Abstract

The flow of dense water through the Samoan Passage accounts for the major part of the bottom water renewal in the North Pacific and is thus an important element of the Pacific meridional overturning circulation. A recent set of highly resolved measurements used CTD/LADCP, a microstructure profiler, and moorings to constrain the complex pathways and variability of the abyssal flow. Volume transport estimates for the dense northward current at several sections across the passage, calculated using direct velocity measurements from LADCPs, range from 3.9 × 106 to 6.0 × 106 ± 1 × 106 m3 s−1. The deep channel to the east and shallower pathways to the west carried about equal amounts of this volume transport, with the densest water flowing along the main eastern channel. Turbulent dissipation rates estimated from Thorpe scales and direct microstructure agree to within a factor of 2 and provide a region-averaged value of O(10−8) W kg−1 for layers colder than 0.8°C. Associated diapycnal diffusivities and downward turbulent heat fluxes are about 5 × 10−3 m2 s−1 and O(10) W m−2, respectively. However, heat budgets suggest heat fluxes 2–6 times greater. In the vicinity of one of the major sills of the passage, highly resolved Thorpe-inferred diffusivity and heat flux were over 10 times larger than the region-averaged values, suggesting the mismatch is likely due to undersampled mixing hotspots.

1. Introduction

The Samoan Passage, a gap in the submarine ridge extending from Fiji to French Polynesia south of the equator, is a major gateway for the flow of deep water of Southern Ocean and North Atlantic origin into the North Pacific (Fig. 1a). Because of the very limited amount of deep water formation in the North Pacific (Warren 1983), the dense water flow through this region accounts for the majority of the bottom water renewal in the North Pacific. Thus, flow through the Samoan Passage, likely hydraulically controlled (Freeland 2001; Alford et al. 2013), is a choke point for the deep limb of the Pacific meridional overturning circulation (PMOC). Several studies indicate long-term changes in the deep branch of the PMOC at the same time as the surplus global incoming heat flux associated with global warming is partially communicated into the deep oceans. The bottom water in both major basins of the Pacific Ocean is warming (Fukasawa et al. 2004; Purkey and Johnson 2010), and the layer of Antarctic Bottom Water is contracting (Purkey and Johnson 2012), freshening (Purkey and Johnson 2013), and showing increasing carbon and decreasing oxygen levels upstream of the Samoan Passage (Sloyan et al. 2013). Overall, the northward transport of bottom water associated with the deep limb of the PMOC may be decreasing (Kouketsu et al. 2011; Purkey and Johnson 2012; Sloyan et al. 2013). Numerical simulations have shown the possibility of a slowing meridional overturning circulation (MOC) in a future warming climate (Schmittner et al. 2005), but still have difficulty simulating the MOC and its associated processes. Because of its vast volume, the North Pacific has large storage capacities for heat and CO2 on climatic time scales. Improved understanding of the physical mechanisms driving the MOC, both in the Pacific Ocean and globally, is therefore sought in the oceanographic community.

Fig. 1.

(a) Bottom topography of the Pacific Ocean around the Samoan Passage from global Smith and Sandwell bathymetry with a resolution of 30 arc seconds (Becker et al. 2009). Arrows with numbers indicate abyssal northward volume transport estimates in 106 m3 s−1 across Robbie Ridge and along the eastern flank of the Manihiki Plateau from a hydrographic survey (Roemmich et al. 1996) and through Samoan Passage from moored current meters (R97). (b) Bottom topography of the Samoan Passage. The bathymetry shown here is a combination of multibeam soundings from two SPAMEX cruises, multibeam soundings from R97, and, where no multibeam data were available, Smith and Sandwell bathymetry. White dots mark locations of CTD/LADCP stations. Stations with VMP microstructure measurements in addition along the eastern channel are shown with reds dots on top. Black letters A through P give CTD/LADCP section names. Thick yellow lines show tow-yos at the northern end of the eastern channel. Pink triangles show moorings P1 through P5. Positions of the R97 moorings are marked with yellow circles.

Fig. 1.

(a) Bottom topography of the Pacific Ocean around the Samoan Passage from global Smith and Sandwell bathymetry with a resolution of 30 arc seconds (Becker et al. 2009). Arrows with numbers indicate abyssal northward volume transport estimates in 106 m3 s−1 across Robbie Ridge and along the eastern flank of the Manihiki Plateau from a hydrographic survey (Roemmich et al. 1996) and through Samoan Passage from moored current meters (R97). (b) Bottom topography of the Samoan Passage. The bathymetry shown here is a combination of multibeam soundings from two SPAMEX cruises, multibeam soundings from R97, and, where no multibeam data were available, Smith and Sandwell bathymetry. White dots mark locations of CTD/LADCP stations. Stations with VMP microstructure measurements in addition along the eastern channel are shown with reds dots on top. Black letters A through P give CTD/LADCP section names. Thick yellow lines show tow-yos at the northern end of the eastern channel. Pink triangles show moorings P1 through P5. Positions of the R97 moorings are marked with yellow circles.

Dense water formation at high latitudes and turbulent mixing and upwelling in the ocean interior have been found to be vital for maintaining a meridional overturning circulation (Sandström 1908). From an energetic viewpoint, interior mixing by far exceeds the role of buoyancy fluxes in maintaining the stratification of the oceans needed to drive the MOC (Wunsch and Ferrari 2004). This interior mixing is not homogeneous but has been observed to be patchy and localized (Polzin et al. 1997; Kunze et al. 2006) and temporally intermittent (Alford et al. 2011). Much of the energy needed for mixing comes from the breaking of internal waves generated by tides and the wind (Munk and Wunsch 1998). The conversion of potential to kinetic energy in the overturning circulation itself, particularly at sills and constrictions, provides additional mixing that may alter the strength and local distribution of the MOC. Such regions with bathymetry constricting and accelerating the flow are found, for example, in the Faroe Bank Channel (Fer et al. 2010), the Vema Channel (Hogg et al. 1982), and fracture zones in the Mid-Atlantic Ridge (Polzin et al. 1997) or Southwest Indian Ridge (MacKinnon et al. 2008). Enhanced mixing was inferred for the Samoan Passage as well (Roemmich et al. 1996) and confirmed by our direct measurements (Alford et al. 2013).

The geography of the Samoan Passage makes it an excellent site for observing the strength of the PMOC. Here, the deep western boundary current, generally sluggish and spread out, is forced through a narrow constriction, increasing the current speed above the levels of instrument noise and background variability and making it easier to span its lateral extent with ship-based measurements. A northward abyssal volume transport was inferred early on from gradients in water mass characteristics between the South and North Pacific (Prestwich 1875; Wüst 1937). The first direct measurements of abyssal currents in the Samoan Passage were carried out during the 1968 Styx expedition by Reid and Lonsdale (1974), using some of the first deep current meters available. Bottom currents with velocities well above 0.05 m s−1 in water colder than 0.7°C clearly showed strong northward flow of waters of Southern Ocean and North Atlantic origin within the passage. Bottom potential temperatures well above 0.7°C north of the passage suggested strong mixing of the abyssal current with overlying waters.

Taft et al. (1991) provided the first volume transport estimate for the flow of abyssal water through the passage based on geostrophic velocities from hydrographic measurements obtained during a cruise in summer 1987. Their estimate for northward volume transport of water with θ ≤ 1.17°C through a section along 10°S at the entrance to the passage was 6.0 ± 1.1 Sverdrups (Sv; 1 Sv ≡ 106 m3 s−1). Noting the sensitivity of the geostrophic velocity calculations to the choice of zero velocity surface, Johnson et al. (1994) calculated geostrophic volume transport estimates of 4.8, 1.0, and 5.6 Sv for their hydrographic section across the passage and the Reid and Lonsdale (1974) and Taft et al. (1991) occupations, respectively.

Studies by Roemmich et al. (1996) and Rudnick (1997, hereinafter R97), based on results from WOCE hydrographic observations (P31) and a WOCE mooring array (PCM-11), marked important steps toward a more precise volume transport estimate of the abyssal flow through the Samoan Passage and the understanding of its variability. The mooring array, deployed at the entrance to the passage at about 10°S (Fig. 1b, yellow circles) from September 1992 to February 1994, was used to estimate the time-mean and temporal and spatial variability of the abyssal flow into the passage (R97). Volume transport estimates for the northward current below 4000-m depth from the moored time series ranged between 1.1 and 10.7 Sv on subinertial time scales, with a mean of 6.0 Sv. This variability, especially pronounced at a time scale of about 30 days, bracketed all previous geostrophic volume transport estimates as well as the one calculated from hydrographic observations that were obtained while the moorings were in place (Roemmich et al. 1996; 7.1 Sv). A later volume transport estimate from hydrographic observations also falls well within the detected natural variability (Freeland 2001; 8.4 Sv).

Motivated by the importance of the abyssal PMOC for the climate system, and stimulated by these earlier findings, the Samoan Passage Abyssal Mixing Experiment (SPAMEX) was conducted to 1) discover the detailed pathways of dense water flow through the complex topography of the region with several sills, valleys, and canyons; 2) determine rates of turbulent mixing in the region and understand their associated processes; and 3) update the long-term volume transport estimate of R97. An overview of initial results, including the first direct mixing measurements from the Samoan Passage with a focus on the eastern channel, was presented by Alford et al. (2013). Long-term volume transport records will be reported after analysis of mooring recoveries in 2014.

Here, we analyze sections at several locations across the passage to study the detailed pathways and turbulent mixing of the dense current. After giving a description of measurements and data processing in section 2, hydrographic station and mooring data are synthesized for a description of the flow along the different pathways of the passage and its temporal variability in section 3. Volume transports and their associated uncertainties are estimated at several locations in section 4. Using these results, vertical turbulent mixing of the abyssal flow is inferred from heat budgets and compared against overturn-derived turbulent mixing estimates in section 5.

2. Instrumentation

This paper is based on measurements obtained during the first two of three cruises within SPAMEX. To assist in the planning process of the SPAMEX project, the first short mapping cruise, in November 2011, was a dedicated seafloor mapping survey of the Samoan Passage using a multibeam system onboard R/V Kilo Moana. The detailed knowledge of the rugged bathymetry of the passage with many volcanic seamounts and ridges on lateral scales of only a few kilometer provided guidance in planning and conducting the following pathways cruise in July and August 2012 onboard R/V Revelle. This cruise consisted of a series of shipboard observations spanning sections across and along the passage, accompanied by a set of five moorings, distributed over the passage and moored for the duration of the cruise (Fig. 1b). To reassess the amount and variability of the abyssal volume transport through the passage on longer time scales, a monitoring mooring array was deployed at the end of the pathways cruise. These moorings, placed at the same locations as the R97 array, were recovered in 2014.

Shipboard measurements of salinity, temperature, oxygen, and pressure were obtained with a Seabird SBE 911plus conductivity–temperature–depth (CTD) attached to a water sample rosette. Water samples were taken at varying depths and analyzed for oxygen onboard by Winkler titration and for salinity on shore, using a Guildline Autosal 8400B and IAPSO Standard Seawater batch number P152. The CTD data were postprocessed to account for time lags between the temperature and conductivity sensor, the thermal mass of the conductivity sensor, and to remove pressure inversions due to ship rolling before averaging into 1-m bins. Nominally, the temperature measurements have an accuracy of 5 × 10−4 °C and a precision of 5 × 10−5 °C (www.seabird.com). Two sets of sensors, pre- and postcruise calibrated, were used during this cruise. While the two temperature sensors had an offset of about 1.5 × 10−3 °C at depth below the thermocline during the first half of the cruise, the secondary temperature sensor failed midcruise, and the newly installed secondary sensor proved to be within 5 × 10−4 °C of the primary sensor at depths greater than 2000 m. Together with pre- and postcruise calibration of the primary temperature sensor showing stability throughout the cruise, this leads us to assign an uncertainty of ±5 × 10−4 °C to the temperature measurements. Conductivity sensors were pre- and postcruise calibrated, leading to an uncertainty of ±2 × 10−3 in salinity calculated from temperature, conductivity, and pressure data. CTD salinity profiles compare with bottle samples within this uncertainty.

Shipboard measurements of the in situ velocity were obtained with a set of two lowered acoustic Doppler current profilers (LADCP) attached to the water sample rosette, a downward-looking Teledyne RD Instruments (TRDI) Workhorse operating at 150 kHz and 16-m bin size and an upward-looking TRDI Workhorse operating at 300 kHz and 8-m bin size. The LADCP profiles were processed using the inversion method of the LDEO software version IX_8 (Visbeck 2002). Velocity profiles, calculated from all pings recorded during downcast and upcast, were constrained using bottom-tracking velocity measurements, ship drift data from GPS, and upper-ocean velocity measurements with a 75-kHz shipboard ADCP operating in broadband mode. Using a dynamic positioning system, the ship drift for each station was negligible with maximum drifts of about 100 m and average drift distances less than 50 m. Fully constrained velocity profiles usually deviate less than 3 cm s−1 from the real water velocity (Thurnherr 2010). For this study, good agreement between LADCP velocity profiles and nearby velocity records from moored ADCPs leads to an LADCP velocity uncertainty estimate of about 2 cm s−1appendix A).

To capture the temporal variability of the flow throughout the duration of the cruise, moorings were deployed at the center of the R97 array (P1), at two of the sills of the western channels (WC; P2 and P3) and at the two main sills along the eastern channel (EC; P4 and P5) (Fig. 1b, pink triangles). The moorings were designed to cover the flow between 3000-m depth and the bottom. All moorings were equipped with McLane moored profilers (MP) carrying CTDs and acoustic current meters. The MPs constantly profiled up and down the mooring line at speeds of 0.25–0.33 m s−1 over depth ranges of more than 1000 m, recording vertical profiles of temperature, salinity, pressure, and velocity about every 1 to 2 h. All MPs returned good data, except for complete data loss of the MP at P2 because of the implosion of its buoyancy sphere and failure of the velocity sensor at P5. Additional ADCPs, single-point acoustic current meters [TRDI Doppler Volume Sampler (DVS)] and CTD sensors (SBE37 and 39) were attached to the top and bottom of the moorings. See Table 1 for a summary of the measurements obtained at the five moorings.

Table 1.

Mooring locations, instruments, sampling parameters, sampling depths, and lengths of sampled time series. Sampling properties are salinity S, temperature T, pressure P, and velocity magnitude and direction V.

Mooring locations, instruments, sampling parameters, sampling depths, and lengths of sampled time series. Sampling properties are salinity S, temperature T, pressure P, and velocity magnitude and direction V.
Mooring locations, instruments, sampling parameters, sampling depths, and lengths of sampled time series. Sampling properties are salinity S, temperature T, pressure P, and velocity magnitude and direction V.

3. Observations

a. CTD/LADCP sections

In total, 109 CTD/LADCP stations were occupied during the pathways cruise. Out of these, we analyze 82 stations that form sections across the various channels of the passage. Data from the meridional section along the main eastern channel are presented in Alford et al. (2013).

The velocity and temperature measurements show the near-bottom transport of water colder than 1.0°C through the passage from south to north (Fig. 2). Previous studies defined the upper interface by potential temperatures between 0.9° (Reid and Lonsdale 1974) and 1.2°C (Taft et al. 1991; Johnson et al. 1994). Here, for reasons clarified later in this paper, we use the 1.0°C isotherm as the general interface definition. The flow pattern appears to be closely connected to the local bottom topography with local acceleration of the deep flow occurring over the shallow sills of the passage. At section A, the entrance to the passage, velocities are generally less than 0.1 m s−1, with a core of higher velocities reaching up to 0.16 m s−1 at 75 km on the x axis. Downward-sloping isotherms toward the west at the western flank of the deep part of section A are accompanied by low northward velocities. At section B, each of the three channels carries a core of cold northward flow. Velocities in the western shallow channel are the highest in this section, reaching up to 0.17 m s−1. As in section A at 150 km, the only southward flow at depth occurs at the very eastern end of the section at 120 km. This may indicate a return flow of water not passing over the downstream sill. However, the velocity amplitude in this single profile is too low to distinguish a possible return flow from high-frequency aliasing. Section C spans the shallowest parts of the western channels and the first main sill of the eastern channel with sill depths of about 4600 and 4900 m, respectively. Here, the abyssal flow has accelerated considerably to velocities of up to 0.3 m s−1 in the western channels and up to 0.2 m s−1 in the eastern channel. Farther north, in the center of the eastern channel at section D, the flow slows down to a maximum of 0.12 m s−1 before reaching above 0.2 m s−1 at the northern sill of the eastern channel in section E. A highly resolved CTD/LADCP tow-yo section across this sill revealed the strong acceleration of the abyssal flow with velocities of up to 0.5 m s−1 (Alford et al. 2013). The high velocity core (υ > 0.3 m s−1) at the eastern end of section F is a remnant of the vigorous acceleration during the descent from the northern sill. The flow through the western channels reaches velocities of about 0.2 m s−1 at sections K, N, and H and about 0.15 m s−1 at the western end of section F. As the passage widens at section G, the flow slows considerably to maximum velocities of 0.1 m s−1. Whether the flow from the eastern channel shifts westward at section G as indicated by the observations is not clear, since the relatively low velocities observed here may be aliased by internal wave variability.

Fig. 2.

Objectively mapped LADCP velocities normal to each section (color) and potential temperatures (contours). Section letters correspond to labels for section locations on the center map. Only data below 3000-m depth are shown. Triangles mark locations of profiles in the section plots. For channels including only one station (L, M, N, and P), the profiles were not objectively mapped but instead extended constantly over a passage width of 8 km for plotting purposes. All sections are shown at the same horizontal and vertical scale. Bathymetry is shown as measured by multibeam echo soundings. For channels including only one station, velocities are shown along the approximate channel direction. Bars on the center map depict amplitude and direction of the transport per unit width at each station for θ < 1.0°C (green). The fraction of the transport per unit width for θ < 0.7°C is shown in pink.

Fig. 2.

Objectively mapped LADCP velocities normal to each section (color) and potential temperatures (contours). Section letters correspond to labels for section locations on the center map. Only data below 3000-m depth are shown. Triangles mark locations of profiles in the section plots. For channels including only one station (L, M, N, and P), the profiles were not objectively mapped but instead extended constantly over a passage width of 8 km for plotting purposes. All sections are shown at the same horizontal and vertical scale. Bathymetry is shown as measured by multibeam echo soundings. For channels including only one station, velocities are shown along the approximate channel direction. Bars on the center map depict amplitude and direction of the transport per unit width at each station for θ < 1.0°C (green). The fraction of the transport per unit width for θ < 0.7°C is shown in pink.

Depth-integrated velocities show the general pattern of the flow field divided between eastern and western channels. The volume transports per unit width of water with potential temperatures θ < 1.0°C are shown for all stations on the map in Fig. 2. The majority of the coldest water makes its way through the deeper eastern channel. The vanishing of water colder than 0.7°C (marked as a fraction of the 1.0°C transport on the map) at the northern end of the eastern channel indicates elevated levels of vertical turbulent mixing in the passage.

The abyssal northward flow is characterized by high neutral density (Fig. 3, contours). Neutral density is a continuous analog of potential density surfaces discretely referenced to certain depths (Jackett and McDougall 1997). Maximum neutral densities reach about 28.195 kg m−3 at section A. At section G, at the northern end of the passage, maximum neutral densities are only about 28.18 kg m−3. The interface definition of 1.0°C corresponds to neutral density of about 28.125 kg m−3. The abyssal flow consists of both Lower Circumpolar Deep Water (LCDW; 28.10 < γn ≤ 28.16 kg m−3; Macdonald et al. 2009) and Antarctic Bottom Water (AABW; γn > 28.16 kg m−3). Neutral density surfaces in the abyssal layer are generally sloping down eastward at all sections, as expected for a geostrophically balanced, dense, northward flow in the Southern Hemisphere.

Fig. 3.

Section plots of objectively mapped salinity anomaly on neutral density surfaces (color) and neutral density (black contours). Figure setup as in Fig. 2. Salinity anomalies are calculated relative to an average salinity–neutral density relation shown in black on the center panel. All measured salinity profiles are shown color coded by potential temperature θ.

Fig. 3.

Section plots of objectively mapped salinity anomaly on neutral density surfaces (color) and neutral density (black contours). Figure setup as in Fig. 2. Salinity anomalies are calculated relative to an average salinity–neutral density relation shown in black on the center panel. All measured salinity profiles are shown color coded by potential temperature θ.

The temperature–density relationship is relatively tight with deviations only around the layer interface, where high salinity anomalies are observed (Fig. 3, shaded). As the flow enters the passage from the south, it has a distinct signature of North Atlantic Deep Water (NADW) in salinity at the upper interface. Positive salinity anomalies relative to an average salinity–density relation mark remnants of NADW (Reid and Lynn 1971) that is warmer and more saline than the underlying AABW. This signature of NADW is intensified toward the west and disappears almost completely at the northern exit from the passage. The water mass modification owes to turbulent mixing as will be demonstrated in section 5.

b. Geostrophic velocities

We calculated geostrophic velocities in addition to the directly measured LADCP velocities to test whether this method gives reasonable results for the abyssal flow over the complex bathymetry of the passage. The common problem of referencing the calculated velocity profile to a barotropic velocity has been dealt with in two different ways in past studies of the Samoan Passage. Both methods attempted to estimate a zero velocity surface (ZVS) where the northward flow vanishes. Reid and Lonsdale (1974) used the depth of maximum buoyancy frequency, approximately corresponding in our data to the 0.9°C isotherm (Fig. 4a). In contrast, Taft et al. (1991) argued that the elevated salinity and oxygen at this depth indicates water of Atlantic or Southern Ocean origin, which must also be part of the northward flow. They associated the potential temperature where the slope in the θS curves change (1.17°C in their dataset) with the upper boundary of North Atlantic Deep Water and thus use this isotherm for a zero velocity reference. Following the latter argument, Johnson et al. (1994), Roemmich et al. (1996), and Freeland (2001) all used the 1.2°C isotherm to reference geostrophic velocities.

Fig. 4.

(a) Profiles of buoyancy frequency N2 averaged into potential temperature classes (black) and standard deviation from a lognormal fit (gray). (b) LADCP velocity profiles rotated normal to their respective section and averaged into potential temperature classes (black) plus or minus one standard deviation (gray). Geostrophic velocity profiles referenced to zero velocity at 1.0°C and averaged into potential temperature classes (red).

Fig. 4.

(a) Profiles of buoyancy frequency N2 averaged into potential temperature classes (black) and standard deviation from a lognormal fit (gray). (b) LADCP velocity profiles rotated normal to their respective section and averaged into potential temperature classes (black) plus or minus one standard deviation (gray). Geostrophic velocity profiles referenced to zero velocity at 1.0°C and averaged into potential temperature classes (red).

The direct current measurements from the LADCPs provide a measure to test these assumptions. The region-averaged mean velocity profile, calculated from individual profiles that were rotated normal to their corresponding section and averaged into potential temperature classes, shows that the northward flow approaches zero in water with potential temperatures above 1.0°C (Fig. 4b). On average, the depth where the flow reaches zero is shallower than the depth of the maximum buoyancy frequency by about 0.1°C (Fig. 4a), and hence the stability maximum should not be used as the ZVS. We use the 1.0°C isotherm to reference geostrophic velocities. Here, the average LADCP velocity is zero, and the average buoyancy profile has reached amplitudes as low as shallower values. The structure of the average geostrophic velocity profile compares well with the average LADCP profile, except for the deepest layers in water with θ < 0.7°C. Referencing the geostrophic velocities to a ZVS at isotherms above 1.0°C leads to worse agreement between average LADCP and geostrophic velocity profiles, primarily at the bottom.

The general structure of the geostrophic velocity fields approximately matches the direct velocity observations from LADCPs (Fig. 4). However, the geostrophic velocity fields have larger horizontal gradients and vertical shear than the LADCP velocity fields. This may be because of aliasing by internal waves. Density time series from the moorings show interface variations of up to 100 m on tidal and near-inertial time scales, comparable in size to the general isopycnal slope of O(100) m over 100 km associated with the geostrophic currents at depth. Furthermore, values near the bottom in the objectively mapped fields are less precise, since the geostrophic profiles only reach to the depth of the shallowest pair of stations needed in the calculation, resulting in fewer velocity estimates close to the seafloor than provided by the LADCP measurements. For these reasons, we will base our volume transport calculation on the directly measured LADCP velocities.

c. Mooring observations

In the Samoan Passage, the northward transport of abyssal water is the dominant signal in the time-averaged flow field at depth. However, both the northward current and the background velocity field fluctuate on various time scales. R97 showed that the most intense temporal variability in the volume transport at the entrance to the passage occurs at semidiurnal, diurnal, and 30-day time scales.

Temporal variability in the tidal and near-inertial range was measured by several short-term moorings. The mooring deployments were too short to identify any variability in the 30-day range. Temperature and velocity time series at section A, sampled by the MP at mooring P1 (Fig. 1), show how the abyssal northward flow below 1.0°C dominates the P1 time series (Fig. 5). Fluctuations on semidiurnal, diurnal, and near-inertial time scales are superimposed. The near-inertial period is about 3 days in the Samoan Passage. Bandpass-filtered time series show amplitudes between 2 and 3 cm s−1 in each of these frequency bands. These fluctuations do not vary much with depth in the semidiurnal band, while the diurnal and near-inertial signals weaken toward the bottom where the water is less stratified. Isotherm displacement amplitudes are as large as about 100 m (peak to peak) in the semidiurnal band, but smaller in the diurnal and near-inertial bands.

Fig. 5.

Velocity (color) and potential temperature (contours) time series from the MP at mooring P1 (see Fig. 1 for mooring location). The velocity component normal to section A (18° eastward from north) is shown. The upper panel shows the total time series over the depth range covered by the MP. The lower panels show the time series bandpass filtered in semidiurnal, diurnal, and near-inertial frequency bands. Note that potential temperature contours are unevenly spaced to highlight the cold bottom layer.

Fig. 5.

Velocity (color) and potential temperature (contours) time series from the MP at mooring P1 (see Fig. 1 for mooring location). The velocity component normal to section A (18° eastward from north) is shown. The upper panel shows the total time series over the depth range covered by the MP. The lower panels show the time series bandpass filtered in semidiurnal, diurnal, and near-inertial frequency bands. Note that potential temperature contours are unevenly spaced to highlight the cold bottom layer.

Velocity variability at the other moorings is similar to P1. Rotary spectra (Gonella 1972) of the moorings P1, P3, and P4 demonstrate that most of the energy is contained in the semidiurnal and near-inertial bands and somewhat less in the diurnal band (Fig. 6). Rotation in the sense of free inertial oscillations [counterclockwise (CCW) in the Southern Hemisphere] dominates the motion in these bands. Only the semidiurnal tide at mooring P1 shows clockwise (CW) levels that are close to their CCW counterpart. At all three moorings, near-inertial frequency band variability is strong above the interface and weakens in the abyssal layer. R97 ascribed this disappearance of the near-inertial peak with depth to bottom topography inhibiting the mostly horizontal wave motions.

Fig. 6.

Rotary spectra of the horizontal velocity field measured by moored profilers at moorings P1, P3, and P4. (left) The CW component of the spectrum and (right) the CCW component. Rotary spectra are calculated individually for each depth level. The inertial frequency f and several tidal constituents are marked with vertical dashed lines. Horizontal dashed lines show the mean depth of the 1.0°C isotherm at each mooring. Note that peaks in the high-frequency range above 4 cycles per day may be due to aliasing caused by the sampling pattern of the moored profilers.

Fig. 6.

Rotary spectra of the horizontal velocity field measured by moored profilers at moorings P1, P3, and P4. (left) The CW component of the spectrum and (right) the CCW component. Rotary spectra are calculated individually for each depth level. The inertial frequency f and several tidal constituents are marked with vertical dashed lines. Horizontal dashed lines show the mean depth of the 1.0°C isotherm at each mooring. Note that peaks in the high-frequency range above 4 cycles per day may be due to aliasing caused by the sampling pattern of the moored profilers.

Harmonic analysis of the velocity time series (Pawlowicz et al. 2002) gives mean amplitudes of the semidiurnal and diurnal tides of about 0.02 and 0.01 m s−1, respectively. Tidal amplitudes found from bandpass filtering the current around the semidiurnal and diurnal frequencies are somewhat higher at 0.02 to 0.03 and 0.01 to 0.02 m s−1, respectively. The difference is probably due to the harmonic analysis focusing on specific constituents, whereas bandpass filtering captures all variability within a frequency band. For comparison, the amplitude of the sum of the dominant barotropic tidal constituents from an inverse model [TOPEX/Poseidon (TPXO); Egbert and Erofeeva 2002] is about 0.01 to 0.02 m s−1 in the Samoan Passage. Observed tidal velocities are generally in phase with TPXO but at larger amplitudes. We ascribe these larger amplitudes to internal tides, but cannot separate them from the barotropic tides as the moorings do not span the whole water column. Average velocity fluctuations in the near-inertial band in the deep layer are generally below 0.01 m s−1, but reach up to 0.03 to 0.05 m s−1 in the highly energetic maxima at or above the 1.0°C interface.

Spectra of the isotherm depth time series show that interface excursions are strong in the semidiurnal band (Fig. 7), especially at mooring P1 at the passage entrance and mooring P5 at the northern sill of the eastern channel. Here, the interface changes by about 100 m between low and high tide. A comparison between these interface time series and the barotropic tide from the TPXO model reveals a strong phase locking in the semidiurnal band at P5, but not at the other moorings. Details of the internal wave field will be examined in another paper.

Fig. 7.

Spectra of the vertical excursion of isotherms at moorings P1, P2, P3, and P5. Isotherm depths were calculated from MP temperature measurements (see, e.g., the contours in Fig. 5).

Fig. 7.

Spectra of the vertical excursion of isotherms at moorings P1, P2, P3, and P5. Isotherm depths were calculated from MP temperature measurements (see, e.g., the contours in Fig. 5).

4. Volume transports

a. Method and error estimate

For estimates of the total volume transport of deep water through the Samoan Passage at the time of our survey, we integrate LADCP current measurements over the sections. Prior to integration, the LADCP velocity component normal to the local angle of each respective section is computed. In most cases, this corresponds to the direction of the local channel axis. Barotropic tides (TPXO) are subtracted and the velocity data are objectively mapped in the xz plane. Each section is extrapolated either to the bathymetric boundaries or over 10 km to account for flow not covered by the section. Velocity and layer interface depth are assumed to be constant from the last profile to the end of each 10-km extension. Most sections are well confined by bathymetry, and the integrated volume transport is only changed by a few percent through the extrapolation. Extrapolation increased the volume transport by more than 10% only for sections F and H. If not stated otherwise, the upper interface for the volume transport integration is the 1.0°C isotherm.

The error of the volume transport estimate at each section stems from both measurement uncertainties as well as spatial and temporal aliasing. Interface and bottom depths along the sections are measured at high precision, but LADCP velocities have an uncertainty of about ±0.02 m s−1appendix A). To estimate the error in volume transport estimates from this measurement uncertainty, we repeatedly added uncertainties from a normal distribution with a width of 2σ = 0.02 m s−1 to velocity profiles at section A prior to integration. The fit of a normal distribution to the calculated volume transports shows that all results lie within ±0.5 Sv.

The variability of the velocity and interface height of the abyssal current on semidiurnal, diurnal, and near-inertial time scales has the potential to significantly alias estimated volume transports from velocity-integrated CTD/LADCP sections. When interfering constructively, the variations in the different frequency bands may amount to up to 0.1 m s−1 and more than 100 m, respectively. An inspection of the phase of the barotropic semidiurnal tide when approaching the bottom of each cast shows that our measurements are distributed randomly in phase for the dominating M2 tidal constituent. Hence, in general, aliasing from diurnal and semidiurnal tides is expected to average out to a certain degree. Variability in the near-inertial band, although not as pronounced in the abyssal layer as in the tides, is more likely to alias the volume transport estimates. The inertial period is around 3 days at this latitude—approximately the time needed to complete a section across the passage at our station spacing.

The velocity mooring time series from the early ‘90s (R97) provides an excellent benchmark to test the influence of natural internal variability on our sampling scheme. The R97 moored velocity time series—located on our section A (Fig. 1b) and with a temporal resolution of 1 h—are objectively mapped in the xz plane to create fields with known velocities over the whole section A. The spatial integral over each of these fields provides a volume transport time series that we consider to be the true transport for the purposes of this test (Fig. 8a, gray curve). The standard deviation of the true transport time series is reduced from 2.9 to 2.0 Sv when barotropic tides (TPXO) are subtracted prior to integration (Fig. 8a, blue curve). However, this does not remove the baroclinic part of the tides or any other internal variability. The 100-h low-pass filtered version of the integrated velocity time series (Fig. 8a, black curve) corresponds very closely to the volume transport time series shown in R97, with only minor discrepancies because of differences in the integration algorithm. We subsample these “true” fields to simulate our CTD/LADCP sampling scheme. The more than 1-yr-long time series is divided into segments long enough to be subsampled at the same locations and with the same relative timing as section A was measured. The difference between the spatial integral over the subsampled profiles and the true low-pass filtered transport at the time of the simulated section occupation then amounts to the uncertainty added by internal variability as resolved in space and time by the moorings. Each red dot in Fig. 8a corresponds to one simulated CTD/LADCP occupation of section A. For most of the 226 realizations, the difference from the low-pass filtered true time series is relatively small. The differences follow approximately a normal distribution (Fig. 8b). The standard deviation of a normal distribution fitted to the probability distribution of the differences is 0.44 Sv. Hence, we expect the ±2σ(≈95% confidence) uncertainty interval of the volume transport estimate from CTD/LADCP data due to aliasing from natural internal wave variability to be ±0.9 Sv. For the case where modeled barotropic tides were not subtracted from the true fields, the standard deviation of the fit to the differences is 0.47 Sv.

Fig. 8.

Simulation of CTD/LADCP-derived volume transport at section A using mooring data from R97. (a) Hourly volume transport time series from objectively mapped moored velocity time series (gray); the same time series but barotropic tide subtracted (blue) and low-pass filtered at a cutoff period of 100 h (black). Volume transport simulating the CTD/LADCP volume transport estimate calculated from subsampled velocity fields (red dots). (b) Probability density distribution of the difference between low-pass filtered volume transport time series and simulated CTD/LADCP volume transport (gray bars) and a normal distribution fit (black) with shape parameters of the fit.

Fig. 8.

Simulation of CTD/LADCP-derived volume transport at section A using mooring data from R97. (a) Hourly volume transport time series from objectively mapped moored velocity time series (gray); the same time series but barotropic tide subtracted (blue) and low-pass filtered at a cutoff period of 100 h (black). Volume transport simulating the CTD/LADCP volume transport estimate calculated from subsampled velocity fields (red dots). (b) Probability density distribution of the difference between low-pass filtered volume transport time series and simulated CTD/LADCP volume transport (gray bars) and a normal distribution fit (black) with shape parameters of the fit.

Adding the uncertainty due to internal natural variability to the instrument uncertainty as the square root of the sum of squares, the total volume transport uncertainty at section A is expected to be about ±1 Sv. For the other sections, we expect errors of similar magnitude.

b. Volume transport through CTD/LADCP sections

The volume transports through the different sections approximately agree within the uncertainty of ±1 Sv (Fig. 9). At section A, the volume transport of water with θ < 1.0°C is 3.9 Sv. The majority of this volume transport occurs for θ < 0.7°C. The volume transport for θ < 1.0°C at section B is lower, with 3.1 Sv, than at section A. This, at least to some extent, is due to section B not covering the very western part of the entrance to the passage. The flow through the corresponding western parts of sections A and C is 0.5 and 1.1 Sv, respectively. Thus, we expect the total volume transport at section B to scale to about 3.6 to 4.2 Sv—that is, about the same volume transport as found at section A. At section C, the combination of the flow through western and eastern channels is 6.0 Sv. Here, the flow is split about equally between western and eastern channels. The flow through the western channels is dominated by water warmer than 0.7°C, while the eastern channel carries mostly colder water. At the northern exits from eastern and western channels, although of relatively small combined magnitude at the time of the occupation (E&H, 4.0 Sv), the abyssal flow is still divided into about equal parts. Both along the western and the eastern channels, the volume transport shifts into higher potential temperature classes. No water colder than 0.75°C leaves the western channels through the main exit at section H. From initially about 2 Sv, the amount of water colder than 0.7°C has dropped to only about 1 Sv at the northern sill of the eastern channel (section E). Volume transports at section F and G are 5.5 and 5.2 Sv, respectively. Because of vigorous mixing downstream of the eastern channel exit (Alford et al. 2013), no water colder than 0.7°C is left at section F, and mixing appears to continue onward to section G where the majority of the abyssal volume transport is warmer than 0.75°C.

Fig. 9.

Volume transports in potential temperature classes through sections from south (A) to north (G). Section labels as in Fig. 2. The volume transport through sections C and E&H is split into transport through the WC (dark) and the EC. Numbers in each panel give the total volume transport below 1°C.

Fig. 9.

Volume transports in potential temperature classes through sections from south (A) to north (G). Section labels as in Fig. 2. The volume transport through sections C and E&H is split into transport through the WC (dark) and the EC. Numbers in each panel give the total volume transport below 1°C.

Two possible exits from the passage were left out in the discussion above: a channel leaving the region in the northeast (station L) and the northwestern part of the western channels (station P). Simple scaling of the LADCP velocity profiles with the channel widths suggests that their volume transports are quite small at 0.2 and 0.1 Sv, respectively. This indicates that the vast majority of the abyssal flow leaves the passage through sections F and G in the north.

The westward intensification of the bottom current and the associated westward elevation of isopycnals allows for more than half of the flow to make its way through the western channels that are considerably shallower than the eastern channel. Comparing the volume transport through the gaps within the western channels (K, N, and M) with the flow through the central eastern channel (section D) provides another estimate for this partitioning of the flow. Since N and M are single stations, we can only obtain volume transport estimates by extrapolating the velocity profiles laterally within the channels. We nevertheless include these transports with those obtained from the interpolation method at K and D. The resulting volume transport through the western channels (2.4 Sv) is slightly, but not significantly, higher than its counterpart through the eastern channel (1.8 Sv). Thus, at the entrance, in the center, and at the exit, the western channels carry about 60% of the total volume transport through the passage. More than 90% of the flow below 0.7°C goes through the eastern channel.

A southward return flow above 1.0°C is evident in the LADCP downstream sections, whereas it is almost zero at section A. It remains inconclusive whether this is connected to an increase in northward volume transport of the abyssal flow with downstream distance. In a steady state, simple mass balance would require entrained water along the passage to be replaced by flow in the upper layer. The increase from south to north, though not statistically significant and well within the natural variability, is about 1 Sv. The southward volume transport in the layer 1.0°C < θ < 1.2°C is 1.5 Sv at section G and 0.6 Sv at section F. Hence, it is of the right order of magnitude to balance entrainment into the abyssal current. However, because of uncertainties in the volume transport estimates of about the same size, we are unable to draw any firm conclusions. Current measurements at the top of mooring P5 (not shown) do not indicate a statistically significant return flow in the upper layers. As pointed out by R97, no single section across the passage can be considered truly representative of the statistical mean flow because of the natural variability of the flow. To put our snapshots into the perspective of low-frequency natural variability over the course of the survey, in the following we turn to time series from the different mooring sites.

c. Temporal variability

Moorings were deployed at five different locations in the Samoan Passage during our shipboard survey (Fig. 1). Positioned at the inflow region (P1) and at several of the sills (P2–P5), they do not allow for integrating the flow to obtain volume transport time series. However, close correlation between the volume transport per unit width at mooring 3 from the R97 array with the overall R97 volume transport time series (Fig. 10) shows that single moorings can be indicative for the overall state of the current field.

Fig. 10.

Volume transport time series from R97 recalculated from all his moorings and low-pass filtered at 100 h (black) and volume transport per unit width at his mooring 3, linearly scaled to the total volume transport and low-pass filtered (red).

Fig. 10.

Volume transport time series from R97 recalculated from all his moorings and low-pass filtered at 100 h (black) and volume transport per unit width at his mooring 3, linearly scaled to the total volume transport and low-pass filtered (red).

The moorings indicate weak low-frequency variability over the 25-day deployments at P3 and P4 and moderate variability at P1 to the south (Fig. 11a). At high frequencies, the transport is strongly influenced by the aforementioned variability of velocity and interface depth on diurnal and semidiurnal time scales. Over periods of only a few hours, the volume transport at the moorings fluctuates by about 50%.

Fig. 11.

(a) Volume transport per unit width of water with θ < 1.0°C at moorings P1, P3, and P4. Thin lines show hourly values; thick lines show volume transports low-pass filtered at a cutoff period of 100 h. (b) Volume transport through LADCP sections at time of occupation (repeated from Fig. 9). Letters correspond to section labels in Fig. 2; Ce and Cw denote the eastern and western part of section C. Gray bars show part of section occupied at other time, for example, the gray bar at E shows H. (c) Depth of the γn = 28.125 kg m−3 isopycnal marking the upper interface of the abyssal flow at moorings P1, P3, P4, and P5.

Fig. 11.

(a) Volume transport per unit width of water with θ < 1.0°C at moorings P1, P3, and P4. Thin lines show hourly values; thick lines show volume transports low-pass filtered at a cutoff period of 100 h. (b) Volume transport through LADCP sections at time of occupation (repeated from Fig. 9). Letters correspond to section labels in Fig. 2; Ce and Cw denote the eastern and western part of section C. Gray bars show part of section occupied at other time, for example, the gray bar at E shows H. (c) Depth of the γn = 28.125 kg m−3 isopycnal marking the upper interface of the abyssal flow at moorings P1, P3, P4, and P5.

The LADCP-derived volume transport estimates (repeated in Fig. 11b) are generally consistent with these mooring records. The flow at mooring P1 shows that section A was measured during a period of weaker transport than the cruise average. This may explain the relatively low volume transport estimate for section A. R97 showed that the abyssal volume transport at section A varied between 1.1 and 10.7 Sv on time scales of about a month. A comparison between the transport per unit width at mooring P1 and data from mooring 3 of the R97 array (R3) from the same location shows that the time-mean transport per unit width at P1 is comparable, but slightly weaker than R3. If R3 were perfectly correlated with the total transport through section A, this would imply that there was 5.7-Sv total volume transport on average during the time of our cruise.1 With the same scaling, the transport would have been about 4.8 Sv at the time when section A was occupied, while our LADCP-derived volume transport estimate is 3.9 Sv.

Section C was measured during two different periods, its eastern part (Ce) around day 211 and its western part (Cw) around day 224. Both moorings P3 and P4, located near Ce and Cw, respectively, indicate steady conditions. The LADCP-derived volume transport at C is the highest of all sections with 6 Sv. If mooring P1, in a high transport state during the occupation of Ce, is indicative for the flow through Ce, it may explain the higher than cruise-averaged LADCP section transport. However, this would mean that P4 does not capture the low-frequency variability at this sill.

The data return from moorings P2 and P5 is not sufficient for a volume transport calculation. A time series of the velocity 20 m above bottom indicates that the velocity of the abyssal current at P2 was about 0.14 m s−1 during the occupation of the western part of section B. Compared to the time mean of 0.17 m s−1 over the whole deployment period, this indicates weaker than average conditions, agreeing with the reduced volume transport we observe at section B compared to C. Weakened transport per unit width at P1, located only slightly upstream of section B, also agrees with lower volume transport here. Missing velocity records at P5 do not allow us to infer the state of the flow across the northern sill of the eastern channel relative to the time mean over the cruise during the time of section E occupation that returned a relatively low volume transport estimate.

The thickness of the abyssal layer in the passage may be related to variations of the inflow from the south. At P5, the interface sank by almost 100 m over the course of the cruise (Fig. 11c). This indicates that the weakening of the inflow at P1 leads to decreasing interface height at the exit from the eastern channel. It remains inconclusive why mooring P4 does not show this trend either in volume transport or in the interface depth time series. The relationship between inflow variations and possible storage in the passage is beyond the scope of this paper. The dominant period of the inflow of about 30 days (R97) is not resolved with the current dataset, but we are hopeful that we will be able to answer this question with data from the long-term mooring array recovered in 2014.

5. Turbulent mixing

a. Advection–diffusion model

The abyssal current undergoes significant changes in its properties as it transits the Samoan Passage (Fig. 9). At the northern section, the coldest isotherms have completely vanished because of turbulent mixing with overlying warmer water. Increased levels of turbulent mixing in the Samoan Passage lead to an erosion of the salinity maximum that is associated with the remnants of NADW at the passage entrance (Fig. 3, following the yellow/orange shading from A to G). Profiles in θS space indicate the development of the deep flow along pathways through the western and eastern channels (Fig. 12). At the passage entrance, before the flow reaches the first sills, the layer of Antarctic Bottom Water is topped by a layer of remnant North Atlantic Deep Water with a local salinity maximum in the potential temperature range 0.7° to 0.8°C showing up as deviations from a straight line between AABW and overlying waters (cf. Fig. 3). The profiles farther downstream approach straight lines in the θS diagram.

Fig. 12.

Plots of θ–S from hydrographic profiles along the (left) WC and (right) EC (colored dots). Profile positions are marked with matching colored dots on the center map. Black contours show neutral density calculated at 9°S, 169.5°W at 4000-m depth. Black profiles show results of the advection–diffusion model applied to the upstream profiles (red) with solutions for spreading scales λ = [50, 100, 150, 200, 300, and 400 m].

Fig. 12.

Plots of θ–S from hydrographic profiles along the (left) WC and (right) EC (colored dots). Profile positions are marked with matching colored dots on the center map. Black contours show neutral density calculated at 9°S, 169.5°W at 4000-m depth. Black profiles show results of the advection–diffusion model applied to the upstream profiles (red) with solutions for spreading scales λ = [50, 100, 150, 200, 300, and 400 m].

We apply an advection–diffusion model to salinity and temperature profiles from the inflow region. The vertical turbulent diffusivity needed to transform these to profiles similar to those from the outflow region downstream is a first simple approach to estimating the average amount of turbulent mixing in the passage. Following Hautala et al. (1996), the vertical mixing of tracer concentration c (salt or potential temperature) can be modeled as

 
formula

with K being a constant for vertical diffusivity. Assuming a steady current field, the material derivative D/Dt is following a water column through the region. The transit time of the water column through the passage sets the duration over which turbulent mixing can act to erode the salinity maximum. In other words, since the salinity maximum has disappeared at the northern end of the passage, a certain vertical diffusivity K is implied by a given advection time scale.

A simple forward differencing scheme is applied to solve Eq. (1) numerically. The concentration c is held constant at 3500 m, while a no flux boundary condition is applied at the bottom, thereby assuming no exchange of the tracer with the seafloor or insulation. The results depend both on the vertical diffusivity K and the mixing time scale t that can be combined into a spreading scale parameter λ = (Kt)1/2.

The model is applied to two different profiles from the inflow region for spreading scales λ = [50, 100, 150, 200, 300, and 400 m] (Fig. 12). Both along the western and the eastern channels, λ has to be greater than 300 m to explain the erosion of the salinity maximum at the exit from the passage solely by vertical mixing.

The mixing time scale t is set by the advective transit time of the flow through the passage. The horizontal distance along the passage is about 300 km. Average LADCP velocities at depth along the eastern channel over this distance give an advective transit time of 37 days. The salinity maximum is at the top of the largest vertical velocity shear (Fig. 4) and moves at only the speed of the dense water average, thereby increasing the residence time by a factor of 10. The volume of the Samoan Passage from section A to G below 4000-m depth is about 4.4 × 1013 m3. With an average volume transport of about 6 Sv, this implies an average residence time of about 90 days.

For advection time scales of 90 and 370 days, a value of λ = 300 m implies vertical diffusivities K of 5 × 10−2 and 3 × 10−3 m2 s−1, averaged at the level of the salinity maximum over the transit time through the passage. In the eastern channel, λ ≈ 150 m is needed to explain the erosion of the salinity maximum up to the first sill (purple profile). Assuming that about half the advection time is needed for the upstream water column to reach the first sill, this implies vertical diffusivities K between 5 × 10−3 and 1.55 × 10−3 m2 s−1 in the eastern channel before the first main sill at about 9°S. These diffusivities are consistent with the Thorpe scale mixing estimates, as described below.

b. Heat budgets

Knowing volume and heat transports of the abyssal flow at several locations through the passage, we can estimate the vertical exchange of heat across interfaces defined by constant temperature. This allows us to infer vertical turbulent heat fluxes by closing the heat budget of the system as previously done, for example, for abyssal flow in the equatorial and South Atlantic (Whitehead and Worthington 1982; Hogg et al. 1982) and the Samoan Passage (Roemmich et al. 1996). A volume-averaged budget can be calculated within a box defined by hydrographic sections to the north and south, shallower bathymetry to the east and west, the ocean floor at the bottom, and an upper-limiting isotherm. For a system in steady state, the difference between the lateral volume transports V into and out of the box gives the area-averaged upwelling velocity across the area of the upper interface AS due to the conservation of mass:

 
formula

As the potential temperature θS is given by the definition of AS as the isothermal surface, the advective upward heat flux through the interface is . Here, ρ and cp are the density and specific heat of the seawater. The divergence of all advective heat fluxes into and out of the box has to be balanced by turbulent heat fluxes QHF across AS. The region-averaged turbulent heat flux for a given isotherm is

 
formula

Here, is the velocity-weighted average potential temperature of inflow and outflow. Geothermal heat fluxes in this region of the South Pacific are small at O(0.1) W m−2 (Pollack et al. 1993) and thus omitted in the budget.

Locally, the turbulent heat fluxes can be expressed as the vertical temperature gradient ∂θ/∂z across the interface times a vertical diffusivity K:

 
formula

Note that K and ∂θ/∂z are likely to be at least partially correlated. Calculating an area-averaged vertical diffusivity from the area-averaged vertical temperature gradient is therefore misleading.

The heat budget calculation is shown in detail for the region between sections A and G in Fig. 13 before presenting results of a number of other regions defined by the section combinations [A–E&H], [A–F], [C–E&H], [C–F], and [C–G] in Fig. 14. We restrict our analysis to water colder than 0.8°C to exclude lateral input of mass and heat from east and west, as these potential temperature classes are at greater depths than the surrounding bathymetry. The area extent of the upper isothermal surface AS of each box is calculated from all isotherm depths at stations embraced by the respective sections. Isotherm depths are objectively mapped horizontally throughout the region, intersected with bathymetry, and the remaining area is integrated between the bounding southern and northern sections. Depending on isotherm and section combination, the surface area size ranges from 3 × 109 to more than 4 × 1010 m2 (Figs. 13a, 14b). Using the volume transport estimates for the inflow and outflow (Fig. 13b), we can estimate the area-averaged vertical advection velocity that is necessary to balance mass fluxes for a constant box volume (Figs. 13c, 14c). The term is highest in the coldest layers at rates above 4 × 10−4 m s−1. It approaches zero or negative values (entrainment) farther up in the water column. Larger vertical velocities for the section C combinations are because of the larger incoming volume transport than at section A. Scaling the volume transport uncertainty of ±1 Sv as approximately 20% (Fig. 13b) leads to uncertainties in of about ±2 × 10−4 m s−1 (Fig. 13c). The downward turbulent fluxes of heat needed to balance the divergence between incoming and outgoing advective heat fluxes (Fig. 13d) are above 20 W m−2 for all section combinations and reach up to about 60 W m−2 for the section C combinations (Figs. 13e, 14d). Turbulent heat flux uncertainties derived from volume transport errors are about 20% in the deeper layers and grow to 50% and more higher up in the water column (Fig. 13). The turbulent heat fluxes for combinations F and G are similar, while the E&H combinations show a somewhat different structure with lower values in the potential temperature classes below 0.75°C, the maximum at a slightly higher potential temperature, and elevated turbulent heat fluxes in the classes up to 0.8°C. This pattern indicates stronger turbulent mixing around the upper interface in the southern part of the passage than in the north and vice versa for the deepest layers—consistent with the Alford et al. (2013) results showing elevated mixing around the interface at the first sill of the eastern channel around 9°S and strong mixing in the deepest layers at the second main sill of the eastern channel at approximately 8°15′S.

Fig. 13.

Contributions to heat budget Eqs. (2) and (3) for the region spanning the whole Samoan Passage between sections A and G. (a) Surface area AS of isotherms θS. (b) Cumulative volume transport below isotherm θS at section A (Vin) and section G (Vout). (c) Upwelling velocity w* through interface θS. (d) Potential temperature transports at section A (Vinθin), section G (Voutθout), and through the upper interface (w*ASθS) and the residual . Temperature transports were referenced to 0°C. (e) Turbulent heat flux calculated from residual in (d). The sign convention in Eq. (3) is such that negative QHF are directed downward. Gray shadings show uncertainties in volume transport estimates (20%) and their impact on upwelling velocity and turbulent heat flux.

Fig. 13.

Contributions to heat budget Eqs. (2) and (3) for the region spanning the whole Samoan Passage between sections A and G. (a) Surface area AS of isotherms θS. (b) Cumulative volume transport below isotherm θS at section A (Vin) and section G (Vout). (c) Upwelling velocity w* through interface θS. (d) Potential temperature transports at section A (Vinθin), section G (Voutθout), and through the upper interface (w*ASθS) and the residual . Temperature transports were referenced to 0°C. (e) Turbulent heat flux calculated from residual in (d). The sign convention in Eq. (3) is such that negative QHF are directed downward. Gray shadings show uncertainties in volume transport estimates (20%) and their impact on upwelling velocity and turbulent heat flux.

Fig. 14.

Heat budget input parameters and results. (a) Color coding for different section combinations. Both sections A (red) and C (blue) in the south are combined with the three sections E&H, F, and G in the north, respectively, yielding six different combinations. (b) Surface area AS for combinations of different sections and isotherms. Each color corresponds to one combination of sections. (c) Area-averaged vertical velocities estimated from the divergence in horizontal volume transports. (d) Area-averaged vertical turbulent heat flux , balancing the divergence of the advective heat fluxes. Gray stars show heat budget estimates for the 0.7° and 0.75°C isotherms from Roemmich et al. (1996). Their estimate for the 0.8°C isotherm is not shown here since it was averaged over a much larger region downstream of the Samoan Passage and is therefore not comparable with our results.

Fig. 14.

Heat budget input parameters and results. (a) Color coding for different section combinations. Both sections A (red) and C (blue) in the south are combined with the three sections E&H, F, and G in the north, respectively, yielding six different combinations. (b) Surface area AS for combinations of different sections and isotherms. Each color corresponds to one combination of sections. (c) Area-averaged vertical velocities estimated from the divergence in horizontal volume transports. (d) Area-averaged vertical turbulent heat flux , balancing the divergence of the advective heat fluxes. Gray stars show heat budget estimates for the 0.7° and 0.75°C isotherms from Roemmich et al. (1996). Their estimate for the 0.8°C isotherm is not shown here since it was averaged over a much larger region downstream of the Samoan Passage and is therefore not comparable with our results.

The only previous heat budget estimate for turbulent mixing of the abyssal current in the Samoan Passage prior to our experiment was given by Roemmich et al. (1996). Using a geostrophic volume transport estimate at the southern entrance and historical hydrographic observations north of the passage (Mantyla and Reid 1983), their heat budget–derived estimate for downward turbulent heat fluxes was 20 W m−2 for the water volume bounded by θ = 0.7°C and 30 W m−2 for θ = 0.75°C. In contrast to our budget method with bounding sections to the north, all of their budget boxes were closed to the north by isotherms intersecting with bottom topography. Therefore, their surface area for the volume defined by θ = 0.8°C was 3 × 1012 m2, about two orders of magnitude larger than the surfaces within the passage in our study. This led to an average downward turbulent heat flux of 1 W m−2 for this class, about an order of magnitude smaller than ours. Despite the differences in the boundary conditions for the heat budget analysis between Roemmich et al. (1996) and our study, the results for θ = 0.7°C and θ = 0.75°C are similar (gray stars in Fig. 14).

On a larger scale, Macdonald et al. (2009) used hydrographic data from the World Ocean Circulation Experiment for an inverse box model of the Pacific Ocean. Average upwelling volume transports in their model are 1.1 and 2.4 Sv across isopycnals γn = 28.2 and 28.1 kg m−3, respectively, for a box spanning the whole Pacific Ocean zonally and reaching from 17°S to 10°N. In this study, we are concerned with fluxes in between these two isopycnal layers as no water as dense as γn = 28.2 kg m−3 was observed in the passage and γn = 28.1 kg m−3 corresponds to approximately 1.1°C in this region. We find diathermal volume transports of about 2 Sv as the volume transport through the passage is warming from the potential temperature class 0.65°C < θ < 0.7°C to 0.75°C < θ < 0.8°C. Thus, for potential temperature ranges below 0.8°C, the diathermal volume transport in the Samoan Passage is almost as large as the inverse box model estimate for the much larger region between 17°S to 10°N. This underlines the importance of the Samoan Passage for abyssal mixing in the equatorial Pacific.

A steady state of the flow through the Samoan Passage, both in terms of fluxes of mass and heat, has to apply for Eqs. (2) and (3) to be valid. This is obviously not the case for the Samoan Passage. We combine two different incoming volume transports with several outgoing transport values taken at different times. A rough estimate of the associated errors is obtained as follows: We know that the incoming volume transport may vary between 2 and 10 Sv over time scales longer than 30 days (R97) and found variation of the inflow to be between 3.9 (section A) and 6 Sv (section C) during the time of our survey. The time series of volume transport per unit width at mooring P1 (Fig. 11a) suggests that the inflow did not differ much more than this over the course of our cruise. We only have two volume transport estimates for the northern exit from sections F and G, amounting to 5.5 and 5.2 Sv, respectively. Thus, it is unclear whether the observed upstream variability is communicated through the whole passage or dampened within the passage to some extent. If all incoming variability was immediately advected through the passage, the difference between Vin and Vout in Eq. (2) would be constant, and hence w* would not change over time. Note that sampling the sections at different points in time could still result in an erroneous upwelling velocity in Eq. (2). If not directly advected through the passage, changes in the incoming volume transport could either be buffered in the passage, thereby inducing changes in the interface height, or induce a stronger upwelling velocity w* by modulating mixing processes. The change in interface height at mooring P5 (Fig. 11b) suggests that variations in the inflow are stored in the passage to some extent. Thus, excess incoming volume transport would not have to be compensated completely by increased levels of turbulent mixing. The diathermal mass transports inferred from the CTD/LADCP sections at different locations (Fig. 9), though taken at different times over the course of the cruise, give a consistent picture of the water mass transformation in the Samoan Passage. Mixing rates may be slightly different if inferred at different states of volume transport as discussed above, but we do not expect the general picture to change. Scaling the inflow volume transport variations of a factor of about 2 suggests that the budget-inferred average turbulent heat fluxes should not vary much more than this same factor.

c. Thorpe scale mixing estimates

We want to compare the heat budget–inferred mixing estimates to more direct measurements of turbulent mixing. To estimate average rates of turbulent mixing for the different heat budget regions, we use CTD density profiles to calculate Thorpe length scales LT from vertical overturns. Thorpe length scales LT have been found to be linearly related to the Ozmidov scale and hence can be used to estimate turbulent dissipation and diapycnal diffusivity (Thorpe 1977; Dillon 1982). See  appendix C for details of overturn detection techniques employed here and a comparison with direct turbulence measurements along the eastern channel. The comparison demonstrates that the Thorpe estimates, when averaged over a sufficient number of overturns, are within a factor of 2 of the direct measurements, as observed in many other locations (Dillon 1982; Moum 1996; Ferron et al. 1998; Alford et al. 2006).

High levels of turbulent dissipation ϵ are found within the abyssal northward flowing layer and around its interface. Profiles of ϵ inferred from LT as (Dillon 1982; Ferron et al. 1998) and averaged into bins of 200-m vertical extent are shown in Fig. 15 for all sections across the passage. Turbulent dissipation is most pronounced at hotspots at the several sills of the passage and downstream thereof, where high velocities were observed (Fig. 2). Here, the levels of ϵ in the deep layers below 1°C reach above 10−8 W kg−1, more than two orders of magnitude higher than oceanic background levels O(10−10) W kg−1. Higher up in the water column, ϵ approaches these background values.

Fig. 15.

Overturn-derived turbulent dissipation ϵ averaged into bins of 200-m vertical extent (color) and objectively mapped potential temperature (contours). White regions indicate the absence of overturns. The map shows vertically integrated ρ(z)ϵ(z) for θ < 1.0°C.

Fig. 15.

Overturn-derived turbulent dissipation ϵ averaged into bins of 200-m vertical extent (color) and objectively mapped potential temperature (contours). White regions indicate the absence of overturns. The map shows vertically integrated ρ(z)ϵ(z) for θ < 1.0°C.

For a comparison with the heat budget results, we average overturn-derived turbulence parameters over the same regions as used in the budget calculations. For each region, the stations of the bounding sections are included in this average to increase the number of data points. This means for the box [A–G] we average over all profiles of the survey. Thorpe length scales LT averaged this way, and into potential temperature classes, are shown in Fig. 16a. Average Thorpe length scales are above 20 m in the coldest layers and less than 10 m in the layers warmer than 0.8°C. Because of the low stratification in the deepest layers, the highest values of turbulent dissipation ϵ are not found at the same levels as the maximum Thorpe length scales, but in the potential temperature range around 0.8°C (Fig. 16b). For the whole layer below 1.0°C, average levels of turbulent dissipation are elevated by one to two orders of magnitude compared to oceanic background levels. Assuming a constant mixing efficiency of Γ = 0.2, diapycnal diffusivities Kρ can be computed from ϵ for each overturn as Kρ = ΓϵN−2 (Osborn 1980). Region averages of Kρ in potential temperature classes are shown in Fig. 16c. The diapycnal diffusivity Kρ is about 6 × 10−3 m2 s−1 in the layer below 0.8°C, more than two orders of magnitude higher than estimates of Kρ over the abyssal plains (Toole et al. 1994; Kunze and Sanford 1996).

Fig. 16.

Estimates of turbulent mixing from overturns averaged over heat budget regions and into potential temperature classes. Colors denote the averaging regions as defined in Fig. 14a for the heat budget calculations. Black curves show results for tow-yo data from the northern sill of the eastern channel, close to mooring P5. (a) Thorpe length scales LT calculated from vertical overturns. (b) Turbulent dissipation ϵ. (c) Diapycnal diffusivity Kρ. (d) Vertical overturn heat fluxes. Dashed lines repeat vertical heat fluxes inferred from heat budgets (Fig. 14d).

Fig. 16.

Estimates of turbulent mixing from overturns averaged over heat budget regions and into potential temperature classes. Colors denote the averaging regions as defined in Fig. 14a for the heat budget calculations. Black curves show results for tow-yo data from the northern sill of the eastern channel, close to mooring P5. (a) Thorpe length scales LT calculated from vertical overturns. (b) Turbulent dissipation ϵ. (c) Diapycnal diffusivity Kρ. (d) Vertical overturn heat fluxes. Dashed lines repeat vertical heat fluxes inferred from heat budgets (Fig. 14d).

Based on the local temperature gradient around the overturn, we calculate overturn-driven turbulent heat fluxes as QHF = −Kρθ/∂z. Region-averaged downward QHF are shown in Fig. 16d. Averaged QHF are below 1 W m−2 in the coldest layer below 0.7°C, where temperature gradients are weak. Between 0.7° and 0.9°C overturn-driven downward heat fluxes are in the range of 5 to 10 W m−2 before approaching background values below 0.5 W m−2 at higher potential temperatures.

Overall, Thorpe scale–inferred estimates for turbulent heat fluxes are about 5 times too small to explain the vertical mixing needed to close the heat budget in the Samoan Passage (see turbulent heat fluxes inferred from budget calculations repeated in Fig. 16c). While heat budgets are an integral over all mixing processes within a defined region, the overturn-derived mixing estimates only include a limited number of measurement locations. Thus, undersampled mixing hotspots could lead to a mismatch. For example, Alford et al. (2013) show that Kρ reaches as high as 10−1 m2 s−1 in the region of highest current velocities downstream of the northern sill of the eastern channel, a region likely to be underrepresented in the area averages here. CTD/LADCP sections were tailored to capture the flow pattern across the several sills of the eastern and western channels. While levels of turbulence at the sills are indeed elevated over the more sluggish flow at the entrance to the passage, the largest values are likely to be found downstream from the sills, as, for example, between sections E and F at the northern end of the eastern channel (see depth-integrated ϵ on the map in Fig. 15).

The highly resolved measurements downstream from this particular sill let us explore one such mixing hotspot in further detail. Here, we conducted two tow-yo sections by cycling the CTD/LADCP package repeatedly between 4200-m depth and 40 m above the bottom while steaming at approximately 0.25 m s−1. See tow-yo section locations on Fig. 1 and section plots of one of the tow-yos in Alford et al. (2013). There were 138 hydrographic profiles in total with a horizontal spacing of only about 250 m recorded during these tow-yos. Overturn-derived turbulence parameters LT, ϵ, Kρ, and QHF calculated from the tow-yo profiles and averaged into potential temperature classes are shown in black in Figs. 16a–d. Larger LT at higher stratification N2 lead to values of turbulent dissipation and diapycnal diffusivity that are about an order of magnitude higher than the area averages over the larger regions. For the potential temperature range 0.7° to 0.9°C, downward turbulent heat fluxes are about 60 W m−2 and thereby higher than the turbulent heat fluxes required to close any of the budgets of the larger regions. This suggests that unsampled mixing hotspots in the LADCP records account for the imbalance between measured and budget heat fluxes.

6. Conclusions

We observed the abyssal flow through the Samoan Passage in July and August 2012. During this period, volume transports were between 3.9 and 6 Sv with an uncertainty of ±1 Sv because of both measurement errors and aliasing by internal waves. About one-half of the volume transport, consistently observed at several sections, makes its way through the shallower western channels. This flow through the western channels was hitherto unexplored, except for a few measurements carried out by Reid and Lonsdale (1974), leading them to assume a pathway for abyssal water in the west in addition to the main channel in the east.

The volume transport shifts considerably into warmer temperature classes as the abyssal flow traverses the Samoan Passage. We use the volume transport estimates, and hydrographic observations, to estimate diathermal mixing of the deep PMOC branch in this region from heat budgets. Downward turbulent heat fluxes between 20 and 60 W m−2 are needed to explain the warming of the abyssal flow along the passage.

The heat budget result provides a constraint for direct observations of turbulent mixing. The sum over all turbulent processes in the passage should match this budget. Studies following this concept usually fail to match the budget results with direct turbulence measurements [with a notable exception being the study of Ferron et al. (1998) in the Romanche Fracture Zone]. When averaging over larger regions in the Samoan Passage, this study also has the difficulty of “missing mixing.” Overturn-derived, region-averaged turbulence, although 100 times larger than oceanic background levels, is not sufficient to explain the turbulent mixing inferred from the heat budgets. However, Alford et al. (2013) showed that mixing in the Samoan Passage is highly localized and influenced by bathymetry. Indeed, a mixing hotspot that was measured at high spatial resolution has levels of turbulent mixing that are an order of magnitude higher than these region averages.

The bathymetry of the Samoan Passage with many sills, channels, and bumps, and our measurements at a few of these sills, suggest that more mixing hotspots are distributed throughout the passage. In the sum, these likely provide the bulk of the turbulent mixing needed to explain the heat budget. Contrasting the region-averaged overturn-derived heat fluxes of 10 W m−2 with the 20 to 60 W m−2 needed to close the budget suggests that between 50% and 80% of the overall mixing in the Samoan Passage takes place at mixing hotspots.

This underscores the potential significance of our discovery that about half the volume transport of the abyssal flow goes through the western channels because their bathymetry differs from the eastern channel. Given the importance of local bathymetry for turbulent mixing, the physical processes governing mixing along the different pathways may not be the same. Thus, it will be important to study the flow across several of these sills and its interaction with bathymetry in attempts to generalize and parameterize turbulent mixing in the Samoan Passage.

Acknowledgments

The authors thank Eric Boget for his exemplary assistance in designing, deploying, and recovering the moorings; Keith Magness, Janna Köhler, Andrew Cookson, Zoë Parsons, Andy Pickering, Kelly Pearson, Tessa Tafua, and Deepika Goundar for their assistance in making the measurements; and the captain and crew of the R/V Revelle for their skill in handling and operating the vessel, without which these measurements would not have been possible. Daniel Rudnick kindly provided previous mooring data. Comments from two anonymous reviewers are greatly appreciated. This work was funded by the National Science Foundation under Grants OCE-1029268 and OCE-1029483.

APPENDIX A

LADCP Uncertainty

Although LADCPs are widely used these days for velocity measurements, there are still only a few studies quantifying their uncertainty. Without adding any constraints to the solution of the final full-depth profile, the uncertainty for velocity profiles obtained with the shear solution (Firing and Gordon 1990; Fischer and Visbeck 1993) is estimated to be between 3 and 5 cm s−1 (Hacker et al. 1996). However, there is no canonical way of estimating the uncertainty of full-depth LADCP velocity profiles calculated from a number of single pings. Formal velocity uncertainties are estimated by the LDEO software for the inversion method, based on the model parameter covariance matrix and the standard deviation of the measurements at each depth level. The error estimate is empirically scaled by the standard deviation between the inverse solution and the shear solution if this standard deviation is larger than the initial error estimate (Thurnherr 2010).

Comparing LADCP velocity profiles with nearby mooring records, Thurnherr (2010) showed that root-mean-square velocity errors are generally <3 cm s−1 as long as LADCP ranges are above a critical value of about 60 m and all additional data sources [GPS, Shipboard ADCP (SADCP), and bottom tracking] are used to constrain the solution. In our case, ranges of the LADCPs at depth were generally about 100 m.

In a few cases in this study, LADCP profiles were measured close enough to one of the moorings to allow for a comparison; however, because of safety concerns, none of the profiles were measured closer than 2 km to any mooring. Two LADCP profiles are worth a closer look because of their close proximity to moorings. In one case, an LADCP profile was measured only a few hours before the deployment of mooring P3 at the exact mooring location. Here, for the overlapping portion of the profiles, the LADCP and MP acoustic current meter (MP-ACM) velocity structures are similar (Fig. A1). The LADCP profile is at the upper-amplitude envelope of all the MP-ACM profiles, but does not exceed it. The MP-ACM profile closest in time to the LADCP profile also shows bottom velocity larger than the time average. In a second case, an LADCP profile was measured just 2.1 km away from mooring P1 (Fig. A2). The LADCP velocity is again within the envelope of all MP-ACM observations. The MP-ACM profile close in time agrees well with the LADCP profile. Differences are generally below 0.03 m s−1 and may be explained by temporal and lateral variability in addition to any uncertainty in the measurement. In some cases not shown here, and at greater distances, velocity profiles are within 2 cm s−1 of the respective ACM profile from the moored profiler, while others show LADCP velocity profiles that differ considerably from the mooring measurement. This may be explained by bottom currents in this region varying significantly over distances of only a few kilometers (Alford et al. 2013).

Fig. A1.

Velocities at mooring P3 and nearby LADCP velocity profile. Colors show velocity distributions in 0.01 m s−1 bins at several depths. Thick black lines show the LADCP velocity profile; thin gray lines show the mooring velocity profile closest in time to the LADCP measurement.

Fig. A1.

Velocities at mooring P3 and nearby LADCP velocity profile. Colors show velocity distributions in 0.01 m s−1 bins at several depths. Thick black lines show the LADCP velocity profile; thin gray lines show the mooring velocity profile closest in time to the LADCP measurement.

Fig. A2.

Velocities at mooring P3 and nearby LADCP velocity profile. As in Fig. A1.

Fig. A2.

Velocities at mooring P3 and nearby LADCP velocity profile. As in Fig. A1.

The good agreement in the two cases shown above, the matching of criteria for low uncertainty given by Thurnherr (2010), and the fact that we are interested in the bottom layer that is well constrained in the inverse solution by the bottom-tracking velocity leads us to assume that the uncertainty in LADCP velocity measurements of the bottom layer is generally below ±2 cm s−1.

APPENDIX B

Objective Mapping

Properties are objectively mapped at several points in this study for plotting, volume transport calculations, and surface area estimation in the heat budget calculations. Contrary to its name, objective mapping is based on a subjective choice of correlation and scale parameters. Observations and the physics governing the flow can help with finding suitable parameters such that the objective mapping is superior to simple two-dimensional linear interpolation of observed property fields.

The objective mapping of a vertical section closely follows Roemmich (1983). First, a large-scale field is fitted in a least squares sense to the data. The fitting is based on a Gaussian function that models the expected products between estimated field and measured values based on spatial decorrelation scales and the allowed deviation between observation and fit. Decorrelation scales of 300 km in the horizontal and 150 m in the vertical were chosen for the large-scale field. The large-scale field is subtracted from the observations and the residuals are fitted again, this time with an exponential function that decays faster than the Gaussian function. The decorrelation scales for the small-scale field were chosen to be 50 km in the horizontal and 25 m in the vertical. The objectively mapped field is finally the sum of modeled large and small-scale fields. For all vertical sections, the same decorrelation scales for large- and small-scale field estimates were used.

The mapping of horizontal fields is also based on a least squares fit to the observations and follows Davis (1985). Based on horizontal decorrelation scales, an assumed Gaussian covariance with 50-km length scale was used to model the observations.

APPENDIX C

Thorpe Scales

The Ozmidov scale,

 
formula

provides a measure of the size of the largest eddies that may overturn in stably stratified water (Ozmidov 1965) and thereby approximates the vertical distance over which water with higher density is carried vertically over lighter water by turbulent motion. The Ozmidov length scale has been found to be linearly related to the empirical overturning, or Thorpe, scale LT (Thorpe 1977). The Thorpe length scale is usually calculated as the root-mean-square of the vertical displacements d needed to sort an unstable density profile into a stable state:

 
formula

The linear relation between LO and LT leads to

 
formula

with the constant c1 found empirically to be 0.64 by Dillon (1982), 0.91 by Peters et al. (1988), and 0.90 by Ferron et al. (1998). This relation holds in an ensemble sense when averaged over profiles that are statistically similar on vertical scales exceeding LT. In the past, comparisons between ϵ directly determined from microstructure measurements and ϵ estimated from hydrographic (CTD) measurements have shown these estimates to be consistent within a factor of about 5 (Dillon 1982; Wesson and Gregg 1994; Moum 1996; Ferron et al. 1998; Alford et al. 2006).

To exclude spurious overturns that may be because of the noise in the measurements, a method developed by Ferron et al. (1998) is employed. Before sorting the density profile into its stable state, an intermediate profile is constructed that takes the noise in the measurements into account by discretizing the measurements at the accuracy level of the density profile (1 × 10−3 kg m−3). To calculate ϵ from LT, the proportionality constant c1 in Eq. (C3) is set to 0.9 following Ferron et al. (1998), as the deep sea environment where their experiment was carried out most closely resembles our region.

Average values of turbulent dissipation ϵ derived from overturns in 15 density profiles along the eastern channels are within about a factor of 2 of directly measured dissipation rates (Fig. C1). For the averaging, ϵ was set to 6 × 10−11 W kg−1 at depths where no overturn was detected as this led to the best agreement with the direct observations. Averaged values of directly observed ϵ from an autonomous vertical microstructure profiler (VMP), recorded in proximity to the CTD casts, are shown for comparison [see Alford et al. (2013) for plots of VMP-measured ϵ profiles].

Fig. C1.

Turbulent dissipation ϵ along the eastern channel derived from microstructure shear (VMP; Alford et al. 2013) and from CTD Thorpe scale using the overturn detection method developed by Ferron et al. (1998). Average values in potential temperature bins are shown with vertical lines. Boxes show the statistical uncertainty of the mean as the 0.03 to 0.97 percentile of a bootstrap distribution calculated from 100 randomly chosen subsets consisting of 50% of all the data in each bin.

Fig. C1.

Turbulent dissipation ϵ along the eastern channel derived from microstructure shear (VMP; Alford et al. 2013) and from CTD Thorpe scale using the overturn detection method developed by Ferron et al. (1998). Average values in potential temperature bins are shown with vertical lines. Boxes show the statistical uncertainty of the mean as the 0.03 to 0.97 percentile of a bootstrap distribution calculated from 100 randomly chosen subsets consisting of 50% of all the data in each bin.

We also calculated overturn-derived turbulent dissipation from temperature instead of density profiles. The comparison with the VMP data shows that this overestimates turbulent dissipation. Deviations are especially high around the upper interface of the abyssal layer where NADW disturbs a linear relationship between temperature and density. Therefore, we used the density-based estimates.

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Footnotes

*

Current affiliation: Scripps Institution of Oceanography, La Jolla, California.

1

The actual correlation between transport per unit width at R3 and the total volume transport at the R97 array is about 0.7.