventilated Thermocline: Implications or the Hawaiian Lee Countercurrent BO QIU AND THEODORE S. DURLAND Department o Oceanography, University o Hawaii at Manoa, Honolulu, Hawaii (Manuscript received 0 December 001, in inal orm 17 May 00) ABSTRACT The ventilated thermocline theory is adapted to include the interaction between an island and the wind-driven subtropical circulation. The primary goal is an understanding o the eect o this interaction on the Hawaiian Lee Countercurrent (HLCC), an eastward current crossing the Paciic west o Hawaii in the latitude band 18 1N. A two-and-one-hal-layer model is used, with the model island located in midgyre and equatorward o the gyre center, simulating the Hawaiian Islands. The presence o the island creates two wakes. A transport wake directly west o the island is characterized by an alteration o the zonal transport caused by the diversion o the interior low incident upon the east coast o the island into zonal jets extending westward rom the northern and southern tips o the island. A potential vorticity (pv) wake embedded in the second-layer streamlines westward and equatorward o the island is characterized by an alteration o the ventilated pv signature and o the baroclinic nature o the low. The eects o the two wakes combine or a signiicant impact on both the transport and the baroclinic structure o the modeled HLCC, indicating that eective modeling o the HLCC should include not only the orcing mechanism, but also the inluence o the large-scale Sverdrup low to the east as modiied by the Hawaiian Islands. In particular, a zonal variation in baroclinic structure is predicted that is consistent with observations. 1. Introduction The establishment o the ventilated thermocline theory by Luyten et al. (1983, hereinater reerred to as LPS) and the potential vorticity (pv) homogenization theory by Rhines and Young (198) has laid a solid oundation or our understanding o the large-scale wind-driven ocean circulation. These two elegant and complementary theories were not only a triumph or theoretical physical oceanography, they also provided new impetus to interpret observed circulation eatures on more solid dynamical bases. LPS, Talley (1985), and De Szoeke (1987, hereinater DS) demonstrated that the ventilated thermocline theory accurately predicts largescale eatures in the North Atlantic, North Paciic, and South Paciic, respectively. The eect o New Zealand on the South Paciic circulation was addressed by DS, but in that case the island lay within the western shadow zone, and the lower layers west o the island were assumed to be motionless. When an island resides in the ventilated region and near the gyre center (as does Hawaii), the likelihood o motion in the lower layer(s) west o the island must be considered, and new assumptions Corresponding author address: Dr. Bo Qiu, Dept. o Oceanography, University o Hawaii at Manoa, 1000 Pope Road, Honolulu, HI bo@soest.hawaii.edu must be made to adapt the ventilated thermocline theory to the vicinity o the island. Our eort to understand the interaction between the island and the ventilated thermocline is motivated by several recent studies describing circulation eatures observed in the lee o the Hawaiian Islands. By analyzing historical surace driter data available or the Hawaiian waters, Qiu et al. (1997) and Lumpkin (1998) showed that a narrow eastward current, dubbed the Hawaiian Lee Countercurrent (HLCC), exists west o the island o Hawaii (the Big Island ) in the latitudinal band o 19 0N (see Fig. 5 in Qiu et al. 1997). Despite being a relatively weak zonal current with a mean surace velocity o about 15 cm s 1, the HLCC is identiiable in climatological surace dynamic topography maps, such as that (Fig. 1) constructed by Kobashi and Kawamura (001) through combining historical and more recent World Ocean Circulation Experiment (WOCE) hydrographic data. In the igure, the HLCC corresponds to the 19 1N band west o the Big Island where the surace dynamic height contours o cm veer abruptly eastward. In contrast to the driter data showing the HLCC to be conined zonally near the Hawaiian Islands rom 158W to168w, Fig. 1 reveals that the HLCC can be detected as an entity as ar west as 160E (see also Aoki et al. 00). Figure shows the zonal ADCP velocity and hydrographic sections or the meridional WOCE transects P14 00 American Meteorological Society

2 DECEMBER 00 QIU AND DURLAND 3409 FIG. 1. Mean surace dynamic topography (cm) relative to 1000 dbar (adapted rom Fig. 5a o Kobashi and Kawamura 001). Dotted lines denote the two WOCE hydrographic/adcp sections: P14 along 179E and P15 along 165W. Results rom these two cruises are shown in Fig.. and P15, both o which show eastward low in the latitude band o the HLCC. WOCE P15 (Figs. a,b) is about 1100 km west o the Hawaiian Islands (Fig. 1), and it reveals an eastward low between 17.5 and 0.5N that is conined to the upper 150 m, with a maximum speed o 0 cm s 1. WOCE P14 (Figs. c,d), about 500 km west o the Hawaiian Islands, reveals a broader and deeper, but still surace-intensiied eastward low. Because the HLCC resides in a region o relatively high eddy activity (Flament et al. 001; Yu et al. 00, manuscript submitted to J. Phys. Oceanogr.), any snapshot in time must be interpreted cautiously, and the exact signiicance o the above-mentioned eastward lows is open to debate. However, we show in section 4 that the dierence in baroclinic structure o the eastward low between Fig. a (P15) and Fig. c (P14) is consistent with the eect o the Hawaiian Islands on the ventilated Sverdrup low rom the northeast. In pursuit o the orcing mechanism o the HLCC, Xie et al. (001) analyzed surace wind measurements rom the Quick Scatterometer (QuikSCAT) satellite and ound the existence o intense positive and negative wind stress curl anomalies west and southwest o the Big Island, respectively. Under the orcing o these localized wind stress curl anomalies, they showed that an eastward zonal current similar to the observed HLCC and extending as ar west as 130E can be simulated in oceanic general circulation models o various dynamic complexity. Xie et al. (001) emphasized the importance o this current to the coupled ocean atmosphere system in that the advection o warm western Paciic surace water to the east generates a positive eedback that sustains the sea surace temperature and surace wind anomalies over the long distance between the Hawaiian Islands and the western boundary. Because the Hawaiian Islands exist in the middle o FIG.. (a) Zonal velocity and (b) temperature distributions along 165W rom shipboard ADCP and CTD observations o the WOCE P15 cruise (Sep Nov 1994). Shaded areas in (a) denote eastward lows. The same distributions along 179E are shown in (c) and (d) based on the WOCE P14 cruise (Jul Aug 1993). For more details o the P14 cruise, see Roden (1998).

3 3410 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 3 the large-scale wind-driven subtropical gyre, detailed circulation patterns west o the Hawaiian Islands are inluenced not only by the regional wind orcing, but also by the interior oceanic low impinging upon the Hawaiian Islands rom the east. Consequently, a complete understanding o the HLCC also requires an examination o how the islands interact with the interior circulation driven by the winds north and east o the islands. It is worth mentioning that the blocking o the barotropic interior transport by the Hawaiian Islands, and its inluence upon the circulation to the west, was considered in an earlier study by White and Walker (1985). They assumed that all o the interior transport incident upon the east coast o the islands would turn north along this coast in a western boundary current. With the insight provided by Godrey s (1989) island rule, we know in hindsight that this assumption is incorrect. Although it should accurately predict the inluence on the barotropic transport directly west o the island chain, it would overestimate the inluence on the zonal band extending west rom the northern tip o the islands and miss the inluence on the zonal band west o the southern tip. In this study, we examine not only the blocking o the barotropic transport, but also the impact o the islands on the baroclinic nature o the low, by adopting the two-and-one-hal-layer ventilated thermocline model as our theoretical basis. In section we develop the methodology to include an island in the LPS theory based on the lowest-order assumptions. Basically, these are 1) the assumption o Sverdrup dynamics everywhere except within an island western boundary current (wbc) and ) some approximations based on the smallness o the island relative to the size o the gyre. In section 3 we apply this methodology to an idealized basin to clariy the eect o these assumptions on the low west and southwest o the island. Section 4 employs a realistic basin geometry, island geometry, and wind orcing (including the above-mentioned dipole) and calculates the transport and baroclinic structure o the HLCC based on 1) the eect o the wind product alone and ) the combined eect o the wind product and the perturbation o the general Sverdrup low by the island. We show that the eect o the island on the ventilated thermocline low is signiicant, particularly with regard to the baroclinic structure o the HLCC. In section 5, we address the eect o horizontal and vertical eddy diusion upon the second-layer pv signal during the crossing o zonal jets produced by the island blocking eect. Results o the study are summarized in section 6.. Model We consider a two-and-one-hal-layer ventilated thermocline model o a Northern Hemisphere subtropical gyre, with major eatures shown in Fig. 3. An island resides in midgyre, well clear o the second-layer eastern shadow zone and western constant pv pool and south FIG. 3. Schematic o the two-and-one-hal-layer ventilated thermocline model o the North Paciic Ocean. o the gyre center, so that the Sverdrup low impinges upon the island rom the northeast. Our model basin and island are chosen to mimic the North Paciic and the major Hawaiian Islands, with the islands modeled as a continuous barrier. Qiu et al. (1997) have shown that this is a reasonable assumption with regard to the Hawaiian Islands. The meridional range o this barrier is small when compared with the gyre but is large enough so that deviations in the Coriolis parameter and in layer depths over this range are dynamically signiicant. Our model island has distinctive northernmost and southernmost points, and we reer to the entire coastline traveling clockwise (counterclockwise) rom the northern tip to the southern tip as the east (west) coast. Our methodology owes much to DS s treatment o New Zealand in a ventilated thermocline model o the South Paciic, but our assumptions regarding the region west o the island dier. He assumed that the lower layers were quiescent in this region, which, in the case o New Zealand, lies within the western shadow zone. We assume that in midgyre ventilated low to the west o the island is probable. Because the ventilated thermocline theory is by now irmly established, we will assume amiliarity with the undamentals and present only the pertinent equations. In addition to the standard assumptions o ventilated thermocline theory, we must make some assumptions about the dynamics in the vicinity o the island. Our irst is to assume that Sverdrup dynamics apply everywhere except in possible wbcs along the east coast o the island, and this has several immediate consequences, as ollows. The possibility o eastern boundary currents and/or cross-isopycnal luxes on the west coast o the island is not considered. Linear, inviscid low along the west coast o the island is implied, allowing us to use Godrey s (1989) island rule to determine the net transport between the island

4 DECEMBER 00 QIU AND DURLAND 3411 and the eastern boundary. Qiu et al. (1997) have shown that this method accurately predicts important eatures o the circulation near the Hawaiian Islands. Imbalances between the net transport and the local value o the interior Sverdrup transport streamunction along the east coast o the island orce western boundary currents and, in general, result in pressure discontinuities between the island and the interior at the north and south tips o the island. Sverdrup dynamics west o the island result in the pressure discontinuities at the north and south tips being translated westward in zonal jets, which can be thought o as extensions o the island wbc. Such zonal jets are ubiquitous in analytical analyses o Sverdrup low interrupted by partial meridional boundaries (Pedlosky 1996, chapter 7) and are reported by Webb (000) in a numerical model o the South Paciic, with some observational support (Webb 000; Stanton et al. 001). With the island in midgyre, the Sverdrup and second-layer transport streamlines will typically intersect these jets rom the north, and continuity o the southward Sverdrup transport requires either that the second-layer low cross the jet or that a diapycnal lux within the jet allows second-layer low rom the north to eed an increased irst-layer low to the south. We choose the irst o these possibilities as the more reasonable one, because we are considering an island that is small relative to the gyre, and we do not anticipate overly energetic jets. It is clear that the jets do not consist merely o a zonal low o the boundary current water, but rather are being constantly ed and depleted by the crossing o the interior low, and this presents two issues that must be addressed in order to incorporate the inluence o the island into the LPS theory: 1) how is the second-layer pv pressure relationship o the interior water aected by the crossing o the jet, and ) because crossing o the jets by the interior low ensures that the wbc water must reenter the interior, how is the pv pressure relationship o this water to be speciied? Our goal is to develop a model that illuminates the basic physics o the island-induced eects with a minimum o complexity, and, with this in mind, we approach item 1 by assuming that second-layer pv is conserved during the crossing o the jets. This is reasonable to expect i the island is small enough so that velocities and gradients within the jet are weak, and the only question is whether a model based on this assumption remains useul or the case o the Hawaiian Islands. In section 5, we estimate the pv change rom vertical and horizontal eddy diusion within the jet, assuming that this change represents a perturbation on the pv-conserving model using realistic winds and basin geometry. The relative change in pv induced by the jet crossing near the northern and southern tips o the Hawaiian Islands is shown to be less than 8% and 5%, respectively, and this eect will decrease to the west as the jets widen and deepen. This small change justiies retaining the pv-conservation assumption, although we recognize that diusive eects within the jets will introduce perturbations on the model results. In the course o determining the interace depths at the island, we must make some assumptions about the island western boundary current structure. Depending again on the smallness o the island, we argue that it is reasonable to expect the horizontal velocity structures within the wbc to show a sel similarity between layers. This expectation, combined with the assumption o pv conservation during the jet crossing, constrains the outlow regions o the northern and southern boundary currents to also exhibit a sel similarity between layers, thus providing a pv pressure relationship at these outlow regions (item ). Our notation and terminology ollow LPS closely, with modiications and additions noted as we proceed. We denote H n as the depth o the bottom o layer n. The layer-1 thickness is then h 1 H 1, and the layer- thickness is h H H 1. We assume that the second layer outcrops at a constant latitude, where the Coriolis parameter takes the value. The absence o alongshore winds at the eastern boundary leads to H 1 0 and H H 0, a constant, at the eastern boundary. At any point o the interior not directly west o the island, H (, ) 1H 1(, ) [H 0 D 0(, )], (1) where n is the reduced gravity o layer n, ( n1 n )g/ 0, and e() E D0 w (, )R cos d. () The notation is standard. Directly west o the island, H (, ) 1H 1(, ) [H i() D 0i(, )] 1H 1i(), (3) where H 1i and H i denote the values o H 1 and H along the west coast o the island, and Iw() D0i w E(, )R cos d. (4) In the above, e () is the longitude o the eastern boundary, and Iw () is the longitude o the west coast o the island. In what ollows, Ie () is the longitude o the east coast o the island, S and N are the latitudes o the southern and northern extents o the island, and S and N are the values o the Coriolis parameter at these latitudes. In the ventilated regions north o N or east o the island, the pv pressure relationship set at the outcropping latitude yields H1 (1 / )H. (5) For regions west and southwest o the island, the pv pressure relationship is to be determined. Although all

5 341 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 3 o the second-layer water in motion can be traced back to the ventilating region north o, in what ollows we will reserve the term ventilated or water that retains the pv signature (5) o the subduction zone. Because the regions north and east o the island are unaected by the presence o the island, we concern ourselves with them only to the extent needed to determine the layer depths at the island and the transports o the island boundary currents. We begin with a somewhat general ormulation, allowing or the possibility o alongshore winds at the island. a. Island boundary currents The irst task is to determine the interace depths at the island, and in this we ollow DS, with minor modiications or the dierent location o our island within the gyre and the addition o alongshore winds. Because only the irst layer interacts directly with the Ekman layer, we will assume that an alongshore wind stress on the west coast o the island will be balanced by a pressure gradient in the irst layer only. This corresponds to an onshore (oshore) geostrophic transport in the irst layer balancing an oshore (onshore) Ekman transport in the mixed layer. The absence o a cross-shore transport in the second layer results in H i () H I, a constant, along the west coast, a condition that extends to the south and north tips o the island. Labeling the irstlayer thickness at the northern tip H 1IN, we have 1i 1IN H () H dl, (6) 0 1 N where H 1i is the variable irst-layer thickness along the west coast, is the vector wind stress, and the line integral is taken along the west coast rom north to south, in keeping with the traditional island-rule integration direction. One equation relating H 1IN and H I comes rom noting that the net transport between the island and the eastern boundary is equal to the sum o the geostrophic and Ekman transports across any given latitude, S N. Applying this equality at N, we have H I 1H 1IN H 0 N[Tir T E( N)], (7) where 1 Tir dl (8) 0( N S) C ir is Godrey s island rule or the net transport between the island and eastern boundary, and 1 ( N) N 0 N Ie( N) T E( N) R cos d (9) is the net Ekman transport between the island and the eastern boundary across N. In the above, is the zonal component o, and C ir is the standard counterclockwise island-rule contour encircling the island and extending to the eastern boundary. Evaluating (7) at S and using (6) to convert H1i( S ) to H1IN gives a relationship between H 1IN and H I identical to that in (7). The conservation o mass transport in layer provides a second relationship between H 1IN and H I : e 1 Ie( S) S e 1 Ie( N) H (H H ) d H (H H ) d, (10) where the lhs is the layer- transport between the island and the eastern boundary across S, and the rhs is the corresponding transport across N. By treating the boundary current and interior transports separately, this equation can be rearranged to give Ie ( N) 1 H 1 N Ie( N) Ie ( S) 1 S Ie( S) N (H H ) d 1 H (H H ) d 1 WN WS (H H ), (11) where the subscript W appended to H denotes the westernmost extent o the interior solution, just outside the island boundary current, and the additional subscript N or S denotes the latitude o the northern or southern island tip. The integrals represent the layer- boundary current transports at the north and south tips o the island, with being the boundary current width, and the integrated term represents the net transport rom the layer- interior low east o the island into the boundary current. To evaluate the boundary current integrals, we need to make some assumptions about the boundary current structure. Because o the smallness o the island, we expect the dynamics to be dominantly linear in both layers [long-term mean current proiles o the northern branch o the boundary current, the North Hawaiian Ridge Current (NHRC), yield a Rossby number o 0.06]. Although vertical shear exists within the boundary current, we expect it to be relatively small, so that crossisopycnal luxes o mass and momentum are negligible. Given that the ocean gets deep rapidly o the Hawaiian coast, we expect the boundary current dynamics in both layers to be dominated by horizontal vorticity diusion, leading to a sel-similarity between the horizontal proiles o velocity in the two layers. This equivalent barotropic picture o the boundary current is supported by ADCP measurements across the NHRC (Qiu et al. 1997, their Fig. 3) and allows H 1 to be expressed as a linear unction o H within the boundary current (appendix A). In this case,

6 DECEMBER 00 QIU AND DURLAND 3413 Ie( N) Ie( N) H (H H ) 1 d (HWN H 1WN) (HI H 1IN) (HWN H I), (1) with a similar expression or the southern integral. Using (1) to evaluate the second-layer wbc transports in (11) produces the second relation between H 1IN and H I : N(HI H 1WS) S(HI H 1WN) H1IN H, (13) I RH N(HI H WS) S(HI H WN) where S 1/ H 1i( S) RH 1 dl. (14) H1IN H 0 1 1IN N The implicit relationship (13) must be solved numerically in conjunction with (7) to yield H 1IN and H I. When the eect o alongshore wind orcing on the west coast o the island is negligible, H 1i () H 1IN and R H 1. 1 In this case, (13) becomes an explicit expression or H 1IN, which, in conjunction with (7), yields a ourthdegree polynomial solution or H I. FIG. 4. Layer- streamlines near the northern tip o the island: N denotes the critical streamline which passes through O Nn, the transition point between the wbc and the zonal jet; N and streamlines to the northwest cross the jet, conserving pv. Streamlines to the southeast o N enter the wbc and lose the subduction-zone pv signature. Streamline IN originates at the northern tip o the island and borders the shadow zone adjacent to the island s west coast. b. Northern tip o island We next look at conditions near the northern tip o the island. We have restricted ourselves to the case in which the Sverdrup transport streamlines approach rom the northeast quadrant, and will urther restrict ourselves to the case in which the layer- streamlines approach rom the same quadrant. It is reasonable to expect this condition to ollow rom the irst, given the beta spiral eect. Wajsowicz (1993) and Pedlosky et al. (1997) have shown that when the circulation o the wind stress around the island is small in comparison with the circulation around the traditional island-rule contour, the net island-rule transport T ir is essentially the average o the Sverdrup transport streamunction values along the east coast o the island. A monotonic decrease in the streamunction rom north to south, consistent with low rom the northeast, would then result in a northward wbc near the northern tip o the island. A strong-enough alongshore wind anomaly on the west coast o the island could conceivably reverse the wbc transport, but this is not true or Hawaii, and we will not consider that possibility here. With the layer- streamlines approaching rom the northeast, the second-layer wbc transport near the northern tip o the island is also northward. Figure 4 shows a schematic o the vicinity o the northern tip with impinging layer- streamlines. The wbc and zonal jet are shown with inite width, although 1 Integration o the climatological European Centre or Medium- Range Weather Forecasts (ECMWF) wind stress along the lee coast o the Hawaiian Islands yields a value or R H that diers rom 1 by less than 3%. in the model they are represented by pressure discontinuities o ininitesimal width. The transect I N O Nn, extending north rom the tip o the island, separates the wbc regime to the southeast rom the zonal jet regime to the west. The interace depths at points I N and O Nn are labeled as previously described or the northern tip o the island and the adjacent interior. Here, N is the layer- interior streamline that intersects the transition rom wbc to zonal jet at O Nn, and it divides the interior low between two dierent ates. Because the secondlayer wbc transport is northward near N, N jogs to the west, rom O Nn to O Ns, as it crosses the jet, and pv conservation across an ininitesimally thin zonal jet ensures that the interace depths remain unchanged during the crossing. All streamlines west o N likewise jog to the west at N while conserving pv, and (5) holds or these streamlines. With (3) and (6), the solution or the region west o N, and between S and N, is ully determined. Streamlines to the south and east o N enter the wbc, thus losing the pv signature carried rom the subduction zone, and rejoin the interior low in the boundary current outlow region between sections I N O Nn and I N O Ns. Because this transition region is bounded by a pv-conserving streamline, conservation o mass transport between streamlines requires that the sel similarity between layers assumed or the boundary current must also hold throughout the transition region, even though the dynamics change rom boundary current to Sverdrup. In appendix B we show that this works or any arbitrary monotonic wbc and Sverdrup structure unctions. The sel-similarity requirement then gives a relationship between h and H at I N O Ns :

7 3414 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 3 where h ( N) H H1 AH N B N, (15) H1WN H1IN AN 1, and (16) H H WN I H1WN H1IN BN HWN H 1WN. (17) H H WN Along streamlines originating rom I N O Ns, pv conservation then gives I H1 1 AN H B N. (18) N Equations (18), (3), and (6) now yield a quadratic equation or H along streamlines originating rom the transect I N O Ns, and the larger o the two roots is the appropriate one. In the absence o alongshore winds on the west coast o the island, the pv-conserving streamline originating at I N must pull away rom the island and create a shadow zone completely equivalent to the shadow zone at the eastern boundary. We label this streamline IN, signiying its origin at the northern tip, and ollow LPS in assuming that the lower layer is quiescent between this streamline and the island. Hence, H (, ) H I, (19) in conjunction with (3) and (6) constitutes the solution between IN and the island. The presence o alongshore winds on the west coast will aect the size o the shadow zone because o the variation in H 1i along the coast and could conceivably eliminate the shadow zone and create a more complicated dynamical situation near this coast. In the case o Hawaii, this eect is small [see ootnote 1 and (14)], and it serves only to shit the location o the shadow zone boundary IN. c. Southern tip o island We now consider the situation near the southern tip o the island. Figure 5 shows a schematic o the critical streamlines near the island, and a labeling o the regions that they delineate. Here N, as discussed above, is an eastern boundary or the ventilated regions (labeled V) west and southwest o the island that retain the pv set at the subduction zone. The streamline IN is the eastern boundary or the region (B N ) where the pv is determined at the outlow o the northern wbc, and the western boundary or the island shadow zone (S). The additional subscript W is appended to a region or streamline label to indicate conditions west o the island where the integration rom the island boundary condition completes the solution [(3)]. The subscript S denotes conditions southwest o the island, controlled by the eastern boundary condition as in (1). At the southern tip, the transition rom wbc to zonal jet happens at the transect I S O Se. N FIG. 5. Layer- streamlines bounding distinct dynamic regimes in the vicinity o the island: V, ventilated regions where the pv signature was determined at the subduction zone; B N, regions where the pv signature was determined at the outlow o the northern wbc; S, island shadow zone where H H I ; B S, region where the pv signature was determined at the outlow o the southern wbc. The additional lower case subscripts w and s distinguish regions and streamline segments directly west o the island rom those south o S. Here, S is the interior streamline that passes through O Se and separates the low to the northwest that enters the wbc and loses its pv signature rom low to the southeast that remains unaected by the presence o the island. The approach o the Sverdrup and second-layer streamlines rom the northeast ensures that near the southern tip o the island the barotropic and layer- transport will be southward in the wbc and westward in the southern zonal jet. Because the second layer is quiescent in the shadow zone north o the southern jet, there can be no second-layer low across the jet bordering this region. The irst layer carries all o the Sverdrup low across the jet, and the consequent pressure gradient in the irst layer also rules out the possibility o a purely zonal, pv-conserving second-layer low within this section o the jet. Consequently, the quiescent second-layer shadow zone is translated across the jet to the south with H H I, and there will be a pvconserving streamline rom the island tip through a point O Sw on the southern boundary o the jet that bounds this region to the east. We label this streamline IS and, ollowing the same logic used at the northern tip, deduce that the wbc water must low southward across O Sw O Se, distributed so as to satisy the Sverdrup constraints. This low leaves the transect O Sw O Se with q S /h, and at points arther south, pv conservation yields H1 1 AS H B S, (0) S S where

8 DECEMBER 00 QIU AND DURLAND 3415 H1WS H 1i( S) AS 1, and (1) H H WS [ ] H1WS H 1i( S) BS HWS H 1WS. () HWS HI The region containing the outlow o the southern wbc is labeled B S, and (1) and (6) complete the solution or this region. Again, the larger root in the quadratic equation or H is the appropriate one. Layer- low in regions V w and B Nw is clearly rom the north, and the bounding streamlines N and IN jog to the west in the crossing o the southern jet. The pvconserving relations in the regions V, B Ns, and S s south o the jet are identical to the relations or the corresponding regions north o the jet. d. Potential vorticity conserving relationships and critical streamlines We compile here the pv-conserving H 1 H relationships or each o the dynamical regimes shown in Fig. 5: I V, V : H 1 H, (3) w 1 B Nw, B Ns: H1 1 AN H B N, (4) S, S : H H, and (5) w s I B S: H1 1 AS H B S, (6) where A N, B N and A S, B S are deined in (16), (17), and (1), (), respectively; H 1WN, H WN and H 1WS, H WS are ound by solving the interior equations, (1) and (5), at [ Ie ( N ), N ] and [ Ie ( S ), S ]; H 1IN and H I are ound by solving (7) and (13); and H 1i () is given by (6). Using the above equations, and the appropriate equation [(1) or (3)], implicit ormulas or the bounding streamlines can be derived, and they are presented below: N S S N Nw: D 0i(, ) [1 1(1 / )]HWN H I 1H 1i(), (7) Ns: D 0(, ) [1 1(1 / )]HWN H 0, (8) INw: D 0i(, ) 1[(1 AN/ N)HI BN/ N] 1H 1i(), (9) INs: D 0(, ) 1[(1 AN/ N)HI BN/ N] H I H 0, (30) IS: D 0(, ) 1[(1 A/ S S)HI B/ S S] H I H 0, (31) S: D 0(, ) [1 1(1 / )]HWS H 0, (3) where 1 1 /. 3. Application to an idealized ocean basin We now look at the consequences o the model in a typical idealized rectangular basin with zonal winds. The wind stress varies sinusoidally with : 0 sin[( c )/W], (33) and the values N m, c 8.5N, and W 6 give an Ekman pumping distribution similar to that inerred or the North Paciic rom ECMWF climatological winds. Other parameters relevant to the two-and-one-hal-layer ventilated thermocline model are listed in Table 1. Figure 6 shows the model basin with the irst- and second-layer isobars unperturbed by the presence o the island. The locations o two separate model islands, A and B, are superimposed on the isobars, with the southernmost (A) approximating the location o the Hawaiian Islands relative to the eastern boundary and the center o the gyre. The islands are modeled as thin meridional barriers with lengths o 4 latitude. a. Island A Figure 7 shows the vicinity o island A, with the layer isobars perturbed by the island. The dynamical regimes discussed in the last section and shown in Fig. 5 are labeled here on the second-layer (lower) plot, and the regime boundaries are shown by dashed lines on each plot. The qualitative eect o the island on the Sverdrup low directly west o the island and between the two zonal jets is expected. In the shadow zone, all o the low is carried by the irst layer, and it is predominantly southward because o the proximity to the island boundary. In the ventilated region V w, the isobars in both layers are merely rotated counterclockwise rom what they would have been in the absence o the island. This is because the westward low impinging upon the island s east coast is diverted to the zonal jets, and the westward low in V w is decreased by an equivalent amount. In the intermediate region B Nw, the direction o

9 3416 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 3 TABLE 1. Parameters used in the two-and-one-hal-layer North Paciic model driven by realistic surace winds. Parameter S N H 0 Value m s m s 35N 19.0N.5N 00 m the irst-layer low is strongly inluenced by the baroclinic structure o the wbc at the northern tip o the island. South o the southern jet, the ventilated low returns to the streamlines o the unperturbed gyre while the eects o the northern wbc, the island shadow, and the southern wbc continue to inluence the low to the southwest o the island. I we ollow these regions to the southwest, the second-layer pv anomalies persist, but their inluence on the irst-layer low decreases as the irst layer carries more and more o the Sverdrup transport. A quantitative measure o this trend is discussed below in relation to the eect on the zonal jets o island B. Perhaps the most interesting consequence o the model is the longitudinal change in the baroclinic structure o the zonal jets, despite the act that their net transports remain constant, ixed by the net wbc transports at the island s northern and southern tips. We ocus on the southern zonal jet because it carries contributions rom all o the dynamical regimes produced by the eect o the island and also because it resides within the latitude band o the HLCC. Figure 8 shows a schematic o a vertical section along the centerline o the island A southern jet, with layer velocities drawn to scale relative to each other and layer thicknesses drawn roughly to scale. Near the island, the baroclinic structure o the southern jet is the same as in the wbc at the southern tip o the island. Farther west, the second layer becomes quiescent because o the shadowing eect o the island, and all o the jet transport is carried in the irst layer. Farther west still, the baroclinic structure is determined by that o the wbc at the northern tip o the island, and west o this region the structure is determined by the structure o the ventilated low. In the northern jet, o course, there are only two regions o diering baroclinic structure: that controlled by the northern wbc and that controlled by the ventilated low. I the jet were viewed as a continuous zonal low, the change in baroclinic structure would be a remarkable prediction, but when we realize that the jet is being continuously ed along its northern edge (and depleted along the southern edge) by waters o diering pv characteristics, this becomes an obvious eature. The possibilities or this variation in structure are even richer than might be inerred rom Fig. 8. In the ventilated FIG. 6. Pressure distributions in a two-and-one-hal-layer ventilated thermocline model driven by the idealized wind stress orcing [(33)]. No island eect is included. Shaded areas indicate the pool region o constant potential vorticity: A and B in the igure denote the two islands whose inluences upon the pressure distributions are presented in Figs. 7 and 9, respectively. Island A corresponds to the position o the Hawaiian Islands within the gyre. part o the jet, H 1 is a constant multiple o H [(5)], so both layers must low in the same direction, but in the sections o the jet corresponding to regions B N and B S, the two active layers could actually low in opposite directions, depending on conditions in the wbc at the island tips. b. Island B To emphasize this point, we investigate the eect o island B, located north o island A, where the irst-layer low impinges upon the island rom the northwest, and the second-layer low still approaches rom the northeast. A similar eect could be achieved by rotating island A clockwise relative to the gyre, but the point is that because o the spiral eect the layer lows are in opposite directions in the northern branch o the wbc. The net transport in this branch is still northward, but the irst-layer transport is southward. Figure 9 shows the layer isobars in the vicinity o island B. Directly west o the island, the picture is qualitatively similar to that or island A. The irst-layer low

10 DECEMBER 00 QIU AND DURLAND 3417 FIG. 7. Pressure distributions in the neighborhood o Island A, located along 160W rom 19N to 3N (A in Fig. 6). Dashed lines denote layer- streamlines delineating dierent dynamic regimes. The broad-scale wind-driven circulation is the same as in Fig. 6. FIG. 8. Vertical section along centerline o the Island A southern zonal jet. Velocity vectors and layer thicknesses are drawn to scale relative to each other. Horizontal dimensions are not drawn to scale: the locations and extents o the individual sections can be seen in Fig. 7. roughly parallels the island in the shadow zone, and in the ventilated region V w the isobars are rotated counterclockwise rom the islandless gyre isobars because o the blocking o the island. The eect on layer 1 might not be so obvious in this case because the layer-1 low east o the island is not primarily westward. It is important to remember, however, that the blocking eect diverts the total Sverdrup westward low east o the island into the zonal jets, thus rotating the total Sverdrup streamlines west o the island. The spiral eect then determines the angle between the irst- and second-layer streamlines. The southward irst-layer low in the northern wbc requires a northward irst-layer low in the northern part o B Nw, resulting in a more pronounced kink in the irst-layer streamlines as they cross rom V w to B Nw. It also orces a small circulation zone west o

11 3418 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 3 FIG. 9. Pressure distributions in the neighborhood o Island B, located along 160W rom 3N to 7N (B in Fig. 6). Dashed lines denote layer- streamlines delineating dierent dynamic regimes. the northern tip: irst-layer water rom the north crosses the northern jet lowing westward and then circulates cyclonically to the south, returning to eed the eastward lowing part o the jet near the island. Figure 10 shows a schematic o a vertical section FIG. 10. Same as Fig. 8, but or the case o Island B. along the centerline o the island-b southern jet, and, as expected, the change in baroclinic structure is much more dramatic than or island A (Fig. 8). Moving westward rom the southern tip, the majority o the net transport shits rom the second layer to the irst layer, back to the second layer, and inally to a roughly equal partition between layers, with a surace intensiication o velocity. In the northern branch o the island-b wbc, the southward irst-layer velocity is almost as great as the northward second-layer velocity, and we might have expected the shear in the B N section o the southern jet to be greater than that shown in Fig. 10. To understand this, we develop a relationship that is valid between any two points in the gyre connected by a pv-conserving secondlayer streamline, but which is particularly enlightening

12 DECEMBER 00 QIU AND DURLAND 3419 in this case. We start by deining a baroclinic indicator 1 as the ratio o the irst- and second-layer meridional velocities: 1 1/x H 1/x 1 1 1, (34) /x H /x where i is the dynamic pressure in layer i, 1 1 corresponds to equal meridional velocities in the same direction, and 1 1 corresponds to equal but opposite meridional velocities. We next notice that pv conservation across a meridionally thin jet results in the layer-1 and layer- streamlines crossing the jet coincidentally, and the zonal gradients o H 1 and H along the northern edge o a jet are mapped by the streamlines onto meridional gradients within the jet such that the ratio H 1 /H remains constant through the mapping. Consequently, 1 gives the layer velocity ratio within the zonal jets as well as at the wbc outlows. For region B N, () 1 1 A, (35) 1 1 N N where A N is deined in (16), and in the ventilated region V () 1 1. (36) 1 1 More generally, it is easy to show that i 1 is known at some latitude, say, N, then at another latitude on the same pv-conserving streamline, 1() 1( N) 1 (1 1). (37) N It is clear that as approaches 0, 1 tends monotonically toward (1 1 ) 1, so that as a pv-conserving streamline is ollowed equatorward, the meridional low and the low in any zonal jet that is crossed tend toward a unidirectional, surace intensiied low. In the case o island B, the velocity ratio changes rom at the outlow o the northern boundary current to where B N crosses the southern jet. For island A, the velocity ratio changes rom at the outlow o the northern wbc to where B N crosses the southern jet. Equation (37) also shows that the dierence between values o 1 on two dierent streamlines decreases monotonically as one moves equatorward. Speciically, we quantiy the change in baroclinic structure rom the B N part o the jet to the ventilated (V) part o the jet as the change in the value o 1 : 1() 1V() 1B N (), (38) and (37) shows that N S 1 S N 1 N ( ) ( ). (39) For island A, this indicator changes rom in the northern jet to in the southern jet, and or island B it changes rom 1.0 in the northern jet to in the southern jet. The above analysis was or an ininitesimally thin zonal jet, and we briely look at the eect o relaxing the width restriction by looking at the jet in the ventilated region. In a jet o inite width, the layer isobars do not cross the jet coincidentally, and the eect must be considered in calculating the ratio o zonal velocities. We ind that u 1 1[1 (x, y)], (40) u where 1 H (x, y). (41) 1( ) H /y For a given pressure jump across the jet, clearly approaches 0 as y approaches 0. For a realistic jet width on the order o 100 km and the model values o H, H, and in the southern jet not too ar west o the island, O(0.1), and 1 is a good proxy or u 1 /u. In the sections B N and B S the expression or is more complicated, but the results are qualitatively similar. The important thing to note, however, is that u 1 /u is now a unction o longitude. For a given jet transport, H /y decreases as H increases, so that arther west where the gyre deepens, we would expect u 1 /u to depend sensitively on longitude. In section 4 we will see that this is indeed the case. c. Conceptual summary The eect o the island on the two-and-one-hal-layer interior low is most easily conceptualized as the creation o two overlapping wakes: a transport wake that alters the barotropic transport patterns directly west o the island, and a pv wake that alters the baroclinic nature o the circulation downstream rom the island, in the sense o second-layer streamlines. The transport wake is characterized by a diversion o the normal component o the interior low incident upon the east coast o the island into two zonal jets at the northern and southern extremes o the wake. In the event that the wind stress circulation around the island is nonnegligible, the zonal jets carry an additional transport orced by the anomalous wind along the west coast o the island. This additional transport is equal in the two jets but is oppositely directed. Between the jets, the eect o the transport wake is to superimpose an anomalous eastward net transport, which or a thin island is equal to the transport blocked by the island within the same zonal band. This anomalous eastward transport is independent o longitude, and over the ull meridional span o the island it is equal in magnitude to the westward transport carried by the jets. In section 4 we will be concerned with how inclusion o the island interior low interaction alters

13 340 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 3 model estimates o the HLCC transport, and the above points make it clear that this eect depends sensitively on the location o the HLCC boundaries within the transport wake. The anomalous eastward transport will be divided between the layers, and how it is divided depends on the pv characteristics o the region. We will see in section 4 that the partitioning between layers is independent o longitude within the ventilated region, but this is not generally true o the other regions. The pv wake is characterized by a loss o the ventilated pv signature in the second layer, and it extends equatorward and westward rom the island, sandwiched between two ventilated second-layer streamlines. It contains three bands o distinct pv characteristics: two sidebands in which the second-layer pv is determined at the northern and southern wbc outlows and a central shadow zone in which the second layer is quiescent. The side band widths are proportional to the net wbc transports at the outlows and are inversely proportional to the strength o the Sverdrup orcing at the outlows. In the shadow zone, the irst-layer streamlines obviously are parallel to the geostrophic Sverdrup transport streamlines. The layer- streamlines that would otherwise have been ound within the area occupied by the shadow zone are squeezed into the pv wake side bands ed by the wbc outlows, thus increasing the secondlayer velocity in these bands while maintaining the unperturbed directionality. The velocity anomalies in the side bands are on the order o 100%; the second-layer thickness anomalies are typically o the order o 10%. To lowest order, then, the eect on irst-layer low in the side bands can be estimated by equating relative velocity and transport anomalies in the second layer. The increased transport in the second-layer demands an equal and opposite transport in the irst layer, causing the irst-layer streamlines to be rotated cyclonically in Figs. 7 and 9. As one ollows the pv wake equatorward, the second-layer pv anomalies persist, but the anomaly in the irst-layer streamlines decreases as the irst-layer thickens and carries proportionally more o the Sverdrup transport. Directly west o the island the transport wake and the pv wake overlap, and the eects discussed above are superimposed. Perhaps the most interesting consequence is the creation o a southern zonal jet with a constant net transport but with a baroclinic structure that changes, possibly dramatically, through our distinct sections. From the island and proceeding westward, the baroclinic structure is controlled by the outlow o the southern wbc, the shadow zone, the outlow o the northern wbc, and the ventilated pv characteristics. For model parameters representative o the North Paciic and the Hawaiian Islands, the layer low in the ventilated part o the jet nearest the island is unidirectional and the velocity ratio is nearly independent o longitude. As the gyre deepens to the west, however, the ventilated jet baroclinicity changes gradually, and the velocities can become oppositely directed beore reaching the western boundary. In a model with more than two active layers, each subsurace layer will have its own pv wake, creating a pv wake an in which the wake directions rotate anticyclonically with depth. This pv wake an is analogous to, although simpler than, the an o characteristics described by Huang and Pedlosky (000) in connection with extratropical buoyancy orcing o a multilayer model. In their case, a pv anomaly introduced at the subduction zone o a deep layer propagates equatorward, creating a cascade o pv anomalies in shallower layers such that the number o new pv anomaly cones (wakes) created doubles at each successive subduction zone. In our case, the island resides equatorward o all subduction zones, it creates pv anomalies in all layers concurrently, and each layer gets a single pv wake (cone). The downstream broadening o the pv anomaly inluence rom the spiral eect would be similar in the two cases. For islands located progressively equatorward, the transport and pv wakes become more colinear (c. Figs. 7 and 9). For an island at the equatorward limit o the subtropical gyre, the wakes would become coincident, the zonal jets would become true extensions o the wbc with no change in baroclinic structure, and the shadow zone would occupy the entire region between the zonal jets. 4. Application to the North Paciic Ocean In this section, we apply the theory o the previous two sections to a more realistic representation o the North Paciic Ocean. For the surace wind stress data, we adopt the climatology rom the European Centre or Medium-Range Weather Forecasts reanalysis. This dataset is one o the wind products used in the numerical modeling study o the HLCC by Xie et al. (001). Figure 11 shows the distribution o the Ekman pumping velocity w E, calculated rom the ECMWF wind stress dataset. The broad-scale pattern is similar to that used in previous ventilated thermocline studies o the North Paciic (Talley 1985; Huang and Russell 1994): the zero Ekman pumping line tilts southwest northeast rom south o Japan at 30N in the west to Vancouver Island at 50N in the east, and w E is on the order o ms 1 over the broad region o the subtropical North Paciic Ocean. A noticeable eature that was missing rom older surace wind stress climatologies, however, is the dipole Ekman pumping velocity structure present southwest o the Hawaiian Islands. As noted by Xie et al. (001), this dipole w E structure is due to the high elevation o the mountains Haleakala, Mauna Loa, and Mauna Kea on the two southern islands o the Hawaiian island chain. In Fig. 11, the maximum w E values associated with the island orography are and ms 1, respectively. In Fig. 1 we plot the pressure distributions or a two-and-one-hal-layer North Paciic model using LPS