Journal of Oceanology and Limnology   2019, Vol. 37 issue(2): 498-512     PDF
Institute of Oceanology, Chinese Academy of Sciences

Article Information

HUANG Chao, XU Yongsheng
Spatial and seasonal variability of global ocean diapycnal transport inferred from Argo profiles
Journal of Oceanology and Limnology, 37(2): 498-512

Article History

Received Oct. 20, 2017
accepted in principle Jan. 4, 2018
accepted for publication Apr. 24, 2018
Spatial and seasonal variability of global ocean diapycnal transport inferred from Argo profiles
HUANG Chao1,2,3,4, XU Yongsheng1,2,4     
1 Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China;
2 Function Laboratory for Ocean Dynamics and Climate, Qingdao National Laboratory for Marine Science and Technology, Qingdao 266000, China;
3 University of Chinese Academy of Sciences, Beijing 100049, China;
4 Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao 266071, China
Abstract: The global diapycnal transport in the ocean interior is one of the significant branches to return the deep water back toward near-surface. However, the amount of the diapycnal transport and the seasonal variations are not determined yet. This paper estimates the dissipation rate and the associated diapycnal transports at 500 m, 750 m and 1 000 m depth throughout the global ocean from the wide-spread Argo profiles, using the finescale parameterizations and classic advection-diffusion balance. The net upwelling is~5.2±0.81 Sv (Sverdrup) which is approximately one fifth in magnitude of the formation of the deep water. The Southern Ocean is the major region with the upward diapycnal transport, while the downwelling emerges mainly in the northern North Atlantic. The upwelling in the Southern Ocean accounts for over 50% of the amount of the global summation. The seasonal cycle is obvious at 500 m and vanishes with depth, indicating the energy source at surface. The enhancement of diapycnal transport occurs at 1 000 m in the Southern Ocean, which is pertinent with the internal wave generation due to the interaction between the robust deep-reaching flows and the rough topography. Our estimates of the diapycnal transport in the ocean interior have implications for the closure of the oceanic energy budget and the understanding of global Meridional Overturning Circulation.
Keywords: dissipation rate    diapycnal transport    upwelling    meridional overturning circulation    

The global meridional overturning circulation (MOC) transports substantial amount of heat, carbon, oxygen and nutrients to form a dynamic equilibrium and modulates the global climate (Wunsch, 2002; Talley, 2003; Wunsch and Ferrari, 2004; Marshall and Speer, 2012). The classical view suggests the balance between the vertical advection and downward turbulent diffusion of buoyancy as a key factor to maintain the steady state circulation (Munk, 1966; Munk and Wunsch, 1998). However, it is still a challenge to determine the processes and pathways by which the deep, dense water returns to the upper ocean (Munk and Wunsch, 1998; Toggweiler and Samuels, 1998). The diapycnal upwelling, which is controlled by the turbulent mixing, is an effective way to draw water masses from the deep sea (Zhang et al., 1999; Wunsch and Ferrari, 2004; Jayne, 2009; Morrison et al., 2015) to the depth where the water can resurface forced by winds. Because the upwelled water from the deep ocean is cold and centuries old, its exposure to the air exerts the modulation of the atmospheric heat storage and the global carbon cycle (Caldeira and Duffy, 2000; Sabine et al., 2004; Khatiwala et al., 2013; Frölicher et al., 2015; Morrison et al., 2015). The diapycnal and isopycnal transports are two key ways to return the deep water, forming the thermohaline circulation. Once the water from deep sea reaches the sloping density layers in the Southern Ocean, it will cost little energy supplying to transport back to the surface through along-isopycnal upwelling (Toggweiler and Samuels, 1998; Wolfe and Cessi, 2011). Although many regional studies (Watson et al., 2013; Morrison et al., 2015) have reported the strength of upwelling according to the general structure of MOC given by model studies, the spatial and temporal patterns of the upwelling in the ocean interior is still a main theme of oceanography. Small scale turbulent mixing is also a significant energy pathway, as well as bottom drag (Huang and Xu, 2018), lee-wave generation (Nikurashin and Ferrari, 2011) and so on, in the global oceanic energy balance (Jayne, 2009; Ledwell et al., 2011; Wu et al., 2011), which dissipates the kinetic energy stored in the small scale flows, altering both the micro- and fine-scale density gradients and the large scale oceanic circulation. We focus on the turbulent mixing and the accompanying diapycnal upwelling at mid depth, tending to assess the spatial distribution and the temporal variation of upwelling.

Typical measurements of mixing include tracer method (Ledwell et al., 2011; Watson et al., 2013) and microstructure observation (Gregg et al., 2003; St Laurent, 2008). Both the tracking of dye tracers and the small fluctuations in temperature, conductivity, and shear require plenty of fieldwork and considerable expense. Hence, the nature of mixing, which is intermittent, makes these observations difficult to capture the near global distribution of the dissipation rate in a long temporal scope. Since many field experiments (Gregg, 1989; Polzin et al., 1995) reveal that the internal wave energy maintains the strength of mixing satisfying the wave-wave interaction theory. Finescale parameterizations offer an inexpensive access to measure the vertical diffusivity by reproducing the observed average microstructure estimates (Polzin et al., 1997; Kunze et al., 2006, Wu et al., 2011; Li and Xu, 2014). It relies on the promise that turbulent mixing at scales of a centimetre or less can be related to the more easily measured intensity of internal waves (Klymak et al., 2006; Whalen et al., 2012). Internal wave intensity is quantified in terms of vertical gradients of the density or the horizontal velocity on a scale of tens to hundreds of meters. At mid depth, the diffusivities derived from finescale methods have been found to agree with that from microstructure measurements (Wijesekera et al., 1993) and ship-based observations (Naveira Garabato et al., 2004). There are two accesses to the diapycnal diffusivity in finescale parameterizations. Vertical shear has been used in shear observation from velocity data (Kunze et al., 2006) that is also sparse in open oceans. Strain from density profiles is another expression of finescale method. We apply this strain method to widely spread temperature/salinity observations to assess the mixing rate in a global scope.

The International Argo Program has created the first global array for observing the subsurface ocean, which provides the temperature and salinity profiles over 20 years. We followed the idea given by Whalen et al. (2012) and made improvements by using more Argo data. Therefore, the gaps in maps of dissipation rate are largely filled in our estimates. Meanwhile, with the improvement in the temporal and spatial coverage, we can study the seasonal variation in a larger geography scope than that described in Whalen et al. (2012). Here, we estimate the dissipation rate using the finescale strain derived from Argo profiles. Subsequently, we calculate the upwelling based on the one-dimensional advection-diffusion balance (Munk, 1966). We present the maps of dissipation rate and diapycnal transport averaged over 10 years, and analyse the seasonal variations. The uncertainty mainly comes from two aspects: 1) the underlying assumptions of finescale parameterizations imply that internal wave is the sole reason to induce the observed strain and breaks through nonlinear wave-wave interaction, which cannot be satisfied everywhere (Kunze et al., 2006; Whalen et al., 2012), for example, intrusions, solitons, and double diffusion; 2) the methodological error in data processing, since the initial Argo profiles have different vertical resolution and accuracy (Wu et al., 2011). We introduce the data we use and the finescale method in Section 2. In Section 3, we present the global maps of dissipation rate and upwelling, including the zonal average in the Atlantic and the seasonal variations. The findings and the underlying mechanisms are discussed in Section 4.

2 DATA AND METHOD 2.1 Argo profiles

The Argo observation network is an international array to monitor the upper 2 000 m of the global ocean. It contains about 3 800 profiling floats drifting freely which record the temperature and salinity continuously. The recent ten-year Argo temperature and salinity profiles over the global ocean, from 2007 to 2016 (, which are more reliable than early data and long enough to present the averaged values of the turbulent mixing and the diapycnal transport, were employed in this paper. We screened the profiles basing on the following criteria before substituting into the finescale parameterizations. 1) The record depth of profiles should be larger than 600 m in order to guarantee the sufficient records in calculation of parameterizations; 2) the number of valid records in each profile was set to exceed 80% of the total records; 3) the vertical resolution of profiles was restricted to shorter than 20 m. This was a reliable threshold value for both the finescale observation and the accuracy in interpolation; 4) the records may contain multiple values at the same depth in a profile after Argo technical processing of the initial data. We checked "quality-flag" and used the first measurement for differencing with the deeper data and the last measurement for differencing with the shallower data as the representation of these positions. There were more than 500 000 profiles satisfying the above criteria. These profiles, wide-distributed spatially throughout the global ocean and temporally in different seasons, were used to study the patterns and the seasonal variation. The maps of number of Argo profiles in 1° grid at different depths are given by Fig. 1. Figure 2 shows a typical temperature and salinity profiles (black dots) from Argo record (49.6°S, 32.3°W).

Fig.1 Maps of number of Argo profiles used in the calculation of dissipation rate in 1° grid at 500 m (a), 750 m (b), and 1 000 m (c) depths Colour bar indicates the range of numbers in grids.
Fig.2 An example of Argo data processing Profiles of temperature (a) and salinity (b) at 49.6°S, 32.3°W.The black dots are the initial Argo records, while the red lines are the fitting result after spline interpolation with 2-m vertical sampling step.The blue, yellow, and green lines represent data in 200-m segments with 50% overlaps.
2.2 Finescale parameterizations

Based on the nonlinear wave-wave interaction, internal wave breaking drives energy cascade to smaller scale and induces the turbulent mixing (Kunze et al., 2006; Waterman et al., 2013). Finescale parameterizations take the shear or strain as the strength of the internal wave field which is a proxy of the turbulent mixing (Kunze et al., 2006; Thompson et al., 2007; Wu et al., 2011). Since the Argo records have different vertical resolutions, a standardized processing was applied. The temperature and salinity in the ocean interior change a little in magnitude along the vertical direction (small vertical gradient). Meanwhile, the density derived from temperature and salinity is usually monotonic in a relative larger range of depth, O(100 m), than the interval of interpolation, O(1 m). In this circumstance, we used the spline interpolation method (De Boor, 1962), which yields negligible spurious peaks, to create profiles of potential density with 2 m vertical sampling step. In this paper, we focused on the diapycnal transport at 500 m, 750 m, and 1 000 m levels. For each reference level, we took three 200-m segments with 50% overlap into account. We present an example to show the processes mentioned above. The red lines in Fig. 2 are fitting results of Argo record basing on the spline interpolation. The blue, yellow, and green lines highlight temperature/salinity results of 300–500 m, 400–600 m, and 500–700 m (we added small shifts to make the segments clear). Then, the estimates of these segments are averaged to represent the final result at 500 m reference level. Build on Gregg (1989), Polzin et al. (1995) reported the finescale parameterizations of turbulent dissipation. The strain method (Eq.1) was presented by Gregg et al. (2003) and Kunze et al. (2006),


where κ is the diffusivity, K0=0.05×10-4 m2/s, <ξz2> is strain variance, GM <ξz2> is strain variance derived from the Garrett-Munk model (GM model; Munk, 1981; Gregg and Kunze, 1991), h2(Rw) and j(f, N) represent the correction terms.

We calculated the strain (ξz) in each segment from the buoyancy frequency (N2) as following,


where with g=9.8 m/s and σ is the potential density, NF2 is the quadratic fitting results of N2 in segments, and represents the mean value of N2. Then, using the Fourier transformation, we calculated the strain spectra ψ(k), where k is the vertical wavenumber. A 10%∙sin2 window (Whalen et al., 2012) transform was used for segments. The spectra ψ(k) is shown in form of the real and imaginary parts (Zr and Zi) from the Fourier transformation with a corrective coefficient (Kunze et al., 2006),


where sinc(x)=sin(πx)/(πx) is the corrective coefficient, Δz is the sampling internal, and λ is the wavelength corresponding to the wavenumber k. The strain variance <ξz2> is derived from the integral of ψ(k),


where kmax and kmin are the upper and lower limits of the integration interval. The range of the vertical wavelength was restricted between 40 m and 150 m (Li and Xu, 2014). Because the estimate of the strain variance could be smaller than the real value of that when the spectral is saturated, the Eq.4 should satisfy the condition, <ξz2>≤0.2, to avoid this saturation effect (Gargett, 1990). The similar integration interval was applied to the calculation of strain variance from the GM model, GM<ξz2> (Eq.5),


where E0=6.3×10-5 represents a dimensionless constant, b represents the vertical scale of the thermocline, j* is the reference mode, and k* is the reference wavenumber in accordance with j*. In this study, we selected b=1 300 m and j*=3. Following Gregg and Kunze (1991), the reference wavenumber for GM spectre is given by with N0=5.24×10-3 rad/s.

Considering the frequency content of the internal wave field (Eq.6) and the latitude dependence on the interval wave field (Eq.7), we calculated the diffusivity by substituting the ratio of the strain variances into Eq.1 with correction terms,


where Rw is the shear/strain ratio, f is the Coriolis frequency, and f30 represents the Coriolis frequency at 30°. The shear/strain ratio is defined in form of the ratio of shear variance <Vz2> and strain variance <ξz2>, , which is a proxy of aspect ratio and frequency content of the internal wave field (Kunze et al., 1990, 2006; Henyey, 1991; Polzin et al., 1995). Due to the poor sampling of velocity profiles in the global ocean, it is difficult to determine precise Rw everywhere. We used constant values of Rw for different regions in our calculations, Rw=10 for the Southern Ocean (south of 40°S; Naveira Garabato et al., 2004; Kunze et al., 2006), Rw=7 for the northern parts of oceans in the north hemisphere (north of 30°S; Kunze et al., 2006), and Rw=3 for the rest of area as the value of the GM shear/strain variance ratio GMRw=3 (Munk, 1981).

2.3 Dissipation rate and diapycnal transport

On the basis of the model study made by Osborn (1980), the dissipation rate ε is computed from Eq.8,


In addition to the diffusivity, the strength of dissipation is related to the stratification (N2) and the efficiency of mixing (γ). Based on the experiments and the numerical simulation (Peltier and Caulfield, 2003), we selected a constant γ=0.2 to describe the energy conversion efficiency of the diapycnal mixing (Kunze et al., 2006; Wu et al., 2011; Whalen et al., 2012). Note that the amount of γ could vary with the background stratification in the real ocean, it may introduce the inaccuracy in estimates.

Finally, the upwelling rate was derived from the classical one-dimensional advection-diffusion balance developed by Munk (1966), which have shown the promising applicability in the vertical distribution of matter and energy (Haugan and Alendal, 2005; Huber et al., 2015). The following equation indicates the upwelling speed (w, in unit of m/s) is the function of the diffusivity (κ) and the potential density (σ),


Substituting σ with N2, we obtained the upwelling rate in form of the stratification,


where g=9.8 m2/s. According to Munk and Wunsch (1998), Eqs.9 and 10 hold only when the diffusivity (κ) is constant with depth. Whalen et al. (2012) used Argo data to show the diffusivity may vary by 10-5 in 100 m vertical range, which may give dκ/dz=10-7 m/s and 10-3 Sv in the diapycnal transport. However, as for the depth from 400 m to 900 m, the diffusivity rate remains the same amount in magnitude (Fig.S5 in Whalen et al., 2012). Meanwhile, Li and Xu (2014) found the diffusivity barely changes at the range from 900 to 1 800 m in the Northwestern Pacific from the CTD profiles. Also, both papers presented the diffusivity rate as the average over a segment of 200 m. In this paper, we calculate the diffusivity rate from finescale parameterizations as the estimates at particular reference depths (500 m, 750 m and 1 000 m). Since it is difficult to get the diffusivity profiles with high vertical resolution, we use the constant diffusivity and the density gradient within 40 m in the advection-diffusion balance. The model results are credible if the diffusivity changes a little in vertical direction, while the estimate at 1 000 m depth may contain inaccuracy due to this assumption. The estimate of the volume of upwelling water masses is derived from the multiplying this upwelling rate and the horizontal area. All of the global maps are presented in one-degree grid in this paper.

3 RESULT 3.1 Dissipation rate

The maps of dissipation rate are shown in Fig. 3, which are centred at the depth of 500 m, 750 m, and 1 000 m, respectively. Compared to the averaged dissipation rate reported by Whalen et al. (2012), we present maps of dissipation rate with a significant improvement in the spatial coverage due to the increased number of Argo data. The estimate of the averaged dissipation rate is derived from three segments described in Section 2. High dissipation rates, which are approximate O(10-3) larger than that in the open-ocean, can be seen in the Southern Ocean, in the mid- to high-latitude northern Atlantic, and in regions with the vigorous western boundary currents and their extensions in maps for all three depths. 1) In the Southern Ocean, the strong large-scale wind stress and the lack of block by landmass lead to 80% wind power input into the oceanic geostrophic currents (Furuichi et al., 2008; Scott and Xu, 2009), making the Antarctic Circumpolar Current (ACC) the strongest ocean current (Donohue et al., 2016). Meanwhile, the robust deep reaching flows interact with seafloor topography to stimulate the internal wave transmitting upward and breaking ultimately, which infers a potential significant energy source to sustain the enhanced mixing in ocean interior. Although it is worth noting that the depth scale of leewave generation is usually ~2 000 m (Nikurashin and Ferrari, 2011; Kunze, 2017), the effect of such internal waves may propagate vertically to a shallower depth, especially in the Southern Ocean. Also, Li and Xu (2014) found an evident correlation between the turbulent mixing and seafloor roughness at 3 300 m above the seabed. The high dissipation rate and the associated diapycnal mixing are most likely an outcome caused by both wind power input and bottom-source energy. Further, the full-depth microscale observations are needed to investigate the vertical scale of the radiating internal waves, with the help of vertical section of dissipation rate starting from the bottom; 2) the air-sea heat fluxes in the North Atlantic Drift (NAD) area drive the formation of deep water (LeBel et al., 2008) and then the thermohaline circulation. The strong dissipative processes there implies the potential vertical water transport, which is consistent with the observational and numerical experiments (Ostrovskii and Font, 2003; Dietrich et al., 2004; Whalen et al., 2012); 3) due to the stirring generated by the massive mesoscale and submesoscale eddies in the western parts of Pacific and Atlantic basins between 20° to 40° north latitude, the dissipative efficiency is underpinned by the movement and evolution of eddies.

Fig.3 Maps of dissipation rate ε (W/kg) calculated from Argo profiles over ten years (2007–2016) Estimates centred at 500 m (a), 750 m (b), and 1 000 m (c) are presented in logarithmic form in 1° grid.

The maps of dissipation rate at 500 m and 750 m indicate the similar pattern throughout the global ocean (Fig. 3a, b). However, compared with the distribution for 1 000 m depth, the values at 500 m increase holistically (Fig. 3a). This is because there is sufficient energy supplement for water masses near surface from wind power input, though the penetration depth of diapycnal mixing generated by wind stress may extent to 1 800 m (Li and Xu, 2014). The extreme high dissipation rates at 500 m emerge in the ACC and NAD areas. Regardless of the sparseness of Argo profiles at 1 000 m depth (Fig. 3c), the dissipation rates are lower than that at the shallow depths, especially at high latitude in both hemispheres. However, Fig. 3c shows a patch of high dissipation rate, larger than 10-6 W/kg, in the east of the Philippines, which is not shown in other maps. Although, despite of the sparseness in spatial sampling, the estimate of averaged dissipation rates over 500–1 000 m and 1 000–2 000 m given by Whalen et al. (2012) did not indicate such signal in the same area, their estimates of diffusivity showed a significant enhancement within the deep ocean. The Argo profiles are sufficient (Fig. 1c) here and we find that the mean value of N2 is one order higher than that in the open ocean. Also, the output of the numerical simulation of internal tides (Simmons et al., 2004) cannot give evidence to support this spurious high dissipation rate. Therefore, we infer this high dissipation rate may connect with the energy from the bottom. First, the seafloor is rough according to the roughness derived from both spectral characteristics (Nikurashin and Ferrari, 2011) and variance in elevation (Whalen et al., 2012). Second, the barotropic component of the surface geostrophic current is relative strong in this area (Huang and Xu, 2018), which could yield robust deep flow with massive kinetic energy. Third, Li and Xu (2014) showed the rough topography influences the turbulent mixing in the ocean interior up to 3 300 m above the seafloor, with CTD measurements in the Northwestern Pacific. Considering the spatial and temporal coverage, we believe both the 500 m and 750 m can be taken as the interface to calculate the vertical movement of the water masses. The upwelling and downwelling are proxies of the diapycnal transport between the deep ocean and subsurface.

3.2 Diapycnal transport

The upwelling speed derived from Eq.10 is in unit of m/s. Since the maps in this paper are presented in 1-degree grid basing on the Mercator Projection, the areas of grids vary with latitude. Here, we focus on the diapycnal transport (m3/s), which is vertical velocity multiplied by area, showing the amount of the upwelling and downwelling throughout the global ocean. Figure 4 shows the distribution of the upwelling and downwelling at different depths, corresponding to the dissipation rate given by Fig. 3. Generally, the high dissipation rates cause the relative large amount of the vertical transport, for example, in the northern North Atlantic and in the Southern Ocean. There is no significant diapycnal transport in the Kuroshio Extension (KE) in the map of 750 m depth (Fig. 4b) due to the effect of the gradient of buoyancy frequency (Eq.10). Although, there is downwelling over 10-3 Sv (1 Sv=1 Sverdrup =1×10-6 m3/s) in KE at 500 m depth (Fig. 4a), the regional integral accounts for a small portion in the global sum because of the limitation of the spatial extent. The robust diapycnal transport at 1 000 m depth in the western Pacific (Fig. 4c) is pertinent to the enhanced dissipation rate in Fig. 3c, with opposite directions caused by the vertical structure of stratification. Typically, the primary zone where the surface water sinks to the ocean interior is in north of 40°N at the Atlantic, while the return path through upwelling mainly occurs in the Southern Ocean. Our estimates underpin the key role of the northern North Atlantic to form the North Atlantic Deep Water (NADW) at mid-depth (Johnson, 2008; Talley, 2013). On the contrary, the upwelling in the Southern Ocean draws deep water up to the surface. Also, Fig. 4 indicates that the strong upwelling locates in the Atlantic sector of the Southern Ocean. The high upwelling rates in the Southern Ocean do not decay with depth, which is different with the change of dissipation rates shown in Fig. 3. The following calculation of global and regional integrals of the diapycnal transport (in unit of Sv) only considers grids with estimates of dissipation rate. Therefore, the coverage of the in-situ observations is vital to the accuracy of the calculation, which should be considered in the future measurements.

Fig.4 Maps of diapycnal transport (Sv, 1 Sv=106 m3/s) derived from dissipation shown in Fig. 3 Positive values (red) indicate the upwelling, while negative values (blue) represent the downwelling. The depths and figure configuration are identical to Fig. 3.
3.3 The Atlantic basin and seasonal variations

Our results indicate that upwelling mainly occurs in the Southern Ocean, especially in the Atlantic sector, and downwelling largely takes place in the northern part of the North Atlantic. Therefore, we took the Atlantic Basin as an example to investigate the amount and seasonal variation of diapycnal transport, showing its role in the MOC. The seasonal variation was only briefly mentioned in Whalen et al. (2012) in the Northwest Pacific. With the help of the recent ten-year Argo observations, we can monitor this seasonal variation in the basin scale. The MOC in the Atlantic basin exhibits a vertical structure with two cells (Schmitz, 1995; Lumpkin and Speer, 2007; Marshall and Speer, 2012). The water in the lower cell comprises Lower Circumpolar Deep Water (LCDW) and Antarctic Bottom Water (AABW). The LCDW has poor ventilation with the atmosphere, which is of great effect on the material and energy cycle. The diapycnal transport in this paper can be considered as a proxy of the water exchange between two cells. Zonal integrals with 1° width of latitude band (Fig. 5) provide the regional features to assess the change of the diapycnal transport with latitude intuitively. Here, we present the zonal averages for different seasons and yearly estimate as well in order to show the contributions of seasons to the diapycnal transport. The zonal average of the yearly transport (black lines in Fig. 5) show the significant upwelling in the Southern Ocean and downwelling in the northern North Atlantic at all depths in our estimates. This pattern, combined with the isopycnal movement of the water masses (Marshall and Speer, 2012), gives hints on the understanding of the MOC. Except for the high latitude regions, there is small amount of the dissipation rate and diapycnal transport in the Atlantic basin, supporting the estimates from measurements from microstructure observations (Gregg, 1987) and tracer experiments (Ledwell et al., 2011). As for the peak at near 15°N (Fig. 5a, b), it arises from a patch of area with high dissipation (Fig. 3), which may relate on the energy source from the bottom because the energy flux into internal lee wave (Nikurashin and Ferrari, 2011) demonstrates a similar elevation in the same area.

Fig.5 Zonal average of the diapycnal transport in the Atlantic with 1° width of latitude band The mean of the diapycnal transport (Sv) along east-west line versus latitude at 500 m (a), 750 m (b), and 1 000 m (c) depths.The seasonal results (green lines:January to March; red lines:April to June; yellow lines:July to September; blue lines:October to December) and the yearly results (black lines) are obtained in each subgraph.

In the Southern Ocean, the robust upwelling spreads from ~50°S to ~65°S at 500 m depth (Fig. 5a), covering most of the ACC area. The wind power input in to the ocean interior provides the substantial energy for water mass to break the blocking by stratification and sustains the relative strong mixing near the surface. Two peaks can be seen at ~50°S and ~60°S in our estimates at all depths (black lines in Fig. 5). According to Orsi et al. (1995), we define the SubAntarctic Front (SAF) and Southern Boundary of ACC (SACC) as the northern and southern boundaries of ACC. Since the mean latitudes of SAF and SACC are 48.7°S and 58.5°S in the Atlantic sector, the positions of these two peaks are generally corresponding to the south and north boundaries of the ACC. The oceanic front causes instability of the internal wave field in the ocean interior, making the breaking of internal wave and inducing the turbulent mixing. The strength of upwelling occurring near 50°S decreases with depth, from 1.2×10-3 Sv at 500 m to about 5×10-4 Sv at 1 000 m, which underpins the explanation mentioned above that the energy comes from the sea surface. However, an opposite trend of the gradient of upwelling in the vertical direction appears near 60°S where the upward diapycnal transport reaches ~2×10-3 Sv at 1 000 m (Fig. 5c). This amount of upwelling is about 40% more than the corresponding crest values at shallow depths, which implies an energy source at the deep ocean. In the northern North Atlantic, the largest values of downwelling appear near 60°N and stabilise at (1±0.2)×10-3 Sv at all three depths. However, the extent of latitude with the high vertical transport rates (absolute values are larger than 5×10-4 Sv) decreases from ~20°(50°–70°N in Fig. 5a) to ~5°(60°–65°N in Fig. 5c) approximately. This phenomenon indicates that the diapycnal downwelling is powered by the energy source at the sea surface.

Figure 5 also plots the seasonal zonal averages (Fig. 5; green lines: January to March; red lines: April to June; yellow lines: July to September; blue lines: October to December). The seasonal variations are obvious in the zonal estimate of 500 m depth (Fig. 5a). The maximum of upwelling in the Southern Ocean moves from ~59°S during January to March (green line) to ~52°S during April to June (red line). Then, the peak of result derived from July to September (yellow line) reaches ~49°S which is the most northerly position in the seasonal zonal integrals. Subsequently, the enhancement of upwelling centres at ~55°S when October to December (blue line). The seasonal cycle of the site of upwelling in the Southern Ocean implies the movement of the area where the wind power works on the ocean surface (i.e., area with high wind stress; Luis and Pandey, 2004; Risien and Chelton, 2008), with the southernmost point during the Southern Hemisphere Summer Seasons and the northernmost point during the Southern Hemisphere Winter Seasons. As the depth increases this cycle vanishes and the amount of upwelling tend to be identical with each other in the Southern Ocean (Fig. 5b). At 1 000 m depth, regardless the magnitude of the upwelling, all seasonal estimates peak near ~60°S showing a time-independent power supply from the deep ocean. A similar movement of the peak of the diapycnal transport can be seen in the northern North Atlantic at 500 m depth (Fig. 5a), with a southnorth shift of the crest values but in a relative constrained range of latitude (~60°–70°N). Besides, this kind of seasonal variation at 750 m and 1 000 m depths is not so evident as that happening at 500 m depth. Different from the deep reinforcement of the upwelling in the Southern Ocean, the downwelling here weakens as the depth increases because of the distant away from the surface. In this paper, we briefly discuss the seasonal cycle and its depth dependence in basin scale, which infers the potential energy sources to sustain the diapycnal mixing at different depths in ocean interior. The long-term full-depth finescale and microscale in-situ observations, with high vertical resolution, should be deployed in regions where the diapycnal transport is robust to give the whole picture of the vertical movement and seasonal variations of water masses.


Based on the estimates of the maps of the diapycnal transport, we obtained the features of the global patterns at different depths. We also presented the time variations according to the zonal averages in the Atlantic basin. The magnitudes of the upwelling and downwelling (Sv) are summarised in Table 1. The unit Sv suggests diapycnal transport as a rate of water carried in one second. Because the spatial coverage of Argo profiles differs in seasons, the comparison among the magnitudes of the global integrals is meaningless. Hence, we scaled the seasonal maps of transport according to the coverage of yearly estimate, using the closest three grid values to represent the transport at the missing position. Because the numbers of Argo profiles within some grids (Fig. 1) are small (<10), we cannot give bootstrapped confidence intervals for every estimate. We used the method reported by Whalen et al. (2012) and derived the similar results (not shown) as their Fig.S4. This uncertainty estimate, 90% confidence interval, is incorporated in the following regional and global integrals. This is only an underestimate of the uncertainty due to the ignorance of errors from the grid points having few Argo profiles. The net diapycnal upwelling at 500 m depth is about 5.2±0.81 Sv which accounts for about a fifth or more in the budget of the formation of the deep water in the global ocean (maximum 25 Sv; Talley, 2013). This proportion indicates the diapycnal upwelling is an important pathway to return the deep water masses back to the surface. Although our estimates are not the exact amount of the inflow and outflow of the deep water, these results can still be taken as an indicator of the water exchange between the deep water and the shallow water. The upwelling in the Southern Ocean makes up 50% or more of either the yearly or seasonal estimates demonstrating the significant role of the Southern Ocean in the MOC. Meanwhile, the global sum of the upwelling increases from 7.1 Sv at 750 m to 8.9 Sv at 1 000 m, which is consistent with the amplification in the Southern Ocean (from 4.0 to 5.1 Sv). Apart from the wind power input into the surface, the energy source at the bottom is another way to sustain the relative strong diapycnal mixing at mid-depth. Many studies (Nikurashin and Ferrari, 2011, 2013; Nikurashin et al., 2013) have suggested the lee-wave generation from the bottom and radiation to the ocean interior supply plenty energy in form of internal wave field. The cascade and breaking of the internal wave away from the seafloor help the dense water masses to do the work against the stratification (Sheen et al., 2013). Li and Xu (2014) reported the topographic roughness may influence the turbulent mixing over 3 000 m above the bottom. Our estimates show a clear enhancement of upwelling at 1 000 m depth near 60°S in the Atlantic sector of the Southern Ocean, as a result of the bottom energy source generated by interaction between the strong deepreaching currents (deep ACC) and rough small-scale topography in the east of the Drake Passage. The seasonal variations are clear at the shallow depth (Table 1, 500-depth). The maximum of the upwelling occurs during July to September, while that of the downwelling emerges in January to March. The magnitude of the global upwelling changes with that in the Southern Ocean synchronously. Generally speaking, although the movement of the fronts in the Southern Ocean is not simple (Sallée et al., 2008), the extend of regions with low temperature expands during the winter in the southern hemisphere. Hence, the area, where the wind power inputs and the bottom internal wave generates, is larger than that in summer, which causes sufficient energy supply to support the higher upwelling rates. Both the amounts of upwelling and downwelling have little difference among seasons at 750 m and 1 000 m depths indicating the effect of surface weakens gradually.

Table 1 The global integral of vertical transport rates (Sv) at particular depths

In this paper, we used the finescale parameterizations to assess the dissipation rate and the diapycnal transport at 500 m, 750 m, and 1 000 m depths, from the Argo profiles over ten years (2007–2016). The global maps of the diapycnal transport and the zonal integrals in the Atlantic basin clarify the majority of upwelling mainly distributes in the Southern Ocean and the downwelling is located in the northern North Atlantic. The global net diapycnal transport is upward (5.2±0.81 Sv) and balances one fifth of the formation of deep water. The seasonal analysis shows our estimates are reasonable because of the consistence with the field experiments and the theory of the MOC. Our estimates show the diapycnal upwelling is an important branch to resurface the deep water. The potential cruxes arise from the inaccuracy of the finescale parameterizations and the vertical resolution of Argo profiles. Besides, the estimates are limited by the spatial and temporal coverage of the observations which should be improved in the future deployment especially in the Southern Ocean and the northern North Atlantic.


The temperature and salinity profiles that support the findings of this study, from 2006 to 2017 in the global ocean, are available in Argo Data Management,

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