## 1. Introduction

Labrador Sea Water (LSW) is one of the main mode waters in the North Atlantic Ocean (Lazier 1973; Lazier et al. 2002). It is formed in winter by deep convection (Clarke and Gascard 1983; Lab Sea Group 1998) and facilitated by the harsh climatic conditions in this region and the regional ocean circulation (Marshall and Schott 1999). It spreads southward and eastward into the North Atlantic Ocean and beyond, where it partly sets the density structure at intermediate depths (Bower et al. 2009). As such, it also contributes to the variability in the global meridional overturning circulation (Eden and Willebrand 2001; Yashayaev 2007; Biastoch et al. 2008).

Besides wintertime atmospheric conditions, one of the key processes that determine the interannual and interdecadal variability of LSW formation (Dickson et al. 1996; Lazier et al. 2002; Kieke et al. 2007; Yashayaev 2007) is restratification after deep convection.^{1} The process is governed both by warming due to solar radiation in summer and lateral influx of heat from the boundary current. On average, about 60% of the total annual heat input over the upper 1600 m is provided by lateral heat fluxes (Yashayaev and Loder 2009), but solar radiative warming is limited to the upper 200 m (Straneo 2006a). Furthermore, the fact that restratification already starts when the atmosphere is still cooling the ocean in early spring (generally in April) (Lilly et al. 1999; Avsic et al. 2006; Yashayaev and Loder 2009) and that it occurs rapidly over a large depth (Lilly et al. 1999; Avsic et al. 2006) indicates an important role of lateral heat fluxes in restratification. In this study we therefore focus on the dynamics of the oceanic part of restratification (lateral fluxes) by ignoring solar radiative forcing.

The characteristics of the boundary current strongly affect restratification. Lateral fluxes (Fig. 1a) adjust the water properties in the central Labrador Sea toward the properties of the very buoyant boundary current (Straneo 2006a). The boundary current water on the shelf is of Arctic origin and is hence cold and fresh. On the continental slope, it is of subtropical origin and therefore relatively warm and saline. Both water masses supply low-density water to the interior Labrador Sea.

Early studies on restratification after deep convection focused on the efficiency of buoyancy exchange across a front (e.g., Jones and Marshall 1993; Maxworthy and Narimousa 1994; Jones and Marshall 1997; Legg et al. 1998). At the front surrounding the convection area, a rim current develops, which becomes baroclinically unstable and generates small eddies with a size on the order of the Rossby deformation radius. These eddies exchange properties across the front and restratify the convection area. As they are formed as a result of deep convection, we will refer to them as convective eddies (CEs), following Chanut et al. (2008).

After the Labrador Sea Experiment in the 1990s (Lab Sea Group 1998), it became clear that the boundary current acts as a major source of buoyancy for the replenishment of the dense water mass in the convected area (Lilly et al. 2003). The buoyant water is brought into the interior by lateral eddy fluxes (Spall 2004; Katsman et al. 2004; Straneo 2006b), whereas the dense convected water is exported out of the Labrador Sea in the boundary current (Straneo 2006b; Brandt et al. 2007).

This process is captured in a conceptual model by Straneo (2006b). With this model, the restratifying effect of eddies originating from the boundary current was investigated. The results of the conceptual model agree nicely with in situ measurements, indicating that restratification in the interior Labrador Sea is indeed primarily caused by eddy-driven interior–boundary current exchange. However, Straneo (2006b) did not distinguish between the contributions of different eddy types to the exchange.

There are two distinct pathways by which eddies may flux buoyancy from the boundary current into the interior. The first mechanism is a buoyancy flux associated with baroclinic eddies that form at the density front between the warm boundary current and the cold interior. Like CEs, the size of these eddies is on the order of the Rossby radius of deformation, but, contrary to CEs, these eddies are present year-round. Following Chanut et al. (2008), this eddy type will be referred to as boundary current eddies (BCEs).

Second, large eddies (15–30-km radius) are shed from the boundary current along the west coast of Greenland (Fig. 1a). These eddies are referred to as Irminger rings (IRs) because of their warm and saline Irminger Water cores (Lilly and Rhines 2002; Lilly et al. 2003; Hatun et al. 2007). The formation of these eddies is triggered by a steepening of the slope along a portion of the western Greenland coast (Bracco and Pedlosky 2003; Wolfe and Cenedese 2006) (Fig. 1a). At the downstream end of this steep slope a large eddy kinetic energy (EKE) signal is detected (Prater 2002; Lilly et al. 2003; Brandt et al. 2004). IRs form spontaneously in model simulations configured with such a steep slope (Eden and Böning 2002; Katsman et al. 2004; Chanut et al. 2008), whereas their formation can be suppressed by defining a more gentle slope for the simulation (Katsman et al. 2004; Chanut et al. 2008). Although IRs are only formed in a localized region in the eastern side of the basin, the eddies are very energetic and long lived (Lilly et al. 2003). They travel southwestwards into the Labrador Sea interior, allowing them to bring buoyant boundary current water to the area of deep convection.

The possibility to eliminate IRs from a model simulation by changing the bathymetry pattern allows a systematic investigation of their role in restratification. Katsman et al. (2004) performed two 6-month spindown simulations of the restratification season in the Labrador Sea, one with and one without IRs, in an idealized regional configuration. Based on the very slow restratification in the case were IRs were absent, it was concluded that these eddies were the dominant contributors to restratification in this area. The authors only considered the contribution of CEs and IRs, however, because the boundary current was too stable for BCEs to form. Chanut et al. (2008) used two 10-yr equilibrium simulations in a realistic configuration to investigate the effects of CEs, BCEs, and IRs on restratification. In contrast to Katsman et al. (2004), they concluded that BCEs make the dominant contribution. Because both of their simulations reached a quasi-equilibrium state, with wintertime convection and restratification over summer and with a similar lateral heat flux into the interior, the authors concluded that the presence of IRs is not crucial for restratification.

However, the two equilibria in the Chanut et al. (2008) study are very different. Because at least one of the equilibria does not resemble the actual situation, the observation that the heat flux into the interior is the same does not justify conclusions on the lateral heat flux mechanisms in the real Labrador Sea. Instead, simulations of a single restratification season can be started from the same realistic end-of-winter state. The efficiency of different eddy types can be assessed by their ability to adjust this end-of-winter state to a realistic end-of-summer state within one restratification season. In this study, we use this approach to address the question as to which eddy type dominates the lateral heat flux, and we explain the opposing conclusions from previous studies.

The model configuration used in this study is described in section 2, as well as the initial state of the model fields, the general characteristics during the spindown simulations, and a description of the simulated cases. In section 3, the model results are discussed with respect to the rate of restratification. In section 4, scalings are derived for the time scale of restratification for the different eddy types, which are used in section 5 to compare the results from this study with results from earlier work. A summary of the results and conclusions is given in section 6.

## 2. Model and initial state

In this study, we used an idealized regional model for the Labrador Sea, which is discussed below. Despite its simplicity, the model reproduced the hydrographic properties and the eddy field in the Labrador Sea well. To assess the effect of the different eddy types on restratification, three spindown simulations were performed where one or more eddy types were eliminated.

### a. Model configuration

The simulations in this study were performed with the Massachusetts Institute of Technology (MIT) primitive equation model (Marshall et al. 1997) in an idealized regional configuration for the Labrador Sea (Fig. 1b). The configuration was similar to the one used in Katsman et al. (2004), but the basin shape was improved and the location of the convection area was, more realistically, in the southwestern Labrador Sea.

The basin (Fig. 1b and Table 1) had a maximum depth of 3000 m, which decreased toward the boundaries to form a slope along the perimeter of the basin. Possible interactions with the Arctic via the Davis Strait have been neglected, and deep boundary currents and the continental shelves were omitted. Note the steepening of the slope along the west coast of Greenland, which has been shown to be essential for the shedding of IRs (section 1). The horizontal grid spacing was 3.75 km in both zonal and meridional directions. This is well below the Rossby radius of deformation (about 7 km in this area) so that the model is eddy resolving. In the vertical, the model consisted of 15 layers with layer thickness ranging from 100 m in the upper layers to 450 m near the bottom. In the simulations, only the influence of temperature was assessed, neglecting the role of salinity for simplicity. A linear equation of state *ρ* = *ρ*_{0}(1 − *αT*) was used, with a reference density *ρ*_{0} and a constant thermal expansion coefficient *α*. The use of a linear equation of state with temperature alone can be justified because the density of seawater is temperature dominated in the restratification season. The values of parameters used in the numerical simulations are given in Table 1.

Standard parameter values.

*T*

_{ref}(

*z*) is the temperature profile at the start of the spinup (based on the average density profile from a summer occupation over the southwestern part of the World Ocean Circulation Experiment (WOCE) AR7W hydrographic section; Katsman et al. 2004). The density difference across the boundary current Δ

*ρ*and the boundary current width

*L*determine the maximum boundary current velocity. The term

_{y}*z*is the bottom depth, and

_{b}*y*

_{0}is the meridional position of the maximum current speed, measured in distance from the south coast of Greenland. The term

*g*is the acceleration due to gravity, and

*f*is the Coriolis parameter. The parameter values (Table 1) were chosen such that the resulting boundary current has the properties seen in the AR7W hydrographic observations. The total transport in the boundary current was 17 Sv (1 Sv ≡ 10

^{6}m

^{3}s

^{−1}), in line with observational estimates (Cuny et al. 2002; Dengler et al. 2006; Fischer et al. 2010) (not taking into account deep currents associated with overflow waters not represented in this model). The maximum current velocity is 0.56 m s

^{−1}, which is in good agreement with the observed velocity over the upper continental slope from surface drifter measurements (Cuny et al. 2002).

The use of open boundaries has been avoided by directing the boundary current behind an artificial island in the southeast of the domain, from the southern Labrador coast back to the restoring region south of Greenland (cf. Spall 2007). One IR bounced against this artificial island in one of the simulations, but because this was far away from the convection region it did not noticeably influence the results. The restoring conditions induce a continuous warming of the basin, but this is small over the limited period of the restratification season (0.06°C averaged over the interior basin in 6 months). The restoring conditions are the only forcing in the model; no surface fluxes are applied in any of the simulations.

### b. Setting the initial state

Earlier idealized model studies of restratification after deep convection (Jones and Marshall 1997; Send and Käse 1998; Katsman et al. 2004) prescribed a convection region by specifying the initial density field in their simulations and an ocean at rest. However, these studies did not consider the effect of the presence of a boundary current. To do so, it is necessary to perform a spinup simulation first to let the warm boundary current encircle the basin and to let the eddy field develop. Once the circulation has spun up, the density field can be altered offline to prescribe a convection region representing the situation at the end of winter. In this way, all simulations of the restratification season can be started from nearly^{2} the same conditions.

Figure 2 shows a zonal cross section of the temperature and meridional velocity at y = 1150 km averaged over the last month of the spinup phase. Because the influence of salinity is neglected, the low density of the cold and fresh surface waters is represented as a warm top layer. The boundary current flows northward along the west coast of Greenland and returns on the Canadian side in southern direction. The southward-flowing boundary current in the west is much weaker and wider and has lost part of its heat to the interior because of eddy activity. On both sides of the basin, the density and velocity structure of the boundary current compare favorably with observations (Cuny et al. 2002; Pickart and Spall 2007).

Zonal cross section of the basin at *y* = 1150 km, time averaged over the last month of the 6-month spinup phase. Temperature (°C) is shaded in color and the meridional velocity is overlaid (contour interval is 0.1 m s^{−1}; dashed represents southward flow). The Canadian (Greenland) side is on the left (right).

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

Zonal cross section of the basin at *y* = 1150 km, time averaged over the last month of the 6-month spinup phase. Temperature (°C) is shaded in color and the meridional velocity is overlaid (contour interval is 0.1 m s^{−1}; dashed represents southward flow). The Canadian (Greenland) side is on the left (right).

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

Zonal cross section of the basin at *y* = 1150 km, time averaged over the last month of the 6-month spinup phase. Temperature (°C) is shaded in color and the meridional velocity is overlaid (contour interval is 0.1 m s^{−1}; dashed represents southward flow). The Canadian (Greenland) side is on the left (right).

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

After the spinup phase, an idealized convection region was constructed synthetically by altering the temperature field of the final state of the spinup simulation offline. The prescribed convection region (Fig. 1b) has a spatially varying mixed layer in the shape of a skewed cone, with characteristics similar to the end-of-winter data published by Pickart et al. (2002) (their Fig. 12d, reproduced in Fig. 1a). At each grid point inside the skewed cone, the temperature throughout the mixed layer is set equal to the temperature found at the base of the local prescribed mixed layer. The temperature field outside the convection region is unaltered (Fig. 3).

The convection area in the model, constructed based on end-of-winter data (see Fig. 1) in the form of a skewed cone. (a) Plan view, grayscale is temperature above 5.4°C. The IR signals are clearly visible in the northeast. (b) Zonal cross section at *y* = 700 km, contours indicate temperature (°C).

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

The convection area in the model, constructed based on end-of-winter data (see Fig. 1) in the form of a skewed cone. (a) Plan view, grayscale is temperature above 5.4°C. The IR signals are clearly visible in the northeast. (b) Zonal cross section at *y* = 700 km, contours indicate temperature (°C).

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

The convection area in the model, constructed based on end-of-winter data (see Fig. 1) in the form of a skewed cone. (a) Plan view, grayscale is temperature above 5.4°C. The IR signals are clearly visible in the northeast. (b) Zonal cross section at *y* = 700 km, contours indicate temperature (°C).

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

We also studied the dependence of the restratification rate on the chosen shape of the convection area. The density gradient across the front was varied by changing the shape from a cone toward a cylinder. For a wide range of the two parameters varied (mixed layer depths between 0.75 and 1.5 times the standard mixed layer depth and frontal density gradients between 0.2 and 4 times the standard density gradient), the final conclusions on the roles of the three eddy types in restratification after deep convection (which are discussed in the remainder of the paper) remain the same.

### c. The eddy field

*V*

_{EKE}calculated from the model velocity fields, as an average over the 6 months of the spindown simulation according to

Surface eddy speed *V*_{EKE} averaged over the 6-month spindown simulation (cm s^{−1}). The field is smoothed with a two-dimensional three-point boxcar filter.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

Surface eddy speed *V*_{EKE} averaged over the 6-month spindown simulation (cm s^{−1}). The field is smoothed with a two-dimensional three-point boxcar filter.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

Surface eddy speed *V*_{EKE} averaged over the 6-month spindown simulation (cm s^{−1}). The field is smoothed with a two-dimensional three-point boxcar filter.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

*V*

_{EKE}as inferred from satellite observations (their Fig. 24). In their altimetry analysis as well as in our model, the maximum

*V*

_{EKE}is found at the location where IRs are shed. From there, the signal fans out in a southwesterly direction and then decays in a southerly direction, broadly indicating the path of the IRs that travel into the basin interior (8 IRs followed this pathway in our 6-month spindown simulation). The somewhat higher values in the model compared to the altimetry-based estimate are likely because of the processing of the altimeter data involving some smoothing that can lead to an underestimation of the EKE maximum. The secondary EKE maximum around

*x*= 500 km and

*y*= 650 km may be the footprints of individual eddies, an effect of the relatively short averaging period. However, a secondary maximum was also reported by Lilly et al. (2003) at this location. Overall, the pattern is in good agreement with observations.

Further support for the realism of the eddy field may be obtained by comparing the characteristics of the model-generated eddies with observations. However, CEs and BCEs are too small to be captured by satellite altimetry, and they are only occasionally sampled by a mooring (Lilly et al. 2003). On IRs, more data are available, both remotely observed by satellites and in situ in mooring records (Lilly et al. 2003), in glider and float records (Prater 2002; Hatun et al. 2007), and occasionally in the World Ocean Circulation Experiment (WOCE) AR7W hydrographic sections (Rykova et al. 2009). Their characteristics can be compared with the model results in more detail.

The IRs in the model are traced by eye from their surface temperature and sea surface elevation signal. In line with observations (Lilly et al. 2003; Prater 2002), most IRs are anticyclonic, but some dipoles and cyclonic features have been observed as well. The maximum velocity in the IRs ranges between 0.4 and 0.8 m s^{−1}, occasionally reaching 0.95 m s^{−1} when just shed off. These results are in excellent agreement with the 0.3–0.8 m s^{−1} range obtained by Lilly et al. (2003). The radius of the model-generated eddies, defined by the distance between its center and the velocity maximum, ranges between 15 and 27 km, again in good agreement with the 15–30 km found by Lilly et al. (2003). As an example, Fig. 5 shows the meridional velocity and temperature profile in a cross section of a representative IR from our model simulation. Its properties are in good agreement with available data (Lilly et al. 2003; Hatun et al. 2007; Rykova et al. 2009), recalling that the density in our model is temperature dependent only. The surface intensification and weakening of the currents below 500–700-m depth is also well reproduced.

Zonal cross section of an example IR from the model (*y* = 630 km and *t* = 3 months; see Fig. 6, top right): (a) meridional velocity (contour interval is 0.25 m s^{−1}) and (b) temperature (contour interval is 0.5°C).

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

Zonal cross section of an example IR from the model (*y* = 630 km and *t* = 3 months; see Fig. 6, top right): (a) meridional velocity (contour interval is 0.25 m s^{−1}) and (b) temperature (contour interval is 0.5°C).

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

Zonal cross section of an example IR from the model (*y* = 630 km and *t* = 3 months; see Fig. 6, top right): (a) meridional velocity (contour interval is 0.25 m s^{−1}) and (b) temperature (contour interval is 0.5°C).

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

### d. Setup of the simulations

Now that we have confidence in our model performance, we can describe three simulations designed to isolate the effects of different eddy types (Table 2). The first case, referred to as ALL_IN, includes all three eddy types discussed in section 1 and is hence the most realistic one (Figs. 2–5 were obtained from this simulation). In the second case, NO_IR, the formation of IRs is suppressed using a bathymetry with a wider slope along the west Greenland coast (Katsman et al. 2004). The effect of IRs on restratification can be assessed by comparing the ALL_IN case with the NO_IR case. The restratifying effect of CEs can be studied from the third case, NO_BC, where the boundary current itself is left out so that both IRs and BCEs are eliminated. The effect of BCEs on restratification may be analyzed by comparing the NO_BC case with the NO_IR case.

Overview of three cases that are studied and the eddy types resolved in these simulations (+ indicates resolved, − indicates not resolved).

## 3. Restratification after deep convection

The results of the three spindown simulations are discussed by first analyzing the evolution of the heat content in the convection area. Next, the amount of LSW exported by the boundary current is discussed.

The evolution of the sea surface temperature may be used as an initial indicator of how the three eddy types act to restratify. It is displayed in Fig. 6 for the three cases listed in Table 2, after 3 months and after 6 months in the simulations. The restratifying effect of the CEs alone (left panels) is clearly insufficient to warm up the Labrador Sea in half a year. The NO_IR case (middle panels) shows stronger surface warming, but the warming is not fast enough. The center of the convection area is only starting to gain some heat after half a year. When IRs are present (right panels), the surface rapidly warms, suggesting fast restratification of the Labrador Sea within 6 months. Also, in the right panels, more violent mixing takes place: after 3 months the blue patch is already diluted. The mixing is caused by the high stirring rate of the IRs (see also Fig. 9, which shows the concentration of a passive tracer that was initialized in the convection area only). They break up the convection area and mix on the large scale. It is likely that BCEs and CEs play a role in mixing to smaller scales and disintegrating the coherent IRs.

Snapshot of the surface temperature field (°C) for the three different cases, (left) NO_BC, (middle) NO_IR, and (right) ALL_IN, for (top) *t* = 3 months and (bottom) *t* = 6 months.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

Snapshot of the surface temperature field (°C) for the three different cases, (left) NO_BC, (middle) NO_IR, and (right) ALL_IN, for (top) *t* = 3 months and (bottom) *t* = 6 months.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

Snapshot of the surface temperature field (°C) for the three different cases, (left) NO_BC, (middle) NO_IR, and (right) ALL_IN, for (top) *t* = 3 months and (bottom) *t* = 6 months.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

The importance of IRs for restratification is confirmed by the evolution of temperature with depth at the center of the convection area for the NO_IR case (Fig. 7a) and the ALL_IN case (Fig. 7b). Without IRs, the first signs of warming can be observed after 3–4 months, but the effect is very shallow and weak. In contrast, when IRs are present, the warming already starts after 1.5 months. This is in line with in situ data (Lilly et al. 1999; Avsic et al. 2006). Figures 6 and 7 thus point toward a dominant role of IRs in the restratification process. In the following, these results will be supported quantitatively.

Time series of the temperature evolution averaged over an area in the center of the convection area (x = 350–450 km, y = 825–925 km) for (a) the NO_IR case and (b) the ALL_IN case. Contours are plotted every 0.1°C.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

Time series of the temperature evolution averaged over an area in the center of the convection area (x = 350–450 km, y = 825–925 km) for (a) the NO_IR case and (b) the ALL_IN case. Contours are plotted every 0.1°C.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

Time series of the temperature evolution averaged over an area in the center of the convection area (x = 350–450 km, y = 825–925 km) for (a) the NO_IR case and (b) the ALL_IN case. Contours are plotted every 0.1°C.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

### a. Heat content change of the convection area

*ρ*

_{0}is a reference density,

*c*the heat capacity, and

_{p}*T*(

*x*,

*y*,

*z*,

*t*) is the instantaneous temperature at a certain location in the convection area. The integral is over the volume of the initial convection cone (Figs. 1b, 3).

Figure 8 shows the evolution of the heat deficit Δ*H*(*t*), normalized by its initial value. The CEs replenish 25% of the initial heat deficit within 6 months. BCEs add another 5% to this, whereas IRs are able to restratify another 45%. At the end of the ALL_IN simulation, about 75% of the initial heat deficit is replenished. Note that the effect of the BCEs and IRs on the heat content includes export of LSW out of the convection area by the boundary current, which is discussed below.

Heat content deficit of the convection area normalized by its initial value. The latter is defined as the reduction in the heat content that arises from the construction of the convection area (section 2b). A zero heat content anomaly implies that the heat content of the convected cone has become exactly equal to the heat content of a cone before convection. The solid line represents ALL_IN, the dashed line represents NO_IR, and the dashed–dotted line represents NO_BC.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

Heat content deficit of the convection area normalized by its initial value. The latter is defined as the reduction in the heat content that arises from the construction of the convection area (section 2b). A zero heat content anomaly implies that the heat content of the convected cone has become exactly equal to the heat content of a cone before convection. The solid line represents ALL_IN, the dashed line represents NO_IR, and the dashed–dotted line represents NO_BC.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

Heat content deficit of the convection area normalized by its initial value. The latter is defined as the reduction in the heat content that arises from the construction of the convection area (section 2b). A zero heat content anomaly implies that the heat content of the convected cone has become exactly equal to the heat content of a cone before convection. The solid line represents ALL_IN, the dashed line represents NO_IR, and the dashed–dotted line represents NO_BC.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

### b. Export of LSW by the boundary current

Export of LSW by the boundary current may be a nonnegligible factor in restratification (Brandt et al. 2007). Simulations in which a passive tracer was added inside the convective cone illustrate this process (Fig. 9). The panels show the depth-averaged tracer concentration after 6 months. Because the NO_BC case has no boundary current, the spreading of the passive tracer is entirely due to CEs.

Depth-averaged concentration of a passive tracer after 6 months in the spindown simulations (a) NO_BC, (b) NO_IR, and (c) ALL_IN. The tracer was initialized to 1 inside the convected area and to 0 in the remainder of the domain.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

Depth-averaged concentration of a passive tracer after 6 months in the spindown simulations (a) NO_BC, (b) NO_IR, and (c) ALL_IN. The tracer was initialized to 1 inside the convected area and to 0 in the remainder of the domain.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

Depth-averaged concentration of a passive tracer after 6 months in the spindown simulations (a) NO_BC, (b) NO_IR, and (c) ALL_IN. The tracer was initialized to 1 inside the convected area and to 0 in the remainder of the domain.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

In the NO_IR case, some of the LSW is exported by the boundary current, which is indicated by the blue tongue extending southward. In our model simulation, 1.6% of the LSW was transported southward past the *y* = 200 km line within 6 months. In the ALL_IN case about 6.7% of the convected water is exported in the boundary current. We hypothesize that this is due to the substantial stirring by IRs, which increases the interaction with the boundary current. The export in the ALL_IN case is equivalent to 1 Sv, in good agreement with the amount of overturning related to the convectively transformed waters formed in the interior (Pickart and Spall 2007). Brandt et al. (2007) reported an export of newly ventilated water of about 9 Sv, but a substantial part of this is formed in the boundary current itself (see their Figs. 1a, 11b). Note also that the export rate shows a large interannual variability and that single-year simulations such as the ones in Brandt et al. (2007) and this study will not cover the whole range. Notwithstanding this uncertainty, the model results indicate that the LSW formed in the interior gives a minor contribution to the total export, as can be expected for a simulation in which convection in the boundary current is absent.

The tracer studies also shed some light on the notably small difference between the restratification rate in the NO_BC case and the NO_IR case. In the case without a boundary current, restratification is expected to be very slow, which is supported by the model results (Fig. 8). Simply adding a warm boundary current without the Irminger rings (NO_IR), however, has little effect (unless the convection area is unrealistically large and immediately adjacent to the boundary current throughout the whole Labrador Sea; not shown). The stirring by the Irminger rings, which act as a catalyst, is thus essential for the boundary current to be truly effective on restratification.

## 4. Restratification time scale

To generalize the results of the numerical simulations, we derive relevant scaling relations for the time it takes to restratify the convection area. This also allows for a direct comparison with observations. Moreover, it provides a framework for an objective discussion of the discrepancies between previous studies (section 5). Jones and Marshall (1997) derived a restratification time scale for a cylinder-shaped convection area with a constant ambient stratification, where only CEs restratified. Here, we extend their analysis by including cone-shaped convection areas. We also derive time scales for restratification by BCEs and IRs. For simplicity, we consider a symmetric cone-shaped convection area rather than the skewed shape used in the model simulations (Figs. 1b, 3). Furthermore, the stratification is assumed to be constant with depth as in Jones and Marshall (1997). A schematic with the definitions used in this section is given in Fig. 10.

Definitions of the variables used in the derivations of the restratification time scales in section 4a.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

Definitions of the variables used in the derivations of the restratification time scales in section 4a.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

Definitions of the variables used in the derivations of the restratification time scales in section 4a.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

### a. Derivation of restratification time scales

*V*

_{cone}is the volume of the cone-shaped convection area,

**n**is the normal unit vector, and

*h*is the maximum depth of the convection area. The eddy buoyancy flux is parameterized as

*c*is a dimensionless eddy efficiency coefficient, Δ

_{e}*b*(

*r*,

*z*) is the buoyancy difference between the convection area and the ambient fluid as a function of depth and radial position (see appendix A), and

*u*

_{0}is the rim current velocity. The latter may be estimated from the thermal wind balance (Jones and Marshall 1997). Combining Eqs. (4) and (5) (appendix A) yields the restratification time scale for CEs only,

*f*is the Coriolis parameter,

*R*

_{max}is the radius of the cone-shaped convection area at the surface, and

*N*

_{bg}is the buoyancy frequency based on the ambient background stratification.

*N*

_{bg}replaced by the stratification of the boundary current

*N*

_{bc}. If the convection area is smaller than the whole basin, as is the case in the Labrador Sea, BCEs exchange heat between the boundary current and the interior, thereby warming up the interior basin. This induces a sharper front around the convection area, which is now surrounded by warmer water. Thus, they enhance the effect of CEs. We define the stratification as

^{3}due to the influx of boundary current water (having stratification

*ϵ*(0 <

*ϵ*≤ 1). If we assume that the heat that is brought into the interior from the boundary current is uniformly distributed and therefore available at the edges of the convection region, we obtain a restratification time scale for the combination of CEs and BCEs (appendix B),

*τ*

_{CE+BCE}<

*τ*

_{CE}.

*f*

_{IR}of such an event,

*r*

_{IR}is the radius of the ring, Δ

*b*

_{IR}(

*z*) is its buoyancy anomaly (see appendix C), and

*h*

_{eff}is the effective depth over which IRs restratify. The effective depth is introduced because most eddies will encounter a part of the cone with a mixed layer depth smaller than

*h*, because

*h*

_{eff}=

*h*/3). This yields a restratification time scale for IRs (appendix C),

#### The eddy efficiency coefficient *c*_{e}

_{e}

The main unknown in the scalings above is the eddy efficiency coefficient *c _{e}*, a measure for the rate at which baroclinic eddies transport buoyancy across a baroclinically unstable front. Estimates for

*c*, based on theoretical reasoning, numerical simulations, and laboratory experiments, mostly vary in the range 0.02 <

_{e}*c*< 0.04 (Visbeck et al. 1996; Jones and Marshall 1997; Spall and Chapman 1998). Larger estimates are also found in a theoretical upper bound of

_{e}*c*= 0.045 (Spall and Chapman 1998), an estimate of

_{e}*c*≈ 0.08 by Haine and Marshall (1998), and an order of magnitude larger estimate (Legg et al. 1996) based on a quasigeostrophic model. The eddy efficiency coefficient in the NO_BC simulation is

_{e}*c*= 0.02, calculated based on the mean lateral eddy fluxes across the edge of the convected cone by CEs. This is on the lower side of the range found in previous studies, because in our cone-shaped convection area the density change across the front is not as large as in those studies.

_{e}### b. Observation-based restratification time scales

The restratifying effect of the three eddy types in this area can roughly be estimated using the scalings derived in section 4a and using representative values for the Labrador Sea. In this section, the restratification time scales are calculated from observed hydrographic properties of the Labrador Sea. In addition, the scalings are applied to values based on the model configuration and compared to the simulations results (Table 3).

Restratification time scales and the parameter values used to calculate them. The time scales under the observations, model, and Chanut et al. (2008) columns are based on Eqs. (6), (8), and (10). The time scales in the simulations column are found by extrapolation of the lines in Fig. 8: *τ*_{CE} from the NO_BC simulation, *τ*_{BCE+CE} from the NO_IR simulation, and *τ*_{IR} from the difference between the ALL_IN and the NO_IR simulations.

#### 1) Convective eddies

If CEs were the only restratifying mechanism at play, Eq. (6) gives an estimate of the time it would take to restratify the whole convection area by lateral fluxes only. The convection area as measured in situ by Pickart et al. (2002) (Fig. 1a) gives *R*_{max} = 300 km and *h* = 1500 m. To obtain an estimate of the background stratification *N*_{bg}, we use the mean of late spring occupations of the WOCE AR7W section as described in Pickart and Spall (2007): In Fig. 11, the average buoyancy frequency *N* in the upper 1500 m of the water column is shown as a function of position along this section. It shows a background stratification of around *N*_{bg} = 1.5 × 10^{−3} s^{−1}. A value for the efficiency constant *c _{e}* cannot be obtained from measurements, because in the real ocean other eddy types are always present. It seems sensible to use the range most commonly found in literature (0.02 <

*c*< 0.04; see section 4a). Combining these values in Eq. (6) yields a restratification time scale

_{e}*τ*

_{CE}for CEs alone of 0.9–1.8 yr, depending on the value of

*c*. With

_{e}*c*= 0.02 as in our model,

_{e}*τ*

_{CE}= 1.8 yr.

Buoyancy frequency averaged over the upper 1500 m of the water column from a mean late spring section over the 1990s (Pickart and Spall 2007). The shaded areas marked by A are used to determine *N*_{bc}, the area marked by B is used to determine *N*_{BCE}, and *N*_{bg} is found from the area marked by C.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

Buoyancy frequency averaged over the upper 1500 m of the water column from a mean late spring section over the 1990s (Pickart and Spall 2007). The shaded areas marked by A are used to determine *N*_{bc}, the area marked by B is used to determine *N*_{BCE}, and *N*_{bg} is found from the area marked by C.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

Buoyancy frequency averaged over the upper 1500 m of the water column from a mean late spring section over the 1990s (Pickart and Spall 2007). The shaded areas marked by A are used to determine *N*_{bc}, the area marked by B is used to determine *N*_{BCE}, and *N*_{bg} is found from the area marked by C.

Citation: Journal of Physical Oceanography 41, 11; 10.1175/JPO-D-11-054.1

#### 2) Convective eddies and boundary current eddies

An exact estimate of *τ*_{CE+BCE} [Eq. (8)] based on observations is not feasible, because neither ϵ nor *N*_{BCE} can be retrieved from measurements directly. Nevertheless, one can estimate an upper bound from the data as follows: The contribution of BCEs to restratification is largest in the southwestern part of the convection area, where the boundary current is closest and the density gradient between the boundary current and convection area is therefore strongest. Moreover, it is expected that the contribution of IRs in this part of the convection area is smallest, because they originate in the northeast and propagate from there toward the interior. If we assume no contribution from IRs on this side of the convection area and take into account that the effect of BCEs is smaller everywhere else, the enhanced stratification between the boundary current and the southwestern part of the convection area thus gives an upper bound for *N*_{BCE}. In Fig. 11, this region is found approximately between 150 and 200 km and has an average stratification of about *N*_{BCE} = 1.75 × 10^{−3} s^{−1}. With *N*_{bc} = 3.0 × 10^{−3} from Fig. 11, it then follows from Eq. (7) that *ϵ* < 0.12. The time scale for restratification for CEs and BCEs is then more than 0.7 yr. Because the very stringent assumptions in determining an upper bound for *N*_{BCE} [the gradient between the convection area and the boundary current is generally much smaller than in the southwestern corner, and part of the IRs follow the boundary current around the basin to the western side (Prater 2002; Hatun et al. 2007) and the influence of IRs on this side is therefore not zero] it is likely to be significantly longer.

#### 3) Irminger rings

For a time scale estimate *τ*_{IR} [Eq. (10)], the work by Lilly et al. (2003) may be used to obtain the frequency of IRs reaching the convection area *f*_{IR}. From their Figs. 40–42, it follows that 15–45 IRs are shed from the coast each year. The number of anticyclones and dipoles, which are the eddies assumed by the authors to have positive temperature anomalies, decline, averaged over 7 yr, from 30 in the northern part of the Labrador Sea to 21 in the southern part (Lilly et al. 2003, their Fig. 40). With roughly 30 IRs shed per year and 70% of them reaching the southern part of the Labrador Sea, a fair estimate of *f*_{IR} is about 15 yr^{−1} (the estimate is lowered to 50% because the southern Labrador Sea box in Lilly et al. 2003 reaches slightly farther east than the convection area). The radius of an IR is approximately 20 km (Prater 2002; Lilly et al. 2003; Hatun et al. 2007). With *R*_{max} = 300 km from Pickart et al. (2002) and *N*_{bg} and *N*_{bc} taken from Fig. 11, this yields a restratification time scale of 1.1 yr.

### c. Model-based restratification time scales

Now that we know the time scales of restratification for the three eddy types based on observed characteristics, we can assess whether our model simulations give similar results. The parameter values from the model used in Eqs. (6), (8), and (10) and the resulting restratification time scales are listed in the model column in Table 3 [*N*_{bg} is based on *T*_{ref}, *N*_{BCE} is based on the NO_IR simulation, *ϵ* is found using Eq. (7), *f*_{IR} is based on the fact that 8 IRs reached the convection area in 6 months in the ALL_IN simulation, and *r*_{IR} is also found from the ALL_IN simulation results]. The resulting restratification time scales are indeed in good agreement with the ones based on observations.

The actual restratification time scale in the model simulations may be estimated by linear extrapolation of the time evolution of the heat deficit in Fig. 8. The time scales thus obtained are listed in the simulations column in Table 3. Given the simplifying assumptions in the derivation of the scalings, the estimates are very similar. Note that none of the eddy types can restratify the Labrador Sea individually within one year, but as we have seen in section 3 their combined effect is much more efficient.

## 5. Discussion

From the model simulations, it is evident that IRs play an important role in the process of restratification in the Labrador Sea. This conclusion is in contradiction to the results from Chanut et al. (2008). Based on the notion that two 10-yr equilibrium simulations (one with and one without IRs) both reach an equilibrium state, these authors concluded that BCEs play a crucial role in the restratification process and that the importance of IRs is only moderate. In our view, however, this result does not justify such a conclusion. A model can still produce a quasi-equilibrium state when a major source of buoyancy (IRs) is removed, but this equilibrium may not be representative for the Labrador Sea. Their simulation without IRs indeed displays a 0.1°C lower basin-averaged temperature compared to the simulation with IRs (Chanut et al. 2008, their Fig. 4b). This is a significant difference representing half the annual cycle, suggesting that IRs do have a nonnegligible impact in their simulations.

The prominent role of BCEs in the Chanut et al. (2008) study results from an overestimation of the effect of BCEs, combined with an underestimation of the effect of IRs. Their results display unrealistically deep mixed layers (2400 m) over a large part of the Labrador Sea for multiple winters in a row. These are caused by the strong surface cooling that is applied, which exceeds the European Centre for Medium-Range Weather Forecasts (ECMWF) values by 50% (Chanut et al. 2008, their Figs. 8 and 14). Such deep mixed layers were so far only observed in a small part of the Labrador Sea basin in the early 1990s (Yashayaev 2007). Because of the large depth and extent of the convection area the density gradient between the interior and the boundary current is very large. This enhances the efficiency of BCEs in restratifying the Labrador Sea interior.

The scaling relations from section 4a [Eq. (8)] illustrate how restratification can be efficient enough in their model to reach an equilibrium, despite the absence of IRs (Table 3). Beside the deep mixed layers (their Fig. 8a), the background stratification is also weak: the mean stratification in the upper 1500 m is only *N*_{bg} = 0.8 × 10^{−3} s^{−1} (their Fig. 7a). To calculate *τ*_{CE+BCE}, the stratification in the boundary current *N*_{bc} is also required, as well as either *N*_{BCE} or the parameter *ϵ*. From the temperature–density cross section, we can infer that the stratification in the boundary current in their simulation (their Fig. 7b) is at least as strong as in the climatology (their Fig. 7a). We will therefore use the climatological value of *N*_{bc} = 3.0 × 10^{−3} s^{−1} (Fig. 11). Using *ϵ* ≈ 0.1 from the observations, Eq. (8) yields a restratification time scale of 0.3–0.6 yr (Table 3). The strongly enhanced boundary current–interior density gradient thus enables restratification to be sufficiently quick to restratify the Labrador Sea before the next winter even without IRs.

The contribution of IRs to restratification [Eq. (10)] in the simulation of Chanut et al. (2008) is very small because the eddies hardly reach the convection area. Their Fig. 11 shows the tracks of IRs in 2 yr of the simulation. Because the tracks lie too far north compared to observations (Lilly et al. 2003), only one or two of all the IRs actually reach the southwestern part of the Labrador Sea, giving *f*_{IR} ≈ 1 yr^{−1}. With the other parameter values as above, the restratification time scale for IRs is 5.9 yr. The time scales (Table 3) clearly show that the restratification mechanism in Chanut et al. (2008) does not match observations.

*c*= 0.03 based on literature. The case studied in Straneo (2006b) is a special case, because the convection area directly borders the boundary current and has the shape of a cylinder. The scalings derived for cone-shaped convection areas in this study are therefore not applicable. Alternatively, the time scale derived by Jones and Marshall (1997) for cylinder-shaped convection areas [their Eq. (2.11)] should be used,

_{e}*R*= 230 km is the radius of the convection area and

*h*(=

*D*−

*h*

_{2}) = 800 m is the depth over which lateral eddy fluxes act (Straneo 2006b, her Fig. 1). The relevant stratification is here the stratification of the boundary current

*N*

_{bc}, which can be found by taking ∂

*ρ*/∂

*z*from the center of the upper layer to the center of the lower layer (Δ

*ρ*= 0.05 kg m

^{−3}and Δ

*z*= 750 m), yielding

*N*

_{bc}= 8.0 × 10

^{−4}s

^{−1}. With these values, the restratification time scale is a very realistic 0.6 yr.

## 6. Summary and conclusions

The contributions of three different eddy types (convective eddies, boundary current eddies, and Irminger rings; see section 1) to restratification after deep convection in the Labrador Sea are assessed using simulations of the restratification season with an idealized numerical model. The model configuration is comparable to the one used by Katsman et al. (2004) but highly improved in terms of basin shape and location and shape of the convection area. Furthermore, the analysis was expanded to include the effect of boundary current eddies.

Three different cases were studied: one with only convective eddies, one with convective eddies and boundary current eddies, and one with all three eddy types. The model results clearly show an essential role of Irminger rings in the restratification process. Convective eddies and boundary current eddies together only replenish 30% of the initial heat loss, whereas IRs add another 45% (Fig. 8). Part of the effectiveness of Irminger rings in restratification is due to enhanced interaction with the boundary current: In the simulation with Irminger rings, the transport of convected water out of the convection region is 4 times larger than in the simulation without Irminger rings. Also, IRs stir the convected water through the basin, thereby facilitating mixing by the smaller eddies. Thus, although we argue that IRs are required for restratification in this region, they may need the smaller eddies to be genuinely effective.

Simple theoretical scalings, used to assess the time it takes the three different eddy types to restratify the convective region, lead to the same conclusion (Table 3). The estimated restratification time scales show that none of the three eddy types can restratify the Labrador Sea by themselves during one restratification season. The contribution of IRs (restratification time scale of 1 yr and 1 month) is slightly larger than the contribution of CEs and BCEs together (restratification time scale of more than 1 yr and 2 months). When all three eddy types contribute to the restratification process, the estimated time scale is a realistic 7 months.

A few interesting questions for further research have arisen from this study. First, it was shown that IRs are an efficient mixer, which suggests that their interaction with the other eddy types may not be a simple linear superposition. Although the scalings, which are based on the assumption of this linear superposition, give very reasonable results, the nature of the interaction might be important for a proper representation of the restratification process. Also, the pathways of the IRs are apparently of vital importance to model the restratification appropriately. It is as yet unclear what determines these pathways and why they are different in the Chanut et al. (2008) model. Third, the frequency of IRs reaching the convection area shows a seasonal and interannual variability in reality. The question of how that affects the restratification process is still unanswered. Last and perhaps most importantly, IRs are not resolved in the current generation of global climate models. Because the eddies play an important role in restratification in this area, they should be adequately parameterized.

## Acknowledgments

This research was funded by a grant from the NWO/SRON User Support Programme Space Research. The useful discussions with Bob Pickart, Mike Spall, and Fiamma Straneo are highly appreciated. We are particularly grateful for the in situ data provided by Bob Pickart.

## APPENDIX A

### Derivation of *τ*_{CE}

*c*is an eddy efficiency coefficient and Δ

_{e}*b*(

*r*,

*z*) is the buoyancy difference between the convection area and the ambient fluid,

*r*and vertical position

*z*in the convected cone. Here,

*N*

_{bg}is the background stratification,

*h*is the maximum convection depth, and

*R*

_{max}is the radius of the cone at the sea surface. Last,

*u*

_{0}is the rim current velocity at the surface, which can be found from the thermal wind balance as follows:

*ρ*. Integrating over the vertical direction gives the velocity as a function of

*z*,

*u*over the mixed layer is zero,

## APPENDIX B

### Derivation of *τ*_{CE+BCE}

*b*(

*r*,

*z*) is now larger. BCEs basically warm up the basin surrounding the convection area, thereby enhancing the effect of CEs. We therefore introduce a new stratification,

*N*

_{bc}is the stratification in the boundary current and

*ϵ*a parameter (0 <

*ϵ*≤ 1). The buoyancy difference [Eq. (A3)] is then

*τ*

_{CE+BCE},

## APPENDIX C

### Derivation of *τ*_{IR}

*r*

_{IR}and account for the frequency

*f*

_{IR}of occurrence of such an event,

*h*

_{eff}, see section 4a. The initial buoyancy deficit, given on the left-hand side of Eq. (C1), is the same as before

*b*

_{IR}(

*z*) is given by

*τ*

_{IR},

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^{1}

In periods of low convective activity, multiyear restratification is also important. However, that is beyond the scope of this study, where we focus on the restratification immediately after a deep convection winter.

^{2}

At the end of the spinup phase, the temperature field in the interior displayed only minor differences between different spinup simulations. As a consequence, the amount of heat removed from the basin by constructing the convection region differs by about 1%.

^{3}

In the model simulations, the fact that restratification of the whole basin must be a multiyear effect is incorporated in the initial density field, which is made based on observations, and the spinup of 6 months to get the boundary current–interior density gradient correct.