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Roxana C. Wajsowicz

Abstract

Assuming the flow over the depth of interest may be described by a 2D streamfunction, ψ, a general analytical method for determining the path of each streamline through a series of channels, which may be western boundary layers or straits, is presented. At each intersection, a channel operator, C a(b) = mid(ψ a, ψ b, ψ C), is defined, where ψ a, ψ C are the values of ψ on either side of the channel, and the operator is applied to the bounding streamlines of the flow ψ b. By assigning water mass properties to each streamline entering the system, the composition of the flow in each channel is determined.

The method is applied to the western equatorial Pacific, where the equatorward western boundary currents, which close the northern and southern wind-driven tropical gyres, meet. Parameters determining whether streamlines of the cold, fresh Mindanao Current and warm, salty South Equatorial Current (SEC) turn east and enter the North Equatorial Countercurrent (NECC), or west and enter the Indonesian archipelago, are identified. Further, their contributions to flow in Makassar Strait, the Maluku passages, and the Halmahera Sea are determined as analytic functions of the values of the streamfunction on Sulawesi and Halmahera, and ψ F(y), the value at the interior edge of the west Pacific boundary layer, at latitudes y N, y P. The latitude y N depends on the degree of nonlinearity assumed, and is defined in general terms as the northernmost of either the latitude of the northern tip of Halmahera or the northernmost latitude at which ocean interior streamlines of the NECC originate from the SEC. The latitude y P is that of the northern tip of Irian Jaya.

In general, outside parameter ranges where the archipelago inflow is from a single source, the model gives that the fractional contributions to the inflow, and so NECC, are less sensitive to variations in the west Pacific, the larger the throughflow. Also, the larger the throughflow, the more South Pacific component is present in the archipelago inflow, and so the fresher the NECC, for given conditions in the western equatorial Pacific. Interestingly, the model’s Indonesian channels act as a dynamic filter on the inflow with that from the North (South) Pacific entering through the western (eastern) channels, which is consistent with observations.

Taking the single channel representation of the Indonesian archipelago so that the fractional contributions are a function of ψ Nψ F(y N) only, the Sverdrup streamfunction for the Pacific is used to represent variations in ψ N on interannual to interdecadal timescales. For Florida State University (FSU) wind stresses from 1961 to 1998, there is substantial variability in ψ N that implies significant composition variations on all timescales considered irrespective of the choice of throughflow magnitude. As expected, the archipelago in-flow composition is dominated by the North Pacific contribution, the more northerly the choice of y N. In contrast, wind stresses derived from European Centre for Medium-Range Weather Forecasts 10-m winds for the period 1987–95 yield a Sverdrup streamfunction that varies little over possible latitudes of y N, and importantly ψ is mainly positive over these latitudes giving a wholly SEC-fed archipelago inflow, and so a relatively fresh NECC. A further contrast is provided by wind stresses derived from SSM/I data for the period 1988–96. These yield a Sverdrup streamfunction, which varies little with time over equatorial latitudes, but takes on substantial negative values, so that the archipelago inflow is almost wholly fed by the Mindanao Current, and the NECC is relatively salty.

Insufficient salinity data exist to confirm or refute the estimated FSU-based composition variations on interannual and intradecadal timescales. However, the interdecadal signal of a tendency toward a greater SEC contribution over the last 15 years can be substantiated. Salinity profile data from the National Oceanographic Data Center show a fresher western equatorial Pacific in the region of the SEC and its retroflection into the NECC in the epoch 1981–95 compared with the epoch 1966–80. The Pacific entrance to the Indonesian archipelago is saltier in the later epoch.

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Roxana C. Wajsowicz

Abstract

The effects of spatial finite-differencing, viscosity and diffusion on unbounded planetary waves in numerical models are investigated using a quasi-geostrophic approximation to the midlatitude, β-plane, shallow-water equations. The two-dimensional Arakawa B- and C-grid numerical schemes are used to illustrate finite-difference effects, which are found to depend on two nondimensional resolution parameters in each spatial direction: wave resolution = 2 × grid-spacing/wavelength and grid resolution = grid-spacing/2 × Rossby radius. The study is particularly relevant to baroclinic waves, for which the latter parameter can he very large.

The properties of the finite-difference frequency dispersion relationships as functions of wave and grid resolutions are studied in detail. If the wave resolution is fine, then both grids perform well, with the C-grid giving a slightly better approximation to the continuum behavior. Neither grid performs well, though, when the wave resolution is poor. In particular, for poor zonal wave resolution, the group velocity is eastward for all meridional wave resolutions and at all grid resolutions on both grids. This latter property explains, though, the dynamics of the western boundary layer in a coarse grid-resolution model in which short waves (in a continuum sense) are not resolved.

The properties of the finite-difference frequency dispersion relationships and their derivatives are tabulated for the planetary wave and the inertia-gravity wave (the other clan of wave of primary importance in interior oceanic adjustment) for ready reference.

Unbounded planetary waves propagating in a continuum are damped by viscosity and diffusion—long waves are most severely affected by vertical and lateral diffusion of heat, short waves by lateral viscosity. For fine wave resolution (“long” waves) on the B- and C-grids, vertical and lateral diffusion of heat are the main damping mechanisms. For coarse wave resolution (“short” waves), lateral and vertical viscosity are the dominant damping mechanisms on the c-grid, but on the B-grid, lateral viscosity is only important at fine grid resolutions. The theory also gives an estimate of the damping required to effectively trap the energy of poorly resolved waves with eastward group velocity on both grids, and hence the scale of the viscous-diffusive western boundary layer.

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Roxana C. Wajsowicz

Abstract

A simple analytical model of the closure of the wind-driven gyres in the tropical west Pacific is developed to illustrate the role of Halmahera and variations in the Pacific wind stress on the water mass composition of the flow from the Pacific to the Indian Ocean through the Indonesian archipelago—that is, the Indonesian Throughflow. The model is expressed in terms of the streamfunction, ψ, for the depth-integrated velocity field. There are three principal dynamical states, and therefore composition regimes. In the absence of Halmahera, the throughflow is composed of water wholly originating from the South Pacific (SP) if the streamfunction at the interior edge of the western boundary layer at the latitude of the northern tip of Papua New Guinea (PNG), ψN, is greater than that on the Asian continent, taken as zero, which is typically the situation in the Northern Hemisphere late summer. The throughflow is composed of water of wholly North Pacific origin (NP) if ψN ≤ ψA, the value of the streamfunction on Australia–PNG, which corresponds to winter conditions. The throughflow is fed by both the fresh Mindanao Current and the saltier South Equatorial Current (SEC) otherwise. If Halmahera is taken into account, the criteria determining the composition regimes are modified. Its presence results in a fresher throughflow, 30% NP–70% SP compared with 100% SP, as ψ typically decreases northwards in the equatorial west Pacific. The result of averaging over perturbations in ψN, ψA is also considered.

Estimates of the throughflow composition from observed hydrography imply a predominantly NP source. A possible explanation is nonlinear retroflection of the SEC into the North Equatorial Countercurrent (NECC), which would lead to the throughflow being fed by the Mindanao Current for much of the year. However, the simple model predicts that a large amount of water of NP origin enters the Indonesian basins before exiting to feed the NECC, even when the throughflow is predicted to be wholly SP. Mixing within the basins would modify the composition of the NECC and throughflow. Different west Pacific states and their effect on the composition are investigated further with a flat-bottomed, homogeneous numerical general circulation model with a simplified geometry and climatological monthly mean forcing.

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Roxana C. Wajsowicz

Abstract

The effect of interannual variations in the Pacific wind stress on the barotropic and baroclinic components of the flow between the Pacific and Indian Oceans through the Indonesian Archipelago, the Indo-Pacific Throughflow, is investigated using a numerical ocean general circulation model (GCM) with a simplified geometry. In agreement with the modified Island Rule, variations in the depth-integrated throughflow are generated by zonal wind stress variations over the Pacific at the latitudes of the tips of the Australian continent, assuming the Pacific basin is flat bottomed. Wind stress variations at other latitudes generate variations in the depth-integrated transport only if they produce a depth-integrated pressure drop along the oceanic eastern boundary through the archipelago. From the Island Rule, alongshore wind stress variations on the west coasts of Australia and South America produce direct variations, but the observed signal is weak at interannual periods. Baroclinic variations in the throughflow are generated by baroclinic waves entering the archipelago, or by interaction between the barotropic component and the sills within the archipelago.

Shallow sills within the archipelago are found to only partially block the throughflow. The dynamical constraint, that quasi-steady flow is parallel to f/H contours, is relaxed by weak friction; the reduction in throughflow is only 30% for sills blocking 70% of the water column at 9°S. In the absence of sills, the throughflow response to a southern midlatitude wind stress anomaly is purely barotropic at interannual periods. Sills within the archipelago induce a baroclinic adjustment resulting in a surface trapping of the transport, which is in phase with the wind stress variations. Also, the depth-integrated pressure gradient through the archipelago produced by the topographic upwelling and downwelling is always directed to reduce the magnitude of the throughflow. For equatorial wind stress variations, the associated equatorial baroclinic Rossby waves are partially scattered into the archipelago. Sills within the archipelago block the transmitted equatorial Rossby waves, which would enhance the throughflow except that the baroclinic response to the topographic upwelling and downwelling negates the effect for part of the forcing cycle. Nonlinearity in the eastern equatorial response to an oscillating equatorial wind stress anomaly results in a mean throughflow from the Pacific to Indian Ocean. The combined effect of equatorial and southern midlatitude wind stresses, as typified by climatological mean values, yields a throughflow that is reduced by the inclusion of sills within the archipelago.

Finally, in a comparison with the response in a GCM with a wholly blocked archipelago, the heat content anomaly (measured as the temperature averaged over the upper 300 m) in the equatorial Pacific is similar. However, the heat content anomaly in the archipelago and Indian Ocean is typically five to ten times larger than the equatorial anomaly difference between GCMs with an open/partially open and blocked archipelago. This is attributable to the difference in widths between equatorial and coastal baroclinic waveguides. The result suggests that the effect of variations in the throughflow on the Southern Oscillation is most likely felt in the archipelago and Indian Ocean.

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Roxana C. Wajsowicz

Abstract

The effect of interannual variability in wind stress on the transport between the Pacific and Indian Oceans through the Indonesian archipelago is investigated using a multilevel, numerical, general circulation model (GCM). The experiments are conducted in a spinup, anomaly mode: the GCM is initially at rest with a horizontally uniform stratification typical of tropical oceans. The wind stress anomalies are derived from the European Centre for Medium-Range Weather Forecasts 1000-mb winds for 1985–89.

The modeled variability is sensitive to the specification of bottom topography and archipelago geometry. Two model configurations are considered: (i) flat-bottomed with the option of sills within a simplified, idealized archipelago and (ii) realistic bottom topography and a complex archipelago.

In the first model, there is northward depth-integrated transport anomaly lasting 2½ years with phase 6 months ahead of the collapse of the equatorial easterlies prior to the 1986–87 El Niño. The peak transport is about 5 Sv (Sv ≡ 106 m3 s−1), which is reduced to 3 Sv if shallow sills are present in the archipelago. There follows a southward transport anomaly, peaking at about 6 Sv during the ensuing U Nina. The baroclinic transport is consistent with cold and warm equatorial Rossby waves partially scattered into the archipelago during El Niño and La Nina, respectively. The reduction in depth-integrated throughflow generated by the reduction in southern midlatitude westerlies over 1985–86 results in a distinct signal in the baroclinic transport, and similarly in their increase again over 1988. Contrasting models with open and wholly blocked archipelagos yields heat content differences, measured as the temperature averaged over the upper 300 m, of typically O(0.05°C) in the west equatorial Pacific and O(0.3°C) in the Pacific western boundary layers and Indian Ocean. This suggests that throughflow variations could have implications for the timing of ENSO.

In contrast, the second model has a very weak throughflow with peak-to-peak amplitude of only 3 Sv. Its archipelago is a relatively poor transmitter of equatorial waves, and its f/H contours are such that the depth-integrated throughflow is driven in part by the southerly extent of the South Pacific midlatitude wind stress anomalies. However, interestingly, the model still exhibits a decrease in throughflow in excess of 1 Sv prior to the onset of the 1986–87 El Niño due to variations in the southern midlatitude wind stress over the Pacific, which is also accompanied by a signature in the baroclinic transport.

Also, contrasting homogeneous and stratified versions of the models demonstrates the importance of JEBAR over direct wind stress forcing of the depth-integrated throughflow. A closed form analytical expression for the transport in terms of an integral over a closed path formed by uniquely defined f/H contours, an island rule, is derived and used to help interpret the results.

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Roxana C. Wajsowicz

Abstract

Prospects for forecasting Indian dipole mode (IDM) events with lead times of a season or more are examined using the NASA Seasonal-to-Interannual Prediction Project (NSIPP) coupled-model forecast system. The mean climatology of the system over the sector is reasonable, as determined from an almost-century-long run without data assimilation. However, the system presents biases, for example, too cool sea surface temperatures (SSTs), too shallow thermocline, and too strong southeasterlies along the Sumatra–Java coast in the east, and too warm SSTs, too deep thermocline, and too weak extension of the southeast trades into the Findlater jet in the west. These suggest coupling between the ocean and atmosphere is stronger, and the SST–clouds–shortwave radiation negative feedback less effective, than observed in the east with the opposite holding true in the west. Also, the negative zonal gradient in SST in the eastern equatorial basin, in contrast with the positive observed, suggests that equatorial Kelvin and Rossby coupled modes may have a different character from observed. Biases identified in the seasonal cycle, which may affect the strength and timing of IDM events, include a delayed onset of the boreal summer monsoon in the west, and a prolonged boreal summer monsoon in the east.

Eight major positive IDM events occur during the almost-century-long run over a range of El Niño–Southern Oscillation phases with a tendency to occur post–El Niño/pre–La Niña. Consistent with the identified air–sea interaction biases, the cold (warm) anomaly at the east (west) pole tends to be stronger (weaker) than observed. Also, the cold anomaly extends much farther westward and is more equatorially trapped than observed; its slow westward propagation and the structure of the associated fields is reminiscent of an unstable, coupled Rossby mode with SST governed by lateral advection due to the westward displacement of the convective anomaly from the heat source. Otherwise, the life cycle of the eight-event composite is similar in seasonal phase locking and mechanisms of evolution and decay to the canonical event.

For the decade from 1993 to the present, there were major positive IDM events in 1994 and 1997/98. Monthly mean SST anomalies over the western pole are well hindcast by the ocean component of the NSIPP system forced by observed surface fluxes with SST damped to observed values, and in which subsurface temperature data available in real time are assimilated; these data are very sparse over the Indian Ocean. Over the eastern pole, the SST anomalies are well hindcast except for the 1997/98 event, when it is too cool. The ensemble mean hindcast of the zonal surface wind anomaly of the central basin by the atmosphere component of the NSIPP system forced by observed SST is too weak during both events. These hindcasts provide initial conditions for the coupled system forecasts. Forecast ensembles for the decade 1993 onward, generated by the coupled system, give monthly mean SST anomalies averaged over the east and west poles of the IDM in agreement with observations at lead times of three months. The cool anomaly at the eastern pole is slightly too large in 1997/98, and the onset of the warm anomaly in 1997 is delayed by a month or so; its peak and decay are correctly timed. At lead times of six months, there is a significant deterioration in the forecast at the eastern pole with either false positive or negative alarms generated annually in boreal fall; that at the western pole remains good. These results are very encouraging and suggest that major IDM events have the potential to be forecast a season or more in advance.

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Roxana C. Wajsowicz

Abstract

Godfrey's Island Rule is rederived in terms of the barotrapic streamfunction for flow in a stratified ocean with a rigid lid. Modifications to include bottom topography and frictional effects along eastern boundaries are derived. The “Island Rule” has an important application in describing the net transport through the Indonesian seas, that is the Indonesian Throughflow. The original rule, derived from a Sverdrup model, yielded an annual mean throughflow of 16±4 Sv (Sv ≡ 106 m3) s−1). Observations of depth-integrated steric height differences indicate that frictional effects within the lndonesian seas will reduce this value by the order of 2 Sv. The reduction estimated from a frictional channel model depends on the parameterization and boundary conditions adopted, and ranges from 5%–20%. Topographic effects could give an increase in transport. For example, if the archipelago is represented as a simple sill, then warmer water on the Pacific slope than on the Indian slope would produce an increase in transport.

A diagnostic island rule for describing interannual variations is proposed. This rule expresses the throughflow as a line integral of the wind stress from the tip of Iria-Jaya along a line of latitude across the Pacific down the South American coast back along a line of latitude across the Pacific to the southern tip of Australia and up Australia's west coast, the original rule, plus a modulation due to the difference between the depth-integrated pressure on the Australian coast at the northern and southern entrances to the Indonesian seas in excess of that required to balance the alongshore wind stress. Frictional and hydraulic effects, which could produce an excess pressure difference are illustrated with a fine-resolution GCM.

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Roxana C. Wajsowicz

Abstract

The adjustment between two interconnecting basins of stratified fluid, resulting from the formation of a pool of dense water in one, is investigated with an 18-level numerical general circulation model (CYCM). It is found that basic features of the adjustment, i.e., (i) the generation of low-frequency, coastally trapped Kelvin waves, which carry information about the alongshore pressure gradient, created by the denser water, toward the dividing ridge; (ii) the subsequent generation of barotropic double Kelvin waves by the JEBAR (Joint Effect of Baroclinicity and Relief) effect, which propagate infinitely rapidly along the ridge setting up an anticyclonic gyre; (iii) the generation of further coastally trapped Kelvin waves at the opposite coast due to an alongshore pressure gradient, created by upwelling at the ridge edge associated with the closure of the barotropic gym; (iv) the generation of a coastally confined cyclonic gyre at the opposite ridge ~ by the JEBAR effect and viscous and diffusive processes as the coastally trapped Kelvin waves crow off the ridge, are reproduced by an equivalent linear, f-plane, two-layer model with the topography confined to the lower layer. Features, which arise from the increased number of vertical degrees of freedom in the GCM, are found to include (i) a further sheltering of the upper levels from the presence of the midge due to energy in the coastally trapped Kelvin waves being redistributed between various vertical modes; (ii) a baroclinic adjustment at the ridge face to eradicate any horizontal density gradients there, which takes the form of a Kelvin-type wave trapped against the face not previously described; and (iii) penetration of the circulation below the top of the ridge in the second basin due to vertical viscous and diffusive effects, as well as the dispersion of coastally trapped Kelvin waves of differing vertical modes.

First-order estimates of the magnitude of the baroclinic signals propagating on and away from the ridge are found by consideration of continuity of man flux. Assuming that the fields may be decomposed into local vertical normal modes, a simple model with uniform stratification is used to derive analytic estimates of the relative amplitudes of the vertical modes which compare favorably with those calculated from the GCM. Assuming that the energy of the coastally trapped Kelvin wave initially incident on the ridge is chiefly in the first baroclinic mode, then it is found that the higher the ridge, the low the energy scattered into the first-order mode propagating across the ridge (that in the higher-order modes remains small), and the greater the energy scattered into a first-order mode propagating along the face of the ridge and along the opposite coast. Also, a higher ridge results in more energy being scattered into higher-order mode, coastally trapped Kelvin waves propagating in the second basin. The magnitude of the barotropic response is found to be such as to cancel the vertical average of the baroclinic flow over the ridge face associated with the incident coastally trapped Kelvin waves for the anticyclonic gyre, and dependent on viscous and diffusive processes for the cyclonic gyre.

As well as ridges of top-hat cross section and differing heights, ridges with a pyramid cross section, i.e., “sloping” sides and with an island (cf. Iceland) on top, are considered.

The implications of features of the adjustment for modeling the Atlantic thermohaline circulation and the transport of passive tracers am discussed, as these highlight aspects of the formulation of topography in Gems, which merit further consideration in the general development of GCMs.

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Roxana C. Wajsowicz

Abstract

A numerical ocean general circulation model is used to investigate the early stages in the adjustment to equilibrium of an ocean initially at rest with imposed uniform meridional potential temperature gradients, which yield density gradients representative of those observed in the North Atlantic. The main feature of the adjustment during the early stages (the first year) is the formation and decay of a “subtropical” (warm core) and a “subpolar” (cold core) density gyre. The gyres are formed by the irreversible winding-up of the initially zonal isotherms by first baroclinic mode, coastally-trapped, dissipative Kelvin waves. This phase and the north–south asymmetry arising from the variation in viscous–diffusive Kelvin wave properties with latitude were discussed in Part I of this series.

Within a month β-effects become significant, especially in the evolution of the southern gyre, which develops a distinct east–west asymmetry through western intensification and long planetary wave propagation of boundary information from the east. In the north, penetration of boundary information into the interior is attributed to diffusive effects, because the maximum allowable planetary wave frequency is lower than that of the Kelvin wave signal. This phase in the adjustment is described in Part A of the present paper. A simple model based on the quasi-geostrophic potential vorticity equation for a single vertical mode is used to explain and quantitatively assess the effects of finite spatial resolution and viscous and diffusive processes on the Kelvin wave–planetary wave dynamics.

The longshore temperature gradients at the middle depths of the ocean are considerably reduced by first baroclinic mode Kelvin wave propagation. The adjustment then enters another phase characterized by the destruction of the density gyres by either planetary wave or diffusive processes, there being no further significant Kelvin wave propagation. This phase is described and investigated in Part B, using the simple model developed in Part A with modified boundary conditions.

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Roxana C. Wajsowicz

Abstract

The mean and seasonal variations in transport through and within the Southeast Asian seas are investigated using a series of simple models. The results are compared with results from a fine-resolution, 3D, numerical simulation of the global circulation from 1987 to 1995 [Parallel Ocean Climate Model (POCM)].

For the mean circulation, the models are based on Sverdrup dynamics with the circulation around each island calculated according to the island rule with overlapping islands taken into account. Assuming all of the passages are wide and deep yields an archipelago circulation vastly at odds with observations. A large westward transport through Torres Strait provides the throughflow between the Pacific and Indian Oceans. A large westward transport through Luzon Strait passes southward through the South China Sea into the Sulu Sea and exits into the Pacific Ocean through the Celebes Sea. There is a northwestward transport through the remainder of the archipelago. By successively blocking straits under the assumption that frictional effects are sufficient to arrest flow in the strait, an understanding is built up of why the mean circulation in the archipelago is as observed and as simulated in POCM. For example, blocking Torres Strait yields a more realistic circulation with southward flow in the archipelago. Greater realism is achieved by blocking off the South China Sea, so making the dominant pathway for the throughflow from the Pacific westward through the Celebes Sea and southward through Makassar Strait.

The weak throughflow in POCM (7.5 × 106 m3 s−1) is found due to the wind stresses derived from the European Centre for Medium-Range Weather Forecasts 10-m twice-daily winds, which are much weaker than the Hellerman and Rosenstein climatology (HR) used in previous studies. Also, POCM’s throughflow is wholly fed by the South Equatorial Current rather than predominantly by the Mindanao Current, as found in models forced by HR climatology. Analysis of the wind stress datasets and that of the Florida State University from 1961 to 1995 shows that the latitude of the zero-Sverdrup-transport streamline near the Pacific entrance to the Celebes Sea has shifted poleward over the decades, so decreasing the absolute amount originating from the Mindanao Current.

Regarding the seasonal cycle, there is negligible transport below 500 m at annual period within the archipelago in POCM, which suggests that the numerous islands and sills within the archipelago enhance the adjustment to the applied wind stress locally. Assuming a local Sverdrup balance, island-rule-based models of the archipelago show that forcing by wind stresses over the archipelago and Australia give reasonable agreement with POCM for the amplitude of the annual harmonic in depth-integrated transport. Better agreement in phase within the straits and seas is obtained by recognizing that frictional effects within certain straits enables the influence of wind stress variations to be felt in directions other than just to the west, as in the original island rule.

It is further noted that the adjustment to semiannual period wind-stress forcing is incomplete within the seas;there is no local quasi-equilibrium response. In POCM, the archipelago fills above 500 m in February–June and September–November, and drains in the remaining months. There is compensating flow below. Also, seasonal variability of the currents in the west Pacific is not sufficient to alter significantly the gyre closure in the west Pacific, and the depth-integrated throughflow is fed by the South Equatorial Current throughout the year, either via a western boundary current or a broad zonal jet.

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