1. Introduction
Large-scale ocean circulation plays a fundamental role in Earth’s climate by transporting heat and freshwater (or salinity anomaly) through ocean basins while mixing internally and interacting with the atmosphere. Of particular focus here is the Atlantic meridional overturning circulation (AMOC), which consists of a net northward flow of warm saline water in approximately the upper 1000 m overlying a net southward flow of colder fresher water. At 26.5°N, the AMOC is responsible for virtually all the observed northward 1.25-PW (1 PW = 1015 W) heat transport (e.g., McCarthy et al. 2015) and 30% more than the observed southward 0.38-Sv (1 Sv = 106 m3 s−1) net freshwater transport (McDonagh et al. 2015) because the subtropical gyre contributes freshwater transport northward (Xu et al. 2016). These large heat/freshwater transports result from the diapycnal transformation of the warm saline water in the northward-flowing upper limb into the colder, fresher, and denser North Atlantic Deep Water (NADW) in the southward-flowing lower limb. Thus, there is a strong need to quantify the magnitude and structure of the water mass transformation in the North Atlantic Ocean.
Part of the warm water in the upper limb of the AMOC flows across the Greenland–Scotland Ridge and is transformed into the Nordic Seas Overflow Water (NSOW) and returned to the North Atlantic (Hansen and Østerhus 2000; Saunders 2001), whereas the remainder flows around the subpolar gyre and is transformed into the Labrador Sea Water (LSW; McCartney and Talley 1982). From observations of the chlorofluorocarbons (CFCs) inventory, LeBel et al. (2008) estimated a long-term averaged NSOW and LSW formation rate of 7.9 and 11.7 Sv, respectively. This formation rate of NSOW (including entrainment) is in reasonable agreement with the volume transports estimated from moored current-meter arrays along the western boundary of the subpolar North Atlantic: 9.0 Sv at 59°N (Bacon and Saunders 2010), 9–10 Sv at 53°N (Fischer et al. 2004, 2010), and 8.9 Sv at 43°N (Schott et al. 2004, 2006). The LSW formation rate of LeBel et al. (2008), however, differs from estimates listed in Table 1 of Pickart and Spall (2007), where 10 observational studies yield an average formation rate of 4.4 Sv with a wide range of 1–10 Sv. It is also unclear as to where and how the LSW water mass transformation takes place. LSW is observed to be formed in the central Labrador Sea by wintertime deep convection (e.g., McCartney and Talley 1982; Marshall et al. 1998) and to spread toward different regions in the subpolar and subtropical basins (e.g., Talley and McCartney 1982; Rhein et al. 2002). Based on the hydrographic and subsurface float data collected from 1990 to 1997 (a period of intense deep convection), Pickart and Spall (2007) estimated a small diapycnal transformation of 2 Sv across the World Ocean Circulation Experiment (WOCE) AR7W line (Fig. 1), suggesting that some of the LSW is actually formed in the Labrador Sea southeast of the AR7W line and in the southern Irminger Sea (Pickart et al. 1997, 2003a,b). More recently, von Appen et al. (2014) estimated about 3 Sv of intermediate water, mostly in LSW density range, from the East Greenland Spill Jet (e.g., Pickart et al. 2005) in the northern Irminger Sea.
Bathymetry of the model domain along with the location of key sections used in this study: the black lines from south to north are the RAPID line at 26.5°N, the WOCE line AR19, and the Greenland–Scotland Ridge; the magenta line in the Labrador Sea is the WOCE line AR7W; the magenta box denotes the subpolar–subtropical transition region.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Bathymetry of the model domain along with the location of key sections used in this study: the black lines from south to north are the RAPID line at 26.5°N, the WOCE line AR19, and the Greenland–Scotland Ridge; the magenta line in the Labrador Sea is the WOCE line AR7W; the magenta box denotes the subpolar–subtropical transition region.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Bathymetry of the model domain along with the location of key sections used in this study: the black lines from south to north are the RAPID line at 26.5°N, the WOCE line AR19, and the Greenland–Scotland Ridge; the magenta line in the Labrador Sea is the WOCE line AR7W; the magenta box denotes the subpolar–subtropical transition region.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Mapping the structure of water mass transformation requires continuous measurements of the large-scale three-dimensional circulation fields (volume transport, temperature, and salinity) with fine spatial resolution. This is challenging, and the existing studies have mostly focused on the transformation that is induced directly by surface buoyancy fluxes (surface-forced transformation hereafter), using the thermodynamic framework of Walin (1982). This framework allows the diapycnal transformation to be calculated from two-dimensional fields of surface density and air–sea buoyancy fluxes (e.g., Speer and Tziperman 1992; Speer et al. 1995; Marsh 2000; Brambilla et al. 2008; Langehaug et al. 2012; Grist et al. 2014). The spatial distribution of the surface-forced transformations in the subpolar North Atlantic was mapped by Brambilla et al. (2008). They show that areas of strong diapycnal transformation coincide with the locations of Subpolar Mode Waters (SPMW) characterized by low potential vorticity and that the transformations take place around the cyclonic subpolar gyre: from the Newfoundland Basin to the Iceland Basin, the Reykjanes Ridge, the Irminger Basin, and finally the Labrador Sea, a vivid illustration of the transformation toward LSW first described in McCartney and Talley (1982).
Surface buoyancy fluxes, however, do not account for all the diapycnal water mass transformation. Diapycnal transformations can also occur across steep isopycnal slopes in the mixed layer via lateral diffusive fluxes, especially at high latitudes (Marshall et al. 1999). Furthermore, using hydrographic data and inverse model calculations, Lumpkin et al. (2008) suggested that much of the LSW exported southward across 48°N is generated within the subpolar North Atlantic by diapycnal mixing rather than directly by air–sea fluxes. Eddy-permitting model results of Marsh et al. (2005, their Fig. 9) also show strong mixing-induced water mass transformation in the North Atlantic, often in opposite direction to the surface-forced transformation. These studies only considered the integrated transformation over large areas, and the spatial distribution remains largely unknown.
The AMOC is normally evaluated by integrating the meridional velocity east–west, along either constant depth or constant potential density (or neutral density) levels, and much of the discussion of ocean circulation is focused on the two-dimensional (latitude vs depth or density) AMOC streamfunction and its maximum amplitude. However, these two-dimensional patterns disguise the three-dimensional structures of circulation and do not represent the spatially complex nature of internal subsurface turbulent mixing and diapycnal velocity. The main goal of this paper is to map the spatial structure of the diapycnal transformation of the surface waters toward denser waters in the North Atlantic that is associated with the upper limb of the AMOC, specifically, where the diapycnal transformation takes place and where the mixing-induced transformation becomes important. The results are based on an eddying Atlantic simulation that has been shown to represent well the structure of the large-scale AMOC and the subtropical/subpolar gyre circulations (e.g., Xu et al. 2016).
The paper is organized as follows: Section 2 describes the model simulation and the diagnostics of the diapycnal water mass transformation. The area-integrated water mass transformation is discussed in section 3. Then in section 4, we discuss the spatial structure of the transformation in the subtropical and subpolar regions of the North Atlantic Ocean. The results are summarized and discussed in section 5.
2. Numerical simulation and diapycnal transformation diagnostics
a. Numerical simulation
The numerical simulation is performed using the Hybrid Coordinate Ocean Model (HYCOM; Bleck 2002; Chassignet et al. 2003; Halliwell 2004), and the model configuration is described in Xu et al. (2016) and references therein. The model domain covers the North and equatorial Atlantic (Fig. 1) with a horizontal resolution of 1/12° and a vertical resolution of 64 layers in potential density referenced to 2000 m (σ2; kg m−3). The southern and northern boundaries are closed, and the modeled potential temperature θ and salinity S within a buffer zone of 3° from these two boundaries are restored toward the ocean climatology. The simulation is integrated using monthly climatological forcing from the 40-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-40; Uppala et al. 2005) and 3-hourly wind anomalies for 2003, a year with neutral North Atlantic Oscillation. The anomalies are based on the Fleet Numerical Meteorology and Oceanography Center 0.5° Navy Operational Global Atmospheric Prediction System (NOGAPS; Rosmond et al. 2002). The surface heat flux forcing includes the shortwave and longwave radiations that are directly from ERA-40 and the latent and sensible heat fluxes that are calculated using the model sea surface temperature (SST) and bulk formulas of Kara et al. (2005). The surface freshwater forcing, prescribed as a salinity flux, includes evaporation, precipitation, and river runoffs. In addition, the model sea surface salinity (SSS) is restored toward ocean climatology with a restoring strength of 15 m per 30 days. A simple thermodynamic model (Semtner 1976) is used for sea ice. The modeled winter sea ice coverage is similar to that observed in the Nordic seas, the Baffin Bay, and the Hudson Bay but is less extensive in the western shelf of the Irminger and Labrador Seas. The thermodynamic model, however, cannot simulate the freshwater input to the Labrador Sea owing to melting of sea ice transported from the north. These limitations can impact the heat and freshwater fluxes in the region. The simulation is integrated for 20 years, and the diagnostics are performed for the last five years of the integration, which is representative of the modeled mean circulation after spinup.
The vertical coordinate of HYCOM is isopycnal in the stratified open ocean, and it makes a dynamically smooth and time-dependent transition to terrain following in shallow coastal regions and fixed pressure levels in the surface mixed layer and/or unstratified seas (Chassignet et al. 2006). In doing this, the model combines the advantages of the different coordinate types in simulating coastal and open ocean circulation simultaneously. In the high latitudes (north of ~55°N), the vertical coordinate is mostly z coordinate in the upper 1000 m because of the small vertical density gradient. As in Chassignet and Garraffo (2001), Xu et al. (2010), and Chassignet and Xu (2017), the horizontal viscosity operator for momentum is a combination of Laplacian 
b. Diagnosis method
The difference between the total and the surface-forced transformations, FT(σ) − FS(σ), is interpreted as the transformation induced by interior mixing FI(σ). Although “interior” is used to differentiate from surface-forced transformation FS(σ), it should be stated that FI(σ) includes all the transformations that are not due to air–sea buoyancy fluxes. Mostly, it is the transformation due to lateral mixing within the wintertime mixed layer depth. The model allows solar radiation to penetrate below the surface, and this effect is not included in the FS calculation in (2). This could impact the results in areas where the surface mixed layer is shallow since a warming to the water below the mixed layer could be falsely attributed to mixing instead of surface-forced transformation.
3. Area-integrated diapycnal transformation
In this section, we focus on the area-integrated diapycnal water mass transformation to provide a large-scale view of the transformation associated with the meridional overturning circulation in the North Atlantic.
a. Meridional overturning streamfunction and diapycnal transformation
Modeled 5-yr (a) mean meridional overturning streamfunction 
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Modeled 5-yr (a) mean meridional overturning streamfunction
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Modeled 5-yr (a) mean meridional overturning streamfunction
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
A comparison of modeled 5-yr mean (a) meridional overturning streamfunction with respect to density 
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
A comparison of modeled 5-yr mean (a) meridional overturning streamfunction with respect to density
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
A comparison of modeled 5-yr mean (a) meridional overturning streamfunction with respect to density
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
The sum of the surface-forced FS and mixing-induced FI transformations for the area north of a given latitude, denoted as 
b. Regional diapycnal transformation of the subtropical and subpolar North Atlantic
To obtain a more quantitative measure of the water mass transformation in the North Atlantic, we calculate the water mass transformations in two regions: one from 26.5°N to the WOCE line AR19 (near 48°N) and the other from the AR19 to the Greenland–Scotland Ridge (see Fig. 1 for location), representing the subtropical and subpolar North Atlantic, respectively. The net transports FN and the corresponding water mass transformations (FT, FS, FI) for these two regions are compared in Fig. 4. The results show that about 12-Sv water in the σ2 range of 31–33.7 kg m−3 is transformed into denser water of 33.7–35.5 kg m−3 in the subtropical region (Fig. 4a). This transformed water flows farther north into the subpolar region and is transformed there into even denser water of 36.68–36.96 kg m−3 (Fig. 4b). These transformations are to a large degree surface forced (green lines). The mixing-induced transformation FI is generally weaker but significant too (orange). In both the subtropical and subpolar regions, the surface-forced transformation FS extends to a denser water than the total transformation FT. This is due to wintertime convection, which deepens the mixed layer toward high densities, whereas the interior mixing with ambient water lowers the density for the transformed water. In the subpolar North Atlantic (Fig. 4b), there is a transformation of ~5 Sv toward lighter water across σ2 of 37.13 kg m−3, induced by submixed layer entrainment mixing of the dense NSOW source water with the ambient water (see also Fig. 2).
Modeled 5-yr mean net horizontal transports FN and the total FT, surface-forced FS, and interior-mixing-induced FI water mass transformations for (a) the subtropical region from 26.5°N to the WOCE line AR19 and (b) the subpolar region from AR19 to the Greenland–Scotland Ridge (see Fig. 1 for section locations). Positive values (Sv) in FT indicate transformations toward denser water. The FT in the subtropical plot shows transformation toward denser water across density surface near 33.7 kg m−3; the subpolar plot shows transformations toward denser water across 36.68 kg m−3 and toward lighter water across 37.14 kg m−3. Both FS and FI are significant.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Modeled 5-yr mean net horizontal transports FN and the total FT, surface-forced FS, and interior-mixing-induced FI water mass transformations for (a) the subtropical region from 26.5°N to the WOCE line AR19 and (b) the subpolar region from AR19 to the Greenland–Scotland Ridge (see Fig. 1 for section locations). Positive values (Sv) in FT indicate transformations toward denser water. The FT in the subtropical plot shows transformation toward denser water across density surface near 33.7 kg m−3; the subpolar plot shows transformations toward denser water across 36.68 kg m−3 and toward lighter water across 37.14 kg m−3. Both FS and FI are significant.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Modeled 5-yr mean net horizontal transports FN and the total FT, surface-forced FS, and interior-mixing-induced FI water mass transformations for (a) the subtropical region from 26.5°N to the WOCE line AR19 and (b) the subpolar region from AR19 to the Greenland–Scotland Ridge (see Fig. 1 for section locations). Positive values (Sv) in FT indicate transformations toward denser water. The FT in the subtropical plot shows transformation toward denser water across density surface near 33.7 kg m−3; the subpolar plot shows transformations toward denser water across 36.68 kg m−3 and toward lighter water across 37.14 kg m−3. Both FS and FI are significant.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Seasonal variation of the net transport streamfunction and the corresponding water mass transformations are illustrated in Fig. 5. In both the subtropical and subpolar regions, the seasonal variability is small for the net transports FN but strong for the total water mass transformations FT (Figs. 5a,b and 5e,f): The magnitude of the total transformation FT in winter/summer is 4–6 times higher than the annual mean FN. Thus, while the FN and FT are approximately the same on an annual mean basis (Fig. 4), they differ significantly on a seasonal scale because of the large volume change: the dense water accumulates in winter and drains out in summer. The large seasonal volume change of upper-ocean water masses in the model is similar to observations as presented in Evans et al. (2017). Their results also show that the interannual fluctuations of the upper-ocean volume budget of the subtropical gyre are primarily set adiabatically by the variability of meridional transport at 26° and 45°N, whereas the (diabatic) air–sea fluxes have a minimal effect. The total FT and surface-forced FS transformations are qualitatively similar in both regions (Figs. 5b,c and 5f,g). The similarity suggests that the surface buoyancy fluxes do explain a significant part of diapycnal transformations in the upper North Atlantic and that the Walin (1982) framework is useful in estimating the large-scale total transformation FT, although the mixing-induced transformations FI are by no means negligible, especially in the dense northern overflows but also in the upper ocean (see Figs. 5d,h).
Seasonal variation of the modeled net horizontal transports FN and the total FT, surface-forced FS, and interior-mixing-induced FI water mass transformations for (a)–(d) the subtropical region from the 26.5°N to the WOCE AR19 line and (e)–(h) the subpolar region from AR19 to the Greenland–Scotland Ridge (Fig. 1 for section locations). Positive values (Sv) indicate transformations toward denser water.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Seasonal variation of the modeled net horizontal transports FN and the total FT, surface-forced FS, and interior-mixing-induced FI water mass transformations for (a)–(d) the subtropical region from the 26.5°N to the WOCE AR19 line and (e)–(h) the subpolar region from AR19 to the Greenland–Scotland Ridge (Fig. 1 for section locations). Positive values (Sv) indicate transformations toward denser water.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Seasonal variation of the modeled net horizontal transports FN and the total FT, surface-forced FS, and interior-mixing-induced FI water mass transformations for (a)–(d) the subtropical region from the 26.5°N to the WOCE AR19 line and (e)–(h) the subpolar region from AR19 to the Greenland–Scotland Ridge (Fig. 1 for section locations). Positive values (Sv) indicate transformations toward denser water.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
4. Spatial distribution of the diapycnal water mass transformation
The previous section gave us a broad overview of the diapycnal water mass transformation in the North Atlantic. In this section, we map the 2D horizontal distributions of the modeled annual mean diapycnal transformation across a series of selected isopycnal surfaces as labeled in Fig. 2b in the subtropical and subpolar North Atlantic Ocean. The goal is to identify where the transformations take place and quantify them, with a focus on the transformations associated with the Subtropical Mode Water [STMW; also known as the Eighteen Degree Water (EDW)], the SPMW, and the LSW.
a. The subtropical North Atlantic
Figures 6, 7, and 8 map the horizontal distribution of modeled time mean total FT, surface-forced FS, and mixing-induced FI transformations per unit area, across eight density surfaces in the subtropical North Atlantic (labeled by the red letters a–h in Fig. 2b). The results are averaged over 5 × 5 model grid points to minimize the noise. Strong transformations toward denser water are found from the Florida Current to the Gulf Stream and to the North Atlantic Current, following progressively denser isopycnals (Fig. 6). This transformation is primarily induced by surface buoyancy loss (dominated by cooling) over the Gulf Stream–North Atlantic Current system (Fig. 8). In addition to air–sea cooling of the surface, observations show that along-current wind stress induces Gulf Stream mixing where Ekman transport forces cold dense water on top of warm water (Thomas et al. 2013). In the model, the Ekman flow transports about 1.5 Sv near surface water southward across a latitude of 40°N (close to the Gulf Stream axis) between 70° and 50°W. Transformations toward denser water are also found in the open ocean over the high surface salinity area east of 50°W (Figs. 7c–f), where excessive E − P also contributes to the transformation. Transformations toward lighter water are generally weaker and found mostly in three regions: in the southern Caribbean Sea (Figs. 6a–d), along the African coast (Figs. 6d–f), and in a broad band across the open ocean (Figs. 6c–h). The transformation in the southern Caribbean Sea and offshore of West Africa are both associated with strong Ekman transport and upwelling that subject cold water to surface-forced warming (Fig. 7f). The transformation in the subtropical open ocean is induced by horizontal mixing in the southwestward subtropical gyre mixed layer (Figs. 8c–f and discussion below).
Distribution of the modeled 5-yr mean, total diapycnal transformation per unit area (velocity unit 10−6 m s−1) across (a)–(h) eight density surfaces in the subtropical North Atlantic (labeled in red letters a–h in Fig. 2). The two magenta lines in (f) mark a latitude band (15°–30°N) over which the zonally accumulated water mass transformations are shown in Fig. 11.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Distribution of the modeled 5-yr mean, total diapycnal transformation per unit area (velocity unit 10−6 m s−1) across (a)–(h) eight density surfaces in the subtropical North Atlantic (labeled in red letters a–h in Fig. 2). The two magenta lines in (f) mark a latitude band (15°–30°N) over which the zonally accumulated water mass transformations are shown in Fig. 11.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Distribution of the modeled 5-yr mean, total diapycnal transformation per unit area (velocity unit 10−6 m s−1) across (a)–(h) eight density surfaces in the subtropical North Atlantic (labeled in red letters a–h in Fig. 2). The two magenta lines in (f) mark a latitude band (15°–30°N) over which the zonally accumulated water mass transformations are shown in Fig. 11.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
As in Fig. 6, but for the surface-forced diapycnal transformation per unit area (10−6 m s−1), calculated from the local density flux D in Eq. (3) and surface density.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
As in Fig. 6, but for the surface-forced diapycnal transformation per unit area (10−6 m s−1), calculated from the local density flux D in Eq. (3) and surface density.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
As in Fig. 6, but for the surface-forced diapycnal transformation per unit area (10−6 m s−1), calculated from the local density flux D in Eq. (3) and surface density.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
As in Fig. 6, but for the interior-mixing-induced diapycnal transformation per unit area (10−6 m s−1); overlaid contours are depth of the density surfaces (bracketed numbers are the minimum, increasing interval, and maximum depths).
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
As in Fig. 6, but for the interior-mixing-induced diapycnal transformation per unit area (10−6 m s−1); overlaid contours are depth of the density surfaces (bracketed numbers are the minimum, increasing interval, and maximum depths).
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
As in Fig. 6, but for the interior-mixing-induced diapycnal transformation per unit area (10−6 m s−1); overlaid contours are depth of the density surfaces (bracketed numbers are the minimum, increasing interval, and maximum depths).
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
The density σ2 surface of 34.11 kg m−3 (corresponding to the red label f in Fig. 2b and σθ of 25.75 kg m−3) marks the center of the local cell in the subtropical North Atlantic and slightly above the STMW/EDW (characterized by σθ of 26.3–26.6 kg m−3). Thus, the transformations across this density surface toward denser/lighter waters (Figs. 6f, 7f, and 8f) connect to the formation/erosion of the STMW, respectively. Most of the modeled STMW is transformed in the Gulf Stream region and continues to flow north as it becomes denser and becomes the source for the SPMW in the subpolar region. This intricate subsurface pathway for the warm northward flow of AMOC has been suggested by Häkkinen et al. (2011) and Burkholder and Lozier (2014). Some of the STMW, however, returns southward in the subtropical gyre and is transformed toward lighter water due to horizontal mixing in the mixed layer. To illustrate this, Fig. 9 shows the modeled time mean velocity and the magnitude of the horizontal diffusive density flux 
(a) Modeled 5-yr mean velocity in model layer 22 associated with the broad transformation across the midocean as shown in Fig. 8f; velocity larger than 10 cm s−1 is denoted with black arrows. (b) The averaged magnitude of horizontal diffusive density 
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
(a) Modeled 5-yr mean velocity in model layer 22 associated with the broad transformation across the midocean as shown in Fig. 8f; velocity larger than 10 cm s−1 is denoted with black arrows. (b) The averaged magnitude of horizontal diffusive density
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
(a) Modeled 5-yr mean velocity in model layer 22 associated with the broad transformation across the midocean as shown in Fig. 8f; velocity larger than 10 cm s−1 is denoted with black arrows. (b) The averaged magnitude of horizontal diffusive density
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
A meridional section view of the annual mean total transformation along 52°W (WOCE line A20) illustrates the relationship between transformation and mixed layer depth more clearly (Fig. 10a): The transformation toward dense water (convection) takes place mostly within the deep wintertime mixed layer depth (MLD); the transformation toward lighter water (restratification) is seen at the base of MLD, which slopes upward to the south of the Gulf Stream deep convection region. Some transformation toward lighter water is also seen below the MLD, especially in the tropics, where there is elevated interior mixing due to double diffusion with saltier water sitting above the fresh Antarctic Intermediate Water. The MLD is defined as density change from surface that is equivalent of a 0.3°C temperature difference. The gray and black lines denote the model coordinates and the modeled isopycnal interfaces, respectively. The two differ in the MLD as the model coordinates switch from isopycnals to hybrid coordinates. Comparison between the model results and the ocean climatology of Schmidtko et al. (2013) shows that the modeled wintertime MLD and the temperature profiles agree well with the climatology (Figs. 10b,c).
(a) Modeled 5-yr mean, total diapycnal transformation (10−6 m s−1) along 52°W. Thick magenta line is the 5-yr averaged wintertime (March) MLD; thick cyan line is the maximum MLD; thin black lines denote the modeled mean isopycnic surfaces (letters a–h correspond to the eight surfaces in Fig. 6); thin gray lines denote the mean locations of the model coordinates (the departure from the black lines indicates nonisopycnic conditions in the model). (b) Mean potential temperature (°C; color shading) and MLD (magenta line) in March based on ocean climatology of Schmidtko et al. (2013) and HYCOM simulation.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
(a) Modeled 5-yr mean, total diapycnal transformation (10−6 m s−1) along 52°W. Thick magenta line is the 5-yr averaged wintertime (March) MLD; thick cyan line is the maximum MLD; thin black lines denote the modeled mean isopycnic surfaces (letters a–h correspond to the eight surfaces in Fig. 6); thin gray lines denote the mean locations of the model coordinates (the departure from the black lines indicates nonisopycnic conditions in the model). (b) Mean potential temperature (°C; color shading) and MLD (magenta line) in March based on ocean climatology of Schmidtko et al. (2013) and HYCOM simulation.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
(a) Modeled 5-yr mean, total diapycnal transformation (10−6 m s−1) along 52°W. Thick magenta line is the 5-yr averaged wintertime (March) MLD; thick cyan line is the maximum MLD; thin black lines denote the modeled mean isopycnic surfaces (letters a–h correspond to the eight surfaces in Fig. 6); thin gray lines denote the mean locations of the model coordinates (the departure from the black lines indicates nonisopycnic conditions in the model). (b) Mean potential temperature (°C; color shading) and MLD (magenta line) in March based on ocean climatology of Schmidtko et al. (2013) and HYCOM simulation.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
The patterns of transformations toward lighter/denser water are not zonal (Fig. 6f), and consequently, the zonally integrated streamfunction in Fig. 2b is not fully representative of the total diapycnal transformation in the subtropical gyre. To quantify this, we zonally integrate the transformations toward lighter and denser water separately in Fig. 11, spanning the overturning cell from 15° to 30°N (see magenta lines in Figs. 6f, 7f, and 8f). The results show that the net FT transformation of 3.2 Sv consists of 4.7 Sv transformation toward lighter water minus the 1.5 Sv transformation toward denser water (black thin solid and dashed lines in Fig. 11, respectively). Thus, the total transformation toward lighter water that takes place within this subtropical band (4.7 Sv) is nearly 50% higher than the net value (3.2 Sv; thick black line in Fig. 11). Decomposing FT into FS and FI shows that the transformation toward lighter water is mostly induced by horizontal mixing in the mixed layer (except that along the western African coast where it is surface forced), whereas the transformation toward denser water is primarily surface forced. Mixing induces a transformation of 5.2 Sv toward lighter water and 0.7 Sv toward denser water (orange thin solid and dashed lines), whereas the surface fluxes lead to a transformation of 1.4 Sv toward lighter water and 2.7 Sv toward denser water (green thin solid and dashed lines).
Eastward accumulation of the modeled total FT (black), surface-forced FS (green), and interior-mixing-induced FI (orange) transformations across 
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Eastward accumulation of the modeled total FT (black), surface-forced FS (green), and interior-mixing-induced FI (orange) transformations across
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Eastward accumulation of the modeled total FT (black), surface-forced FS (green), and interior-mixing-induced FI (orange) transformations across
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
b. The subpolar North Atlantic
Similar to Figs. 6, 7, and 8, Figs. 12, 13, and 14 map the horizontal distribution of total FT, surface-forced FS, and interior-mixing-induced FI transformation per unit area, across eight isopycnals in the subpolar region (labeled by blue letters a–h in Fig. 2b). As for the subtropics, the area of strong transformation toward denser water follows the gyre circulation (Fig. 10): from the North Atlantic Current that extends eastward in the polar front, to the Iceland Basin and over the Rockall Plateau, westward over the Reykjanes Ridge and around Greenland, and finally into the Labrador Sea. A significant part of this transformation is surface forced (Fig. 13), and the model results are very similar to Fig. 4 in Brambilla et al. (2008) derived from observations. However, the surface buoyancy loss does not account for all the transformation, and mixing in the mixed layer is responsible for significant transformations around the subpolar gyre (Fig. 14), particularly strong along the steep isopycnal slopes as noted by Marshall et al. (1999). Unlike the annual mean surface-forced transformations FS that are mostly toward denser water in the subpolar region (Fig. 11), mixing-induced transformations FI are in both directions (Fig. 12): toward lighter water along the deeper part of the isopycnal slope (the inshore side of the boundary current) and toward denser water along the shallow part of the isopcynal slope (the offshore side of boundary current and the interior). A similar overturning circulation pattern was inferred in the Labrador Sea from tracer observations by Khatiwala et al. (2002).
Distribution of the modeled 5-yr mean, total diapycnal transformation per unit area (10−6 m s−1) across (a)–(h) eight density surfaces (blue lines a–h in Fig. 2b) in the subpolar North Atlantic. The two magenta lines in (g) mark a latitude band (52°–65°N) over which the zonally accumulated water mass transformations are shown in Fig. 15. Both surface cooling (Fig. 13) and interior mixing (Fig. 14) create ribbons of transformations toward lighter water (red) and denser water (blue) in boundary currents and fronts.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Distribution of the modeled 5-yr mean, total diapycnal transformation per unit area (10−6 m s−1) across (a)–(h) eight density surfaces (blue lines a–h in Fig. 2b) in the subpolar North Atlantic. The two magenta lines in (g) mark a latitude band (52°–65°N) over which the zonally accumulated water mass transformations are shown in Fig. 15. Both surface cooling (Fig. 13) and interior mixing (Fig. 14) create ribbons of transformations toward lighter water (red) and denser water (blue) in boundary currents and fronts.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Distribution of the modeled 5-yr mean, total diapycnal transformation per unit area (10−6 m s−1) across (a)–(h) eight density surfaces (blue lines a–h in Fig. 2b) in the subpolar North Atlantic. The two magenta lines in (g) mark a latitude band (52°–65°N) over which the zonally accumulated water mass transformations are shown in Fig. 15. Both surface cooling (Fig. 13) and interior mixing (Fig. 14) create ribbons of transformations toward lighter water (red) and denser water (blue) in boundary currents and fronts.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
As in Fig .12, but for the surface-buoyancy-forced diapycnal transformation per unit area (10−6 m s−1), calculated from the local density flux D in Eq. (3) and surface density. Note that the progression of SPMW convection sites around the subpolar gyre with increasing density is similar to Brambilla et al. (2008).
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
As in Fig .12, but for the surface-buoyancy-forced diapycnal transformation per unit area (10−6 m s−1), calculated from the local density flux D in Eq. (3) and surface density. Note that the progression of SPMW convection sites around the subpolar gyre with increasing density is similar to Brambilla et al. (2008).
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
As in Fig .12, but for the surface-buoyancy-forced diapycnal transformation per unit area (10−6 m s−1), calculated from the local density flux D in Eq. (3) and surface density. Note that the progression of SPMW convection sites around the subpolar gyre with increasing density is similar to Brambilla et al. (2008).
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
As in Fig. 12, but for the interior-mixing-induced diapycnal transformation per unit area (10−6 m s−1); overlaid in contours are the depth of isopycnic surfaces (50, 100, 200, 300, 400 m, respectively). Restratification of deep winter mixed layers by mesoscale eddy mixing creates the red upwelling (warming) regions surrounding convection sites.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
As in Fig. 12, but for the interior-mixing-induced diapycnal transformation per unit area (10−6 m s−1); overlaid in contours are the depth of isopycnic surfaces (50, 100, 200, 300, 400 m, respectively). Restratification of deep winter mixed layers by mesoscale eddy mixing creates the red upwelling (warming) regions surrounding convection sites.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
As in Fig. 12, but for the interior-mixing-induced diapycnal transformation per unit area (10−6 m s−1); overlaid in contours are the depth of isopycnic surfaces (50, 100, 200, 300, 400 m, respectively). Restratification of deep winter mixed layers by mesoscale eddy mixing creates the red upwelling (warming) regions surrounding convection sites.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
As for the subtropics, the patterns of modeled total and mixing-induced transformations FT and FI do not align zonally, and thus the zonally integrated streamfunction underestimates the transformations (discussed in section 4a). To quantify this, we zonally integrate the transformations toward lighter and denser water separately in Fig. 15, across the σ2 density surface of 36.815 (σθ ≈ 27.72) over a swath of subpolar latitudes approximately 52°–65°N (see magenta lines in Figs. 12g, 13g, and 14g). The net transformation FT across this density surface is 10 Sv toward denser water west of 25°W (including the Labrador and Irminger Seas). This transformation is similar to the zonally integrated value in Fig. 2b in this latitude range, and it can be divided into a transformation of 6.1 Sv toward lighter water and 16.1 Sv toward denser water, respectively. Thus, the transformation that is canceled out by the zonal integration (6.1 Sv) has an amplitude that is approximately 60% of the zonally integrated transformation in the AMOC at this level. For the same region, the mixing-induced transformation FI is 2 Sv toward denser water, consisting of transformation of 7.5 Sv toward lighter water and 9.5 Sv toward denser water, respectively (Fig. 15).
Eastward accumulation of the modeled total FT (black), surface-forced FS (green), and interior-mixing-induced FI (orange) transformations across 
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Eastward accumulation of the modeled total FT (black), surface-forced FS (green), and interior-mixing-induced FI (orange) transformations across
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Eastward accumulation of the modeled total FT (black), surface-forced FS (green), and interior-mixing-induced FI (orange) transformations across
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
The transformation toward denser and lighter water in Figs. 14g and 14h is connected with the deep convection and restratification of the LSW, respectively. This (horizontal) mixing-induced transformation takes place in the mixed layer; thus, the pattern is very similar to distribution of wintertime MLD in Fig. 16a. The modeled maximum wintertime MLD in the Labrador Sea is about 2000 m, which is deeper than the value of 1200 m based on the ocean climatology of Schmidtko et al. (2013); it also covers a larger area. However, a large area of MLD as deep as 2400 m has been observed in the Labrador Sea during the early 1990s when wintertime deep convection was particularly intense (e.g., Yashayaev 2007). The corresponding model temperature and salinity across the Labrador Sea along the WOCE line AR7W is shown in Figs. 16b and 16c. The modeled vertical layer structure of the water masses is consistent with the observations (Pickart et al. 2002), but the model salinity is higher than observed (by ~0.04 for LSW). This positive salinity bias exists because the model lacks the input of buoyant low-salinity, cold shelf water that originates from the Arctic Ocean and ice-melt/runoff from Greenland and is observed in the East Greenland Coastal Current (e.g., Bacon et al. 2014). Without this upper-ocean buoyancy resistance, the Labrador Sea in model is more prone to intense deep convection (e.g., Bailey et al. 2005; Hátún et al. 2007).
(a) Modeled average wintertime (March) MLD (m) in the subpolar North Atlantic; the magenta line marks the location of WOCE AR7W line across the Labrador Sea. The corresponding modeled mean (b) potential temperature 
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
(a) Modeled average wintertime (March) MLD (m) in the subpolar North Atlantic; the magenta line marks the location of WOCE AR7W line across the Labrador Sea. The corresponding modeled mean (b) potential temperature
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
(a) Modeled average wintertime (March) MLD (m) in the subpolar North Atlantic; the magenta line marks the location of WOCE AR7W line across the Labrador Sea. The corresponding modeled mean (b) potential temperature
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Eddies play an important role in the transformations toward lighter water (Figs. 14g,h) that mostly surround the Labrador/Irminger Sea convection region, including the narrow boundary current. In the Labrador Sea interior after deep convection, eddies spawned by the baroclinic instability around the edge of newly convected dense water are one of the main mechanisms for restratification. These eddies and filaments can be seen in a snapshot of the modeled temperature in winter (Fig. 17a), and the results are quite similar to those presented in idealized models (e.g., Jones and Marshall 1997; Rousset et al. 2009). In addition, the western Greenland Current becomes unstable near 60°N (Eden and Böning 2002; Brandt et al. 2007). It meanders to the west and often sheds eddies of warm saline Irminger water into the Labrador Sea interior, providing the buoyancy supply for restratification (Hátún et al. 2007). The boundary current instability and associated eddy shedding create an area of high eddy kinetic energy (EKE) near 62°N that can be seen in both the model results and observations (Fig. 17b). The exact location of the modeled high EKE region is slightly to the north and east, compared to the altimetric observations of Lilly et al. (2003). This shift can impact the stratification, deep convection, and water mass transformation in the northwestern Labrador Sea.
(a) A snapshot of modeled potential temperature 
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
(a) A snapshot of modeled potential temperature
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
(a) A snapshot of modeled potential temperature
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
The eddy stirring in model, as evidenced in the snapshot in Fig. 17a, increases the horizontal density gradient and mixing. Where the eddy stirring becomes important can be shown in the eddy density flux. The average magnitude of eddy density flux 
In the rest of this section, we focus on the water mass transformation in two regions of the subpolar North Atlantic: 1) the northwestern Labrador Sea between the WOCE/CLIVAR line AR7W and the Davis Strait and 2) the western Newfoundland Basin.
1) The northwestern Labrador Sea
The water properties and circulation in the Labrador Sea are often observed along the AR7W line (e.g., Pickart et al. 2002; Yashayaev 2007; Pickart and Spall 2007; Hall et al. 2013). The modeled mean velocity across this section is shown in Fig. 18a. The modeled strong boundary currents over the continental slopes, stronger on the Greenland side, and the barotropic (or depth independent) interior recirculation patterns agree well with the observations based on six lowered acoustic Doppler current profiler (LADCP) surveys during 1995–2008 (Hall et al. 2013, their Fig. 5). The barotropic nature of the velocity components in the Labrador Sea has also been documented in Lilly et al. (1999) and Lilly and Rhines (2002) and in Cuny et al. (2005) using moored current-meter data. The modeled time mean overturning streamfunctions 
(a) Modeled mean normal velocity (cm s−1) across the WOCE AR7W line in the Labrador Sea; positive values indicate northwest flows; three cyan lines denote 
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
(a) Modeled mean normal velocity (cm s−1) across the WOCE AR7W line in the Labrador Sea; positive values indicate northwest flows; three cyan lines denote
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
(a) Modeled mean normal velocity (cm s−1) across the WOCE AR7W line in the Labrador Sea; positive values indicate northwest flows; three cyan lines denote
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
The time mean streamfunction 
Modeled 5-yr mean net transport FN and the total FT, surface-forced FS, and mixing-induced FI diapycnal water mass transformations in the northwestern Labrador Sea between the WOCE AR7W line and the Davis Strait. The water masses shown are SPMW, upper and classical Labrador Sea Water (uLSW; cLSW), and NSOW. Blue labels c–h are density surfaces corresponding to panels (c)–(h) in Figs. 12–14.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Modeled 5-yr mean net transport FN and the total FT, surface-forced FS, and mixing-induced FI diapycnal water mass transformations in the northwestern Labrador Sea between the WOCE AR7W line and the Davis Strait. The water masses shown are SPMW, upper and classical Labrador Sea Water (uLSW; cLSW), and NSOW. Blue labels c–h are density surfaces corresponding to panels (c)–(h) in Figs. 12–14.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Modeled 5-yr mean net transport FN and the total FT, surface-forced FS, and mixing-induced FI diapycnal water mass transformations in the northwestern Labrador Sea between the WOCE AR7W line and the Davis Strait. The water masses shown are SPMW, upper and classical Labrador Sea Water (uLSW; cLSW), and NSOW. Blue labels c–h are density surfaces corresponding to panels (c)–(h) in Figs. 12–14.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
It should be noted that the hydrographic data along AR7W line are collected mostly in spring. Thus, it is unclear if or to what extent the results of Pickart and Spall (2007) represent the annual mean. To examine this, the seasonal variability of the modeled net volume transports FN and the water mass transformations FT, FS, and FI is displayed in Fig. 20, corresponding to the annual mean profiles of Fig. 19. The net transport FN does vary on a seasonal time scale, with stronger (weaker) transports across a higher (lower) density in April (December). The average of FN over May–July actually is similar to the annual mean, which implies that the diapycnal streamfunction 
Seasonal variation of the modeled (a) net transport FN and the modeled (b) total FT, (c) surface-forced FS, and (d) mixing-induced FI diapycnal water mass transformations in the northwestern Labrador Sea as shown in Fig. 19. The thick dashed black line denotes the seasonal variation of density surface across which the net transport FN into the region is largest.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Seasonal variation of the modeled (a) net transport FN and the modeled (b) total FT, (c) surface-forced FS, and (d) mixing-induced FI diapycnal water mass transformations in the northwestern Labrador Sea as shown in Fig. 19. The thick dashed black line denotes the seasonal variation of density surface across which the net transport FN into the region is largest.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Seasonal variation of the modeled (a) net transport FN and the modeled (b) total FT, (c) surface-forced FS, and (d) mixing-induced FI diapycnal water mass transformations in the northwestern Labrador Sea as shown in Fig. 19. The thick dashed black line denotes the seasonal variation of density surface across which the net transport FN into the region is largest.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
The above discussion suggests that the 2-Sv diapycnal overturning in Pickart and Spall (2007) should be representative of the annual mean water mass transformation in the northwestern Labrador Sea. However, it is worth pointing out that the 2-Sv overturning of Pickart and Spall (2007) is somewhat at odds with the total LSW production rate based on the observed CFC tracer inventory [11.7 Sv in LeBel et al. (2008)]. Note that the production rate based on tracer inventory, termed ventilation rate in Brandt et al. (2007), can be higher than the formation rate. But the difference is primarily in the upper LSW, which contributes a small part of total LSW [3.5 out of 11.7 Sv in LeBel et al. (2008)]. The repeat LADCP surveys along the AR7W by Hall et al. (2013) show that the volume transport of the eastern boundary current above σθ of 27.74 is 4–5 Sv higher than that of the western boundary current, indicating that the diapycnal transformation in the northwestern Labrador Sea can be higher than 2 Sv. Perhaps some of this disagreement also comes from the neglect of eddy transports between boundary current and interior in the Pickart and Spall (2007) estimate, which argues that much of the water mass transformation occurs within the narrow boundary current. Nevertheless, we believe our model Labrador Sea transformation is too large.
2) The western Newfoundland Basin
Similar to Figs. 19 and 20 for the northwestern Labrador Sea, Figs. 21 and 22 display the mean and the seasonal variability of the net transports FN and the water mass transformations (FT, FS, and FI) in the western Newfoundland Basin, defined as the longitude/latitude range of 55°–35°W, 40°–53°N (Fig. 1). The western Newfoundland Basin is a transition region between the subpolar and subtropical gyres as well as between the upper and lower limb of the AMOC. Significant transformation takes place in this relatively small region: in the surface mixed layer, approximately 8-Sv light water (<35.15 kg m−3) is transformed into denser water of 35.15–36.3 kg m−3. This transformation is mostly surface forced (see Figs. 6h, 7h, and 8h and 12a, 13a, and 14a). Below the mixed layer, about 5-Sv LSW is transformed toward the lighter SPMW density range via interior mixing (Fig. 21). This transformation, opposite to that which takes place in the northwestern Labrador Sea (Fig. 19), closes the modeled local diapycnal overturning cell in subpolar region as seen in Figs. 2a and 3a. On the seasonal time scale, the variation of the overturning density of the FN in the western Newfoundland Basin (Fig. 22a) matches that of FN in the northwestern Labrador Sea (Fig. 17a). As a result, the densities of the modeled maximum overturning streamfunction vary seasonally in the subpolar North Atlantic but are nearly constant south of this transition region. The seasonal variation of the diapycnal transformations in Figs. 22b–d further show that transformation toward lighter water is interior-mixing-induced FI and the transformation toward lighter water is primarily surface-forced FS.
Modeled 5-yr mean net transport FN and the total FT, surface-forced FS, and mixing-induced FI diapycnal water mass transformations in the subpolar–subtropical transition region (55°–35°W and 40°–52°N; see Fig. 1). The upper part shows transformation of the warm water in the North Atlantic Current toward denser water due to (primarily) surface cooling (blue patch in Figs. 7h and 13a); the low part shows the transformation of Labrador Sea Water in the southward deep western boundary current toward lighter water due to interior mixing (red patch in Figs. 14e–g).
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Modeled 5-yr mean net transport FN and the total FT, surface-forced FS, and mixing-induced FI diapycnal water mass transformations in the subpolar–subtropical transition region (55°–35°W and 40°–52°N; see Fig. 1). The upper part shows transformation of the warm water in the North Atlantic Current toward denser water due to (primarily) surface cooling (blue patch in Figs. 7h and 13a); the low part shows the transformation of Labrador Sea Water in the southward deep western boundary current toward lighter water due to interior mixing (red patch in Figs. 14e–g).
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Modeled 5-yr mean net transport FN and the total FT, surface-forced FS, and mixing-induced FI diapycnal water mass transformations in the subpolar–subtropical transition region (55°–35°W and 40°–52°N; see Fig. 1). The upper part shows transformation of the warm water in the North Atlantic Current toward denser water due to (primarily) surface cooling (blue patch in Figs. 7h and 13a); the low part shows the transformation of Labrador Sea Water in the southward deep western boundary current toward lighter water due to interior mixing (red patch in Figs. 14e–g).
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Seasonal variation of the modeled (a) net transport FN and the modeled (b) total FT, (c) surface-forced FS, and (d) mixing-induced FI diapycnal water mass transformations in the subpolar–subtropical transition region (55°–35°W and 40°–52°N). The dashed white line denotes the density seasonal variation of density surface across which the net transport FN out of the region is largest.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Seasonal variation of the modeled (a) net transport FN and the modeled (b) total FT, (c) surface-forced FS, and (d) mixing-induced FI diapycnal water mass transformations in the subpolar–subtropical transition region (55°–35°W and 40°–52°N). The dashed white line denotes the density seasonal variation of density surface across which the net transport FN out of the region is largest.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Seasonal variation of the modeled (a) net transport FN and the modeled (b) total FT, (c) surface-forced FS, and (d) mixing-induced FI diapycnal water mass transformations in the subpolar–subtropical transition region (55°–35°W and 40°–52°N). The dashed white line denotes the density seasonal variation of density surface across which the net transport FN out of the region is largest.
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Detailed circulation pattern and model layer structure are examined in Fig. 23 to illustrate how the diapycnal transformation toward lighter water takes place in the Newfoundland Basin. Figures 23a and 23b show zoomed transformation distribution across the density surface 36.752, along with the transport vectors per unit width for the warm water above and for the LSW below. The full-water column meridional velocity and the diapycnal transformation along 47°N are shown in Figs. 23c and 23d. The results show that the transformation takes place between the southward-flowing deep western boundary current (DWBC) and the northward-flowing North Atlantic Current (NAC). This diapycnal transformation occurs in the model domain where the vertical coordinate is fixed (i.e., level and nonisopycnic) and that is below the wintertime mixed layer depth. Thus, one can expect numerically induced diapycnal mixing (when in nonisopycnic space), and it will be a function of the model vertical configuration and horizontal mixing parameterization (Griffies et al. 2000). Observations do show intensified vertical mixing in the western boundary current near 47°N (Walter et al. 2005), and the modeled circulation pattern along 47°N as shown in Fig. 23c is very similar to observations (Mertens et al. 2014). Since we cannot easily differentiate between physical and numerically induced mixing in this area, one cannot be certain if significant diapycnal mixing actually occurs between the DWBC and the NAC in the real ocean. It is known, however, that isopycnal mixing between the DWBC and the NAC occurs in this region, which explains the different oxygen content between the NAC and its upstream source water in the Gulf Stream (Clarke et al. 1980). The LSW south of the Newfoundland Basin is also warmer and saltier than its upstream source in the Labrador Sea (LeBras et al. 2017).
Modeled time mean mixing-induced diapycnal transformation (10−6 m s−1) across 
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Modeled time mean mixing-induced diapycnal transformation (10−6 m s−1) across
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
Modeled time mean mixing-induced diapycnal transformation (10−6 m s−1) across
Citation: Journal of Physical Oceanography 48, 10; 10.1175/JPO-D-17-0223.1
5. Summary and discussion
The Atlantic meridional overturning circulation (AMOC) is a fundamental element in Earth’s climate, being responsible for a large amount of heat and freshwater transports. The essence of AMOC and the associated heat/freshwater transports lies in the diapycnal transformation of the warm saline water in the upper limb into the cold fresh North Atlantic Deep Water (NADW) in the lower limb in the North Atlantic (as well as the transformation toward lighter water in other basins to close the cycle). Many studies have examined the transformation in the North Atlantic that is forced by the surface buoyancy fluxes, using the thermodynamic framework of Walin (1982) and Speer and Tziperman (1992). Interior mixing can also induce diapycnal water mass transformation, yet basic questions, such as to what extent the water mass transformation is surface forced, where and how the mixing-induced transformation becomes important, remain largely unanswered.
This study maps the three-dimensional structure of the total and surface-forced transformations in the upper North Atlantic Ocean (with their difference interpreted as transformation due to interior mixing). Using high-resolution numerical results that have been shown to represent quite well the large-scale AMOC and subtropical/subpolar gyres in the North Atlantic, we show the following:
Strong transformation toward denser water takes place seamlessly from the subtropical to subpolar North Atlantic, first along the western boundary current system of the Florida Current, the Gulf Stream, and the North Atlantic Current and then along the cyclonic subpolar gyre from the polar front toward the Iceland basin, around the Reykjanes Ridge and Greenland, and into the Labrador Sea. A large part of the transformation is forced directly by the surface buoyancy loss along the northward pathway of the upper AMOC limb and is captured in the framework of Walin (1982). Surface-forced transformation also occurs in warming of upwelled cold water near West Africa.
Mixing plays a significant role in diapycnal transformation in several regions:
In the southern part of subtropical gyre, 4.7-Sv Subtropical Mode Water (SPTW) is transformed into lighter water along a basinwide rim between 15° and 30°N (Fig. 8). This transformation is due to horizontal diffusive mixing in the southwestward Sverdrup flow in the wintertime mixed layer before it is subducted into the isopycnic domain (Figs. 9 and 10).
In the northwestern Labrador Sea, lateral mixing within the deep mixed layer transforms about 5-Sv SPMW into LSW and about 4 Sv of dense cLSW (that was transformed by surface buoyancy fluxes) into lighter cLSW (Fig. 18). Eddies play an important role in stirring warm water into the convected region and increasing the horizontal mixing.
In the western Newfoundland Basin, horizontal mixing between DWBC and NAC transforms about 5-Sv LSW toward lighter water. This mixing occurs along nonisopycnic coordinates below the wintertime mixed layer and is the result of numerical mixing when in level space.
The patterns of diapycnal transformations toward lighter/denser water are not zonal. Thus, the zonally integrated, two-dimensional representation of the meridional overturning streamfunction with respect to density and latitude underestimates the total diapycnal transformation: In the southern subtropical gyre, the transformation of STMW is about 4.7 Sv, nearly 50% higher than the zonal integration value of 3.2 Sv (Fig. 11). In the western subpolar North Atlantic, the transformation in the LSW regime is about 16 Sv, 60% higher than the zonally integrated value of 10 Sv (Fig. 15).
Despite a history of intensive observations in the North Atlantic, it remains a challenge to map the structure of water mass transformations observationally. The understanding of the diapycnal water mass transformation has been limited mostly to those based on hydrographic sections (e.g., Lumpkin and Speer 2003; Lumpkin et al. 2008) and tracer measurements (e.g., LeBel et al. 2008), which are often temporally too sparse to represent the time-mean transformation and/or do not provide spatial details. In the recent observations such as the Rapid Climate Change (RAPID) program (e.g., Cunningham et al. 2007), the focus is the zonally integrated volume transports without spatial distribution (of both transports and water properties). Further measurements of both volume transports and water properties along key sections, such as the newly implemented Overturning in the Subpolar North Atlantic Program (OSNAP; Lozier et al. 2017) are essential to our understanding of the water mass transformation and to determine if the modeled transformations are realistic.
Acknowledgments
XX and EPC are supported by the NOAA Climate Program Office MAPP Program (Award NA15OAR4310088) and the NSF Physical Oceanography Program (Award 1537136). PBR is supported by the NASA Ocean Surface Topography Science Team Program. The numerical simulations were performed on supercomputers at the Navy DoD Supercomputing Resource Center, Stennis Space Center, Mississippi, using computer time provided by the U.S. DoD High Performance Computing Modernization Program.
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