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  • View in gallery

    The model bathymetry from ETOPO2 is shown. The bathymetry is smoothed linearly, except along the thick black line, where the bathymetry steepness is crucial for IR generation.

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    The (a) mean kinetic energy during each spinup cycle, (b) the mean kinetic energy from September 2006 to December 2008 for experiments with different spinup cycles, (c) the mean potential temperature from September 2006 to December 2008 for model runs with different spinup cycles, and (d) the mean salinity from September 2006 to December 2008 for model runs with different spinup cycles. All variables are obtained at 100-m depth in the domain where water depth exceeds 1000 m.

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    (a) The Labrador Sea currents at 30-m depth are averaged from November 2006 to October 2008. (b) The mean surface velocity derived from weekly gridded dynamic height data by AVISO. (c) Mean EKE in terms of root-mean-square EKE velocity at 30-m depth are for the same time period as in (a), but have been smoothed by a 0.3° Hanning window. (d) Snapshot of relative vorticity at 30-m depth for 9 Jun 2008.

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    (a) Mixed layer depth derived from Argo data from January to March in 2008, and (b) the maximum mixed layer depth indicated from model output during the latter half of March 2008. Dashed circles in (a) and (b) denote where the mean heat loss during the same period exceeded 350 W m−2. The gray lines in (b) are the monthly mean 20% sea ice concentration border, as color darkens from January, February, to March in 2008. The thin gray line in (a) and the white line in (b) indicate the 3000-m isobath.

  • View in gallery

    Mean seasonal EKE in terms of root-mean-square velocity at 30-m depth from November 2005 to October 2008: (a) from January to March, (b) from April to June, (c) from July to September, and (d) from October to December. The data have been smoothed using a 0.3° Hanning window. The black box in (b) is the area that will be looked into in Fig. 6. Here, only the region where the ocean bottom is deeper than 900 m is included.

  • View in gallery

    The zonally averaged EKE of cycle 5 from 48° to 54°W is mapped from 56° to 62°N. The black arrows mark the southward propagation of the EKE, and the speed is approximately 4.73 cm s−1. To be consistent with Brandt et al. (2004), only the region where the ocean bottom is deeper than 900 m is included.

  • View in gallery

    An ensemble of eddy trajectories of cycle 5 is shown from November 2006 to October 2008, and the filled gray circles (anticyclones) and lighter gray triangles (cyclones) denote the last locations of the trajectories. At the light gray patch in the central Labrador Sea, the maximum mixed layer depth exceeds 1000 m at the end of the convection season in 2008, as shown in Fig. 4b. The light gray contour lines are 2000- and 3000-m isobaths. (a) The eddies whose lifespan is longer than 50 days, and (b) the eddies whose lifespan is no longer than 50 days.

  • View in gallery

    (a) The latitudes where the eddies shown in Fig. 7a are initially identified. (b) The latitudes where these eddies are lost track of. (c) Latitude of eddy identification vs the longitude at which they are lost track of. The circles represent anticyclones, and triangles represent cyclones. The gray color denotes eddies that eventually enter east of 54°W, and the black color denotes eddies that enter west of 54°W. The criteria to select those eddies shown here are specified in text.

  • View in gallery

    The vertical structure of an IR-type eddy: (a) the temperature, (b) the salinity, and (c) the horizontal velocity. The snapshots are taken on 6 May 2008. Contours of constant density are indicated in (a) and (b).

  • View in gallery

    The evolution of two IR-type eddies, one in gray, the other in black: (a) the area mean relative heat content of the eddies between the surface and 200-m depth (solid lines), and the relative heat content between 200- and 500-m depth (dashed lines); (b) the radii of the two eddies; (c) the maximum relative vorticity of the two eddies at 50-m depth; and (d) the area mean surface heat flux over the eddy surface.

  • View in gallery

    The surface heat flux and heat content variation in the convection area during the simulation time, here the convection area is the same as in Fig. 7. (a) The total surface heat flux from NCEP reanalysis 2 and actual forcing after correction over the convection area are represented by thin black and gray lines respectively, and the 1-month moving boxcar filtered surface flux are represented by thick lines. (b) The heat content of the upper 200-m water column, and the integrated surface heat flux from the minimum heat content in each year. (c) The relative ocean heat content (HC, black lines) between surface and 1900 m referenced to the maximum value of each year, and the model surface heat flux accumulated from the same reference value. The referenced value is set to zero, and dashed lines indicate the ocean loses heat, while solid lines indicate the ocean gains heat. (d) The relative heat content (see text for definition) variation for the upper 200 m, the water column between 200 and 500 m, and the layer between 500 and 1000 m.

  • View in gallery

    (a) The trajectories of eddies that propagate into the convection area after the lower level’s restratification starts in 2008. The heat content of eddies 1 to 4 for (b) 200–500 m and (c) 500–1000 m. The heat flux across the lateral boundary for eddies 1 to 4 in the (d) 200–500 m and (e) 500–1000 m.

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Lateral Heat Exchange after the Labrador Sea Deep Convection in 2008

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  • 1 School of Marine Science and Policy, University of Delaware, Newark, Delaware
  • | 2 University of Delaware and Xiamen University Joint Institute of Coastal Research and Management, and School of Marine Science and Policy, University of Delaware, Newark, Delaware
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Abstract

The mechanisms through which convected water restratifies in the Labrador Sea are still under debate. The Labrador Sea restratification after deep convection in the 2007/08 winter is studied with an eddy-resolving numerical model. The modeled mixed layer depth during wintertime resembles the Argo observed mixed layer very well, and the lateral heat flux during the subsequent restratification is in line with observations. The Irminger rings (IRs) are reproduced with fresher caps above the 300-m depths, and they are identified and tracked automatically. The model underestimates both the number of IRs in the convection area and the heat they carry. The underestimation is most likely caused by the errors in the direction of the west Greenland currents in the model, which causes more IRs propagating westward, and only the IRs originating south of 61.5°N are able to propagate southward, yet with speed much slower than observed speed. The model still observed three eddies propagating into the convection area during the restratification phase in 2008, and their thermal contribution ranges from 1% to 4% if the estimation is made at the time when they enter the convection area. If all newly generated eddies are considered, then the ensemble-mean contributions by the IRs become 5.3%. The more detailed and direct heat flux by IRs is difficult to derive because of the strong fluctuation of the identified eddy radius. Nevertheless, the modeled lateral heat flux is largely composed of the boundary current eddies and convective eddies, thus it is possible for the model to maintain an acceptable thermal balance.

Corresponding author address: Dr. Xiao-Hai Yan, School of Marine Science and Policy, University of Delaware, 261 S College Avenue, Newark, DE 19716. E-mail: xiaohai@udel.edu.

Abstract

The mechanisms through which convected water restratifies in the Labrador Sea are still under debate. The Labrador Sea restratification after deep convection in the 2007/08 winter is studied with an eddy-resolving numerical model. The modeled mixed layer depth during wintertime resembles the Argo observed mixed layer very well, and the lateral heat flux during the subsequent restratification is in line with observations. The Irminger rings (IRs) are reproduced with fresher caps above the 300-m depths, and they are identified and tracked automatically. The model underestimates both the number of IRs in the convection area and the heat they carry. The underestimation is most likely caused by the errors in the direction of the west Greenland currents in the model, which causes more IRs propagating westward, and only the IRs originating south of 61.5°N are able to propagate southward, yet with speed much slower than observed speed. The model still observed three eddies propagating into the convection area during the restratification phase in 2008, and their thermal contribution ranges from 1% to 4% if the estimation is made at the time when they enter the convection area. If all newly generated eddies are considered, then the ensemble-mean contributions by the IRs become 5.3%. The more detailed and direct heat flux by IRs is difficult to derive because of the strong fluctuation of the identified eddy radius. Nevertheless, the modeled lateral heat flux is largely composed of the boundary current eddies and convective eddies, thus it is possible for the model to maintain an acceptable thermal balance.

Corresponding author address: Dr. Xiao-Hai Yan, School of Marine Science and Policy, University of Delaware, 261 S College Avenue, Newark, DE 19716. E-mail: xiaohai@udel.edu.

1. Introduction

Deep convection in the Labrador Sea is one of the branches composing the Atlantic meridional overturning circulation (AMOC). The deep-water formation process depletes the gravitational potential energy in the AMOC system and sets the interhemisphere shape and strength of the overturning cells (Kuhlbrodt et al. 2007). In winter, strong surface cooling over weakly stratified open ocean induces vigorous convection, whose product contributes to the Labrador Sea Water (LSW) (Marshall et al. 1998), a source of North Atlantic Intermediate Water (Lazier 1973; Marshall et al. 1998; Marshall and Schott 1999).

Marshall and Schott (1999) suggested that strong buoyancy loss at the surface and weak stratification underneath were both recurring conditions for deep-reaching convection. It has been shown that convective plumes form and extend deeper than 1 km, right below an idealized extreme cooling disk (800 W m−2) (Jones and Marshall 1993), whereas Legg et al. (1998) observed deep convection development in an inhomogeneously stratified system subject to homogeneous cooling. For a numerical model with resolution less than 1 km, plume scales cannot be resolved. Nonetheless, the overlap of weak stratification and strong surface heat loss is crucial for deep convection to occur (Marshall et al. 1998).

Right before strong surface cooling ceases in late March, convection reaches its maximum (Prater 2002; Lilly et al. 1999), and the subsequent restratification will affect the stratification in the central Labrador Sea, hence the temperature and the salinity of the future LSW. The thermal restratification of the interior includes two aspects: one is the surface warming due to an increase in solar radiation, while the other is the lateral heat exchange with the boundary currents through eddy advection or diffusion (Lilly et al. 2003; Straneo 2006). Because the solar radiation cannot penetrate into the deeper ocean, and the ocean is losing heat to the atmosphere in the long-term, heat flux brought by eddies originating from the boundary currents or rim current is the more promising source (Katsman et al. 2004; Chanut et al. 2008, hereinafter Chanut08; Gelderloos et al. 2011, hereinafter Gelderloos11).

Eddies present in the Labrador basin are categorized as three types, according to their origin, generation mechanisms, and structures (Chanut08; Luo et al. 2011; Gelderloos11). The first type is convective eddies (CEs). These are generated from the rim currents of convection patches due to baroclinic instability of the steep isopycnal (Jones and Marshall 1997), and their radii range from 5 to 15 km, about the same scale as local Rossby deformation radii (about 7 km in the Labrador Sea).

The second type is referred to as Irminger rings (IRs) (Katsman et al. 2004; Chanut08), and they are shedded from the West Greenland Current (WGC). The IRs are triggered by the strong topography gradient just downstream of Cape Desolation. Former model studies have shown the fundamental importance of bathymetric steepness preservation along the WGC for IRs formation (Katsman et al. 2004; Chanut08; Luo et al. 2011). The eddy kinetic energy can be converted from either barotropic (Eden and Böning 2002) or baroclinic (Bracco et al. 2008) instability. IRs can be further categorized as cyclones, anticyclones, or dipoles.

The vertical structures of anticyclonic IRs have been well documented (Lilly et al. 1999; Hátún et al. 2007; Rykova et al. 2009). The upper 200- or 300-m layer is always buoyant, their surface layer can be colder or warmer than their ambient water, and the surface layer can be fresher or saltier (de Jong et al. 2014). However, the eddy caps will lose the freshness if they have been through convective mixing (Rykova et al. 2009). Unlike CEs, the currents of IRs are usually surface intensified. IRs may have a potential impact on deep convection in winter. Numerical studies have shown that when IRs are suppressed by bottom topography smoothing, deep convection can occur excessively to the northeast of the observed site (Chanut08). Moreover, McGeehan and Maslowski (2011) reported unrealistic deep convection in the area where active IRs were present and surmised that it was because of the lack of freshwater caps above them. Indeed, not only the presence of the IRs but also their realistic vertical buoyancy structures are crucial for models to reproduce deep convection (Chanut08; McGeehan and Maslowski 2011). Additionally, some very long-lived anticyclonic IRs found in the central Labrador Sea may have experienced convective mixing during one or more winters (Lilly et al. 2003; Rykova et al. 2009).

The third type is the boundary current eddies (BCEs), following Chanut08 and Gelderloos11. The sizes of these eddies are also on the order of the Rossby deformation radius. BCEs are driven by baroclinic instability of the boundary currents. Their presence is not limited to the postconvection period and the rim current enclosing the convection area. Instead, they are active all the time due to the fronts between interior and boundary currents (Gelderloos11). Spall (2004) showed a significant heat balance between fluxes of BCEs and the surface buoyancy loss in the interior of idealized marginal seas, which may apply to the Labrador Sea as well (Chanut08).

Some studies have attempted to assess the restratifying contributions by different eddies (Jones and Marshall 1997; Katsman et al. 2004; Chanut08; Gelderloos11). Both Katsman et al. (2004) and Gelderloos11 used an idealized model and concluded that IRs were the major players. Katsman et al. (2004), however, set the convection region much farther north than reality. Gelderloos11 corrected the location offset and differentiated the contributions of BCEs and IRs by whether to preserve the bathymetric steepness along the west Greenland shelf and replaced part of the interior water mass with a preconvected, cone-shaped one for restratification. They concluded that IRs were responsible for replenishing 45% of the winter heat loss, whereas BCEs had only a marginal contribution. Contrary to the findings by Gelderloos11, experiments by Chanut08, with or without the IR generation mechanism, showed neither direct IRs’ propagation into the convection area (south of 58°N), nor significant difference of downgradient eddy heat fluxes. However, Chanut08 did not calculate the contribution by IRs explicitly. Gelderloos11 pointed out that experiments by Chanut08 represented different equilibriums for different end-of-winter states from the real situation in the Labrador Sea, since some of the IRs have been observed in the convection area. Furthermore, for some reason, the simulated convection activity by Chanut08 is too strong in both its horizontal span and vertical extension, resulting in exceedingly strong boundary current eddy activity.

It has been difficult for numerical models to estimate the eddy heat flux because modeled IRs tend to propagate westward outside the 3000-m isobaths in the Labrador Sea (Chanut08; Luo et al. 2011). Although Gelderloos11 have simulated the impact of IRs when they directly break into the convection area, the bathymetry configuration is quite different from the Labrador Sea. This model study will focus on the mesoscale eddy activity and the IRs’ pathways and intends to assess the restratification process and the thermal contribution by mesoscale eddies after a strong convection event in 2008.

The remainder of the paper is organized as follows: Section 2 describes the details of model configuration and numerical experiments. In section 3, model results will be discussed in terms of the general performance of the model relative to observations. Section 4 will show the eddy activities in the Labrador Sea. Section 5 analyzes the restratification and heat budget in the convection area. Last, section 6 discusses the thermal contributions by the modeled Irminger rings.

2. Model configuration

In this study, a Regional Ocean Modeling System (ROMS version 3.4) is used for a realistic simulation of the Labrador Sea current system. ROMS is a free-surface, terrain-following model and solves the primitive equations with Boussinesq and hydrostatic approximation in an orthogonal curvilinear coordinate system on the Arakawa C grid. Its time-splitting technique integrates the vertically averaged barotropic equations with external time steps and baroclinic equations with internal time steps. In the vertical direction, equations are discretized over topography on s coordinates (Song and Haidvogel 1994; Shchepetkin and McWilliams 2005).

IRs’ lifetimes can be as long as several months or even a few years (Lilly et al. 2003), thus the model eddy viscosity is implicit, and eddy diffusivity is set to 0.5 m2 s−1. The vertical turbulent mixing is significant in this study because vigorous convection occurs during wintertime in the central Labrador Sea, when vertical velocity can reach 10 cm s−1 (Lavender et al. 2002). K-profile parameterization (Large et al. 1994) is chosen to compute the vertical eddy mixing coefficient, and the vertical background viscosity is set to 10−5 m2 s−1. The numerical domain is shown in Fig. 1. It has 380 longitudinal by 400 latitudinal grid points and 30 vertical levels. The grid size varies from 3.2 to 4.3 km, smaller than the Rossby radius of deformation. An adaptive open boundary condition is applied to all four boundaries. The radiation condition is used to determine whether the boundary is passive or active, so that the nudging time scale can be applied: 1 day for inward propagation and 120 days for outward propagation (Marchesiello et al. 2001).

Fig. 1.
Fig. 1.

The model bathymetry from ETOPO2 is shown. The bathymetry is smoothed linearly, except along the thick black line, where the bathymetry steepness is crucial for IR generation.

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0198.1

Bathymetry data are obtained from the 2-Minute Gridded Global Relief Data (ETOPO2) dataset, which combines satellite altimetry observations and shipboard echo-sounding measurements (Smith and Sandwell 1997). Haidvogel et al. (2000) suggested that in order to obtain robust results, the topography difference between two neighboring grids should not significantly exceed 20% of their summation because the s coordinates may cause horizontal pressure gradient error when dealing with steep topography (Haney 1991). However, in this study, maintaining steep gradients of topography along the continental shelf at west Greenland is necessary for IR formation (Katsman et al. 2004; Chanut08; Luo et al. 2011). A 2D-modified Shapiro smoother (Penven et al. 2008) is applied to the logarithm of bathymetry where the topographic slope is too steep, except along the continental slope marked by the thick black line in Fig. 1. The corresponding spurious currents due to the pressure gradient induced by vertical coordinates are less than 10% of the mean currents. The Simple Ocean Data Assimilation (SODA version 2.1.6) (Carton and Giese 2008) is used for initial conditions, boundary conditions, and SST reference for surface heat flux correction.

The 6-hourly National Centers for Environmental Prediction (NCEP)–Department of Energy (DOE) reanalysis 2 (Kanamitsu et al. 2002) surface flux data are used, including the surface latent and sensible heat flux, the downward and upward radiation flux of both shortwave and longwave, and the zonal and meridional surface momentum flux. To avoid excessive drift of sea surface temperature (SST) due to NCEP surface heat flux errors (Renfrew et al. 2002), a surface heat flux correction is applied:
e1
The term is calculated based on the algorithm by Barnier et al. (1995). In this study, the SODA monthly temperature at the uppermost level is used as .

The model is initialized with the conditions of 16 August 2005 and stops on 15 December 2008. To spin up the model, the same boundary and surface forcing condition from 16 August 2005 to 15 August 2006 is applied once (cycle 1), three times (cycle 3), four times (cycle 4), and five times (cycle 5) to an ensemble of experiments, then each experiment continues until 15 December 2008. When the same forcing and boundary condition is applied repeatedly, the mean kinetic energy at 100-m depth decreases, but cycles 3 to 5 have a very similar magnitude (Fig. 2a). The mean kinetic energy from August 2006 to December 2008 shows more consistency among cycles 3 to 5, but in general there is no significant difference caused by repetition of the spinup cycles (Fig. 2b). Larger differences between cycle 1 and cycles 3 to 5 are found in the mean potential temperature and salinity from August 2006 to December 2008; however, the two variables seem to be able to converge toward the end of the experiments (Figs. 2c,d). Given the small discrepancy among cycles 3, 4 and 5, the model is considered spun up after two to four repetition cycles.

Fig. 2.
Fig. 2.

The (a) mean kinetic energy during each spinup cycle, (b) the mean kinetic energy from September 2006 to December 2008 for experiments with different spinup cycles, (c) the mean potential temperature from September 2006 to December 2008 for model runs with different spinup cycles, and (d) the mean salinity from September 2006 to December 2008 for model runs with different spinup cycles. All variables are obtained at 100-m depth in the domain where water depth exceeds 1000 m.

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0198.1

3. General circulation in the Labrador Sea

The mean currents of experiment cycle 5 at 30-m depth in the Labrador Sea from November 2005 to October 2008 are characterized by strong counterclockwise circulation with two maxima (Fig. 3a). One maximum occurs along the West Greenland Current, the other occurs along the Labrador Current (LC). The barotropic streamfunction of the whole model domain has been calculated, and the maximum southward transport in winter is about 39 Sverdrups (Sv; 1 Sv ≡ 106 m3 s−1) at the west side of the basin around 3000-m isobaths, which is in line with observations (Pickart et al. 2002). The maximum around Cape Farewell suddenly decreases right before reaching the IR-shedding zone. The cross-shelf shear of the currents increased at this maximum, upstream of the eddy spawning location. The other maximum location in the LC is found between 53° and 56°N, which has been observed at middepths by Funk et al. (2009). Figure 3b shows the mean surface circulation during the same time span, using the weekly gridded velocity derived from the dynamic height data by Archiving, Validation, and Interpretation of Satellite Oceanographic (AVISO) data. The “reference” series of the mapped absolute geostrophic velocities is used here, and the data are accessible online (at ftp://ftp.aviso.oceanobs.com) with a subscription. Except that the overall strength of the modeled current strength is significantly stronger, the modeled general pattern in terms of the boundary current meandering and locations for extremely strong currents agrees well with the observation.

Fig. 3.
Fig. 3.

(a) The Labrador Sea currents at 30-m depth are averaged from November 2006 to October 2008. (b) The mean surface velocity derived from weekly gridded dynamic height data by AVISO. (c) Mean EKE in terms of root-mean-square EKE velocity at 30-m depth are for the same time period as in (a), but have been smoothed by a 0.3° Hanning window. (d) Snapshot of relative vorticity at 30-m depth for 9 Jun 2008.

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0198.1

Eddy kinetic energy (EKE) in the Labrador Sea (Fig. 3c) has been calculated following similar methods by Chanut08 and Luo et al. (2011). A seasonal mean is removed from the modeled zonal and meridional currents, and the four seasons span from January to March, April to June, July to September, and October to December. The total mean current instead of the seasonal-mean current has also been removed, and the resulted EKE only shows slight increase, compared to Fig. 3c. The mean EKE of cycle 5 from November 2005 to October 2008 has a maximum originating from the west Greenland continental slope, and it is concentrated between 60° and 62°N. This EKE maximum has been observed by altimetry (Prater 2002; Lilly et al. 2003; Brandt et al. 2004). This modeled mean EKE maximum extends westward between 60° and 62°N, then extends southward south of 60°N. The maximum extensions indicate two IRs pathways, which have been observed by floats and gliders (Prater 2002; Hátún et al. 2007). One pathway extends westward first, then it becomes southward, and the other pathway extends southward. Since the two pathways are characterized by different propagation speed (Prater 2002; Lilly et al. 2003; Hátún et al. 2007), with the westward pathway associated with a faster eddy propagation speed yet a longer journey reaching the convection area, they may result in a different restratification rate by the mesoscale eddies for the convection area. The pattern of EKE is very similar to what has been derived from along-track altimetry data (Lilly et al. 2003, their Fig. 24).

A cycle 5 snapshot of the relative vorticity on 9 June 2008 at 30-m depth (Fig. 3d) during the effective restratification season shows several closed cores of negative relative vorticity surrounded by positive values, which is a typical feature of nonisolated anticyclonic eddies (Carnevale et al. 1991). The IRs in Fig. 3d have radii ranging from 15 to 24 km. On this snapshot, more than two IRs are located between 57° and 58°N. To directly affect the stratification in the convection region, it is important that IRs are able to propagate to latitudes lower than 58°N because that is where the deep convection (mixed layer depth over 1 km) was most frequently observed in the winters of 1997/1998 as well as in 2008 (Lavender et al. 2002; Pickart et al. 2002; Våge et al. 2009). Moreover, all the modeled anticyclonic IRs in this study have colder but fresher caps, which are more buoyant than ambient water mass at the surface. Those anticyclonic IRs are less likely to be disintegrated by winter heat loss and vertical mixing than the cyclonic ones (Legg and McWilliams 2001), possibly because of the strong stratification in the buoyant caps. Indeed, hydrographic data show deepened mixed layers in some anticyclonic IRs, and they are thus termed convected ones as well (Rykova et al. 2009).

Mixed layer depth is a good proxy for deep convection in the Labrador Sea. The model reproduced the 2008 winter deep convection event in the central Labrador Sea, and the 2007/08 convection is deeper than the former 2 yr. Argo profiles available from January to March 2008 are used to derive the observed mixed layer depth. These data were collected and made freely available by the Coriolis project and programs that contribute to it (www.coriolis.eu.org). The mixed layer depth is calculated based on the algorithm designed by Pickart et al. (2002) and Våge et al. (2009). There are two basic steps to derive mixed layer depth from floats data. The first step is to visually inspect all the profiles and determine the approximate mixed layer depth for each of them. The second step is to compute the mean and standard deviation of the potential density over this depth range, so a more accurate mixed layer depth is the depth where the density exceeds the two standard deviation envelope. The result is shown in Fig. 4a. Following the criteria set by previous modeling studies (Chanut08; McGeehan and Maslowski 2011), the modeled mixed layer is defined as a depth where potential density exceeds the surface value by 0.005 kg m−3, and the maximum mixed layer depth of cycle 5 during the latter half of March 2008 is shown in Fig. 4b. It is noted that the criteria for the mixed layer depth is different for Argo data and model output; furthermore, the Argo data are single profiles sampled at a different time. A longer period in winter will have more data available; while the “end of convection” modeled mixed layer is used for qualitative comparison. The core of maximum mean surface heat loss in the 2008 winter in NCEP data (dashed circles in Figs. 4a,b), over 350 W m−2, includes an area to the west and farther north of the observed locations where the mixed layer depth exceeds 1000 m. The modeled convection area is similar to Argo observation in the central Labrador Sea. In the central Labrador Sea between 1000- and 2000-m depths, the model vertical resolution ranges from 100 to 150 m, so the model-derived mixed layer deeper than 1000 m will include errors due to the resolution and will not be as accurate as the Argo data–derived mixed layer depth. The model did not reproduce the convection events south of Greenland, which have been observed by Argo floats (Våge et al. 2009). Because of the difference of the Argo data source in this study from the data source of Våge et al. (2009), there is only one profile showing mixed layer depth over 1200 m to the south of Greenland. The discrepancy may result from possible errors in NCEP forcing or that the model fails to reproduce a weakly stratified area south of Greenland. The monthly sea ice concentration data in winter from the Hadley Center for Climate Prediction and Research (Rayner et al. 2003) is shown in Fig. 4b. The concentrated convection area in the central Labrador Sea is not in contact with the area where the sea ice coverage exceeds 20%. Here, any modeled mixed layer depth over 1000 m is referred to as a concentrated convection area.

Fig. 4.
Fig. 4.

(a) Mixed layer depth derived from Argo data from January to March in 2008, and (b) the maximum mixed layer depth indicated from model output during the latter half of March 2008. Dashed circles in (a) and (b) denote where the mean heat loss during the same period exceeded 350 W m−2. The gray lines in (b) are the monthly mean 20% sea ice concentration border, as color darkens from January, February, to March in 2008. The thin gray line in (a) and the white line in (b) indicate the 3000-m isobath.

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0198.1

4. Eddy activity in the Labrador Sea

a. EKE seasonality

The EKE in the Labrador Sea is characterized by strong seasonal variability (Eden and Böning 2002; Lilly et al. 2003; Luo et al. 2011), directly contributed by the IRs shedded from WGC (Lilly et al. 2003) and contributed by the seasonality of wind stress as well (Spall and Pickart 2003). Seasonality of both the boundary current from east Greenland (Eden and Böning 2002) and the boundary–interior heat contrast (Katsman et al. 2004) is responsible for the seasonal cycle of the EKE maximum originating from the WGC. Since the model resolution is about to , and the C-grid model skill deteriorates for wavelengths more than 4 times the grid size, the EKE at 30-m depth is smoothed by a 0.3° Hanning window. Then the EKE is mapped over the region deeper than 900 m (Fig. 5). The EKE maximum between 60° and 62°N is strong in winter (Fig. 5a) when convection is most active in the central Labrador Sea. The EKE in the central Labrador Sea is relatively weaker in winter than in the later season from April to June (Fig. 5b). During the convection season, the EKE is strongest in the origination area, with limited westward and southward extension. It is obvious that the large EKE extends toward the west and south, corresponding to two paths for IRs to propagate away. The first one is westward, and the second is southward. After March when heat loss and convection ceases, the IRs start to propagate farther south in the central Labrador Sea convection area, especially along the second path (Fig. 5b). In the meantime, EKE in the modeled convection area (Fig. 4b) increases during this season, which can be contributed by the IRs’ penetrating and stirring effect as well as smaller baroclinic eddies that could be CEs. Similar to the findings by Brandt et al. (2004), the modeled EKE peaks in winter and spring in the West Greenland Current and the Labrador Current area, while EKE peaks in the springtime in the central Labrador Sea area. In general, the modeled EKE is weaker than altimeter-derived EKE (Lilly et al. 2003; Brandt et al. 2004), which may be caused by the model resolution and numerical dissipation and also by the removal of a 3-yr mean instead of a 7-yr mean when deriving the eddy flow field. After significant wave height correction, Brandt et al. (2004) found about 20% and 60% reduction of EKE in the northern and central Labrador Sea respectively from January to March (their Fig. 5). Another reason that the model tends to underestimate the EKE in areas other than the IRs’ spawning region seems to be that the modeled eddies have shorter life time, and a different preference of propagation from observation. The shorter lifetime of eddies will constrain the strong EKE close to their origination location in the model. The westward pathway preferred by the modeled eddies tend to increase the EKE on the west side of the northern-central Labrador Sea, while they decrease the EKE on the east side of the southern-central Labrador Sea.

Fig. 5.
Fig. 5.

Mean seasonal EKE in terms of root-mean-square velocity at 30-m depth from November 2005 to October 2008: (a) from January to March, (b) from April to June, (c) from July to September, and (d) from October to December. The data have been smoothed using a 0.3° Hanning window. The black box in (b) is the area that will be looked into in Fig. 6. Here, only the region where the ocean bottom is deeper than 900 m is included.

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0198.1

The evolution of zonally mean EKE from 48° to 54°W are shown from 56° to 62°N in Fig. 6, and only the area with a water column thicker than 900 m is included. Brandt et al. (2004) selected this area in order to observe the general propagation of the high EKE originating in high latitudes from altimeter data. Again, it is noted that the modeled EKE is weaker than the observation (Brandt et al. 2004). However, the modeled EKE shows a strong annual cycle, with its maximum EKE onset in January. The maximum EKE also propagates southward, and the approximate speed is 4.73 cm s−1, which is very close to the observations (Lilly et al. 2003; Brandt et al. 2004). The EKE maximum is mainly confined to the north of 59.5°N in 2008. While in 2007, the EKE maximum propagates farther southward to about 59.5°N.

Fig. 6.
Fig. 6.

The zonally averaged EKE of cycle 5 from 48° to 54°W is mapped from 56° to 62°N. The black arrows mark the southward propagation of the EKE, and the speed is approximately 4.73 cm s−1. To be consistent with Brandt et al. (2004), only the region where the ocean bottom is deeper than 900 m is included.

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0198.1

b. Irminger rings’ propagation

To look into the eddy behavior more closely, a series of procedures have been applied to identify and track the modeled eddies. First, the normalized Okubo–Weiss (Okubo 1970; Weiss 1991) parameter has been used to identify the vortex cores in the model output; second, only those cores containing rotating current directions covering all four quadrants are marked as vortex cores. The first step of the tracking procedures is to dissociate eddies that rotate in different directions. Then based on the flow speed in the Labrador Sea, it is not likely for eddies to propagate faster than 20 cm s−1 (Cuny et al. 2002; Lavender et al. 2000); however, the ranges for their propagation speed may reach as large as about 50 cm s−1 (de Jong et al. 2014). Given the time step interval in this study is 3 days, the maximum distance an eddy can propagate from one time step to the next is about 129 km. When applying the distance criteria, the majority of eddies can be disassociated. The distance criteria can largely reduce the computations, but the association of eddies at different time steps is not sensitive to the estimation on the propagation speed. Then, an eddy m at time step i will be compared to all the eddies that have not been disassociated with at time step i + 1. Both the relative vorticity and the radius will be compared. For instance, the vortex core m at time step i and vortex core n at time step j are compared in terms of the relative change of their relative vorticity RV and radii R, and the relative change is defined as the minimum of the ratios of m to n and n to m. The summation of the two minima is defined as similarity index (SI):
e2
The larger the SI value is, the more likely it is for eddy m and n to be the same one. To further improve the tracking efficiency, the minimum ratios of RV and R are required to be more than 0.4. Therefore, the range of SI in this study is 0.8 to 2. Finally, if there are M eddies at time step i and N eddies at time step j, the following two conditions have to be satisfied for m and n to be considered the same one:
e3
If an eddy at time i is not associated with any at time step i + 1, then the same tracking procedures will be applied for time step i + 2. If still no association is found at time step i + 2, then the eddy is considered dissipated at time step i.

Trajectories of eddies generated after 1 November 2006 are shown in Fig. 7. They are selected by the following criteria: the eddies have to be generated from the north part of the box (north of 59°N) in Fig. 5b, the maximum radii during their lifespan should be more than 20 km, and the eddies with a lifespan of longer than 50 days are shown in Fig. 7a, while those with a lifespan of no longer than 50 days are shown in Fig. 7b. During tracking procedures, eddies of all time spans are taken into account. In Fig. 7b, eddies with a lifespan no longer than 50 days are shown because they mostly concentrate on the origination area and cannot propagate where they may have a direct impact on the restratification of the convection area, they will not be considered in the restratification process. Under these criteria, the trajectories shown in Fig. 7a are most likely to be IRs. The lifespan of eddies has to be longer than 50 days because this is the approximate southward “flushing” time scale out of the northern generation region (Lilly et al. 2003), so eddies of shorter lifespan are not likely to enter the central Labrador Sea and play an active role in the restratification process. If the eddies propagate westward, it may take even longer for them to enter the central Labrador Sea. From 15 August 2005 to 15 December 2008 for cycles 3, 4, and 5, there are 40, 49, and 47 anticyclones generated and 23, 24, and 18 cyclones generated. The eddy trajectories of cycle 5 in Fig. 7a show two major pathways for IRs to enter the central Labrador Sea. One is westward between 2000- and 3000-m isobaths, then southward along the 3000-m isobaths. The other goes southward soon after generation. Thus, these eddies enter the central Labrador Sea either west or east of 54°W. Both pathways have been identified by in situ observations (Prater 2002; Hátún et al. 2007; Rykova et al. 2009) and numerical study (Luo et al. 2011). For those eddies taking the pathway west of 54°W, some of them may enter the convection area, while some of them will join the Labrador Current and may never directly bring heat flux into the convection area.

Fig. 7.
Fig. 7.

An ensemble of eddy trajectories of cycle 5 is shown from November 2006 to October 2008, and the filled gray circles (anticyclones) and lighter gray triangles (cyclones) denote the last locations of the trajectories. At the light gray patch in the central Labrador Sea, the maximum mixed layer depth exceeds 1000 m at the end of the convection season in 2008, as shown in Fig. 4b. The light gray contour lines are 2000- and 3000-m isobaths. (a) The eddies whose lifespan is longer than 50 days, and (b) the eddies whose lifespan is no longer than 50 days.

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0198.1

The southward propagation of IRs into the central Labrador Sea may be an important process for its restratification depending on the heat and freshwater carried at subsurface and surface, respectively, given the surface freshwater and midlevel heat deficit after convection ceases (Hátún et al. 2007; Gelderloos11). Both the lifespan and pathways of these eddies can affect their final contribution to the convection area. The lifespan of the 37 eddies in Fig. 7 are shown against their generation and disintegration latitudes (Figs. 8a,b). Generally, the cyclones have a shorter lifespan than the anticyclones, and only anticyclones have lifespans longer than 200 days. Most of these large eddies, or IRs, are generated between 60° and 62°N (Fig. 8a) and disintegrate in lower latitudes from 56° to 61°N (Fig. 8b). Among anticyclones of lifespan longer than 200 days, the filled gray circles in Figs. 8a and 8b disintegrate east of 54°W by taking the southward pathway, and the filled black ones disintegrate west of 54°W by the other pathway. However, those taking the southward pathway do not reach to lower latitudes as those taking the westward pathway do. Interestingly, the majority of these eddies disintegrating east of 54°W are generated south of 61°N (Fig. 8c). Figure 3a showed the West Greenland Current diverted westward at about 61.5°N, and the velocity is 10 to 15 cm s−1, of similar magnitude to what has been deduced from surface drifters by Cuny et al. (2002). However, the modeled current direction (Fig. 3a) is more westward than southward as observed (Fig. 3b). This modeled current direction may be responsible for the westward propagation of the eddies originating around it, so the eddies originating south of it can propagate southward, but the propagation velocity is slower than observation (about 5 cm s−1) because of the lack of a relatively strong background current.

Fig. 8.
Fig. 8.

(a) The latitudes where the eddies shown in Fig. 7a are initially identified. (b) The latitudes where these eddies are lost track of. (c) Latitude of eddy identification vs the longitude at which they are lost track of. The circles represent anticyclones, and triangles represent cyclones. The gray color denotes eddies that eventually enter east of 54°W, and the black color denotes eddies that enter west of 54°W. The criteria to select those eddies shown here are specified in text.

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0198.1

c. Vertical structure of Irminger ring

Vertical temperature and flow structure of an eddy captured by the model is shown in Fig. 9. This eddy is generated on 8 April 2008, and it is lost track of 9 August 2008. The life time of this eddy is 123 days. Its cap is fresher as well (Fig. 9b), which is crucial to maintain its buoyancy in the upper layer. On the other hand, the lower layer, extending from 200- to about 900-m depth, is about 0.8°C warmer than the ambient water. Glider observations (Hátún et al. 2007) have captured an IR with a middepth core that was 0.7°C warmer, and hydrographic data (Rykova et al. 2009) also identified some anticyclonic IRs with middepth cores that were 1.0°C warmer. The inward and outward flow field of the eddy (Fig. 9c) is surface intensified, with maximum velocity exceeding 0.7 m s−1 near the surface, 0.5 m s−1 in the upper 200 m, and 0.3 m s−1 above the 1-km depth. Hátún et al. (2007) found the maximum rotation velocity of IRs to be 0.7 m s−1. Generally speaking, the observed IRs’ rotation velocity is between 0.2 and 0.8 m s−1 (Lilly et al. 2003; Prater 2002). The modeled eddies of the Irminger ring type are always fresher in the surface 200 to 300 m, but some of them are colder, while others are warmer than the ambient water in the surface layer.

Fig. 9.
Fig. 9.

The vertical structure of an IR-type eddy: (a) the temperature, (b) the salinity, and (c) the horizontal velocity. The snapshots are taken on 6 May 2008. Contours of constant density are indicated in (a) and (b).

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0198.1

The eddies that have maximum radii larger than 20 km during their lifetime have been examined in terms of the evolution of their mean heat content within the eddy area, the radius, the maximum relative vorticity, and the mean surface heat flux over the eddy surface. The evolution of two of the eddies are shown in Fig. 10, with either a short lifetime or a longer lifetime. All the eddies examined show unanimous decrease in size and maximum relative vorticity toward the end of their lifetime. The mean heat content at two different layers within the area of eddies (Fig. 10a) show short periods of fast heat loss in between that of slow heat loss periods. For some eddies, the mean heat content decrease can be very small, except the sudden decrease when they enter a much colder area. This sudden decrease does not seem to be related to the surface heat loss; however, stronger oscillation of the mean surface heat loss can be observed before the eddies are lost track of or before they finally dissipate. This oscillation may be related to the model resolution, since toward the end of the tracking, the radii can drop to around 10 km, which the model can barely resolve. It is possible that during the sudden decrease of mean heat content, the eddies can deliver a significant amount of buoyancy to the ambient water; however, the time scale for this sudden decrease varies among eddies; stronger and larger eddies tend to have a significant buoyancy release over a longer time period, about 20 days and 10 days in Fig. 10a.

Fig. 10.
Fig. 10.

The evolution of two IR-type eddies, one in gray, the other in black: (a) the area mean relative heat content of the eddies between the surface and 200-m depth (solid lines), and the relative heat content between 200- and 500-m depth (dashed lines); (b) the radii of the two eddies; (c) the maximum relative vorticity of the two eddies at 50-m depth; and (d) the area mean surface heat flux over the eddy surface.

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0198.1

5. Heat budget of the convection area

The convection area in this study is defined as where the maximum mixed layer exceeds 1000 m at the end of the convective season, and the convection area of cycle 5 is shown in Fig. 7b, compared to the Argo observed mixed layer depth in Fig. 7a, The equivalent radius of the convection area is approximately 153, 169, and 160 km for experiment cycles 3, 4, and 5. Both the original NCEP reanalysis 2 surface heat flux and the heat flux with model correction are shown in Fig. 11a. Both datasets are filtered with a 1-month boxcar window, and the corrected heat flux is very close to the original forcing except from June to October, when the model SST is higher than the reference SST. The postconvection heat regain in the surface layer of the central Labrador Sea is mainly controlled by the surface heat flux, while the lower-layer heat regain is contributed by lateral eddy flux from the boundary currents (Lilly et al. 2003; Straneo 2006). In Fig. 11b, the surface heat flux is integrated from the minimum heat content in the upper 200-m water column, and it is closely followed by the heat content variation until after December. Upon the onset of convection, lower layers below 200 m begin to lose heat and display relatively steep decrease in heat content, and the affected depth depends on the vertical extent of convective mixing.

Fig. 11.
Fig. 11.

The surface heat flux and heat content variation in the convection area during the simulation time, here the convection area is the same as in Fig. 7. (a) The total surface heat flux from NCEP reanalysis 2 and actual forcing after correction over the convection area are represented by thin black and gray lines respectively, and the 1-month moving boxcar filtered surface flux are represented by thick lines. (b) The heat content of the upper 200-m water column, and the integrated surface heat flux from the minimum heat content in each year. (c) The relative ocean heat content (HC, black lines) between surface and 1900 m referenced to the maximum value of each year, and the model surface heat flux accumulated from the same reference value. The referenced value is set to zero, and dashed lines indicate the ocean loses heat, while solid lines indicate the ocean gains heat. (d) The relative heat content (see text for definition) variation for the upper 200 m, the water column between 200 and 500 m, and the layer between 500 and 1000 m.

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0198.1

The heat content of the water column from the surface to 1900-m depth is integrated each year from the beginning of the decrease, following Yashayaev and Loder (2009). In Fig. 11c, the vertical coordinate is reversed as by Yashayaev and Loder (2009), thus the increasing trend of heat content indicates ocean heat loss (dotted line), while the decrease trend indicates heat gain (solid line). During the heat loss phase, the whole water column does not lose heat as much as dictated by the integrated surface heat loss. By the time of the next heat loss cycle, the difference between the gray and black solid lines should be compensated by lateral heat gain. The convection area in 2008 winter lost heat at a rate of 3.8 GJ m−2 and gained at a rate of 2.7 GJ m−2 during both phases (a complete cycle). Although the area for the total water column heat content calculation in this study is different from (smaller than) the Argo observation by Yashayaev and Loder (2009), the total lateral heat gain is very similar to their findings (their Fig. 4b). Our results are also qualitatively similar to the findings by Luo et al. (2012, their Fig. 10a). For example, during the 3 yr of study, the winter heat loss is increasing year by year, and both our study and the study by Luo et al. (2012) show that the central Labrador Sea regain more than its heat loss during the 2006 restratification, and both reach almost balance between heat loss and heat gain during the 2007 restratification, while both show serious heat deficit after the 2008 deep convection.

To examine the responses of the surface layer and the lower layer to surface forcing together, the relative heat content change is defined as
e4
where HC0 is the referenced value of heat content that is arbitrarily determined, and HC is the heat content that varies with time. The HC0 in Fig. 11d is the heat content on 2 May 2006. In the winters of 2006 and 2007, the convection is shallow, so the heat content of the layer between 500 m and 1 km did not decrease significantly, and the heat content between 200 and 500 m decreases about 12%. During the winter of 2008, the heat content decreases at least 20% in both lower layers. The lower water layer has a two-phase annual cycle: first, a steep decrease during the convection season, then a slower and longer reheating process during the restratification season. The surface layer heat content decreases from September and slows down after December when convection starts because of the mixing downward with warmer water (Fig. 11d).

Since the restratification trend in the lower layers are nearly linear, a linear regression can provide estimation of the general lateral heat flux in the two lower layers, as listed in Table 1. The integrated surface heat flux is relatively small compared to the lateral heat flux, and it usually can only affect the surface 200 m of the water column. The magnitude of the lateral flux is in line with observations (Straneo 2006). The convections in 2006 and 2007 are relatively shallow in this region, and the area where the mixed layer exceeds 1000 m in those 2 yr is smaller than in 2008, hence the smaller lateral heat flux in the layer between 500 and 1000 m. In 2007, the lateral heat flux and heat content increase during restratification are both larger than 2006, in both layers, because the winter heat loss is larger during 2007, and heat is extracted from deeper layers than 2006. In 2008, the lateral flux is 29 and 25 W m−2 in the two layers, respectively; however, by the end of the restratification, the heat content still does not reach the preconvection level (Figs. 10c,d).

Table 1.

Integrated surface heat flux (ISHF; GJ m−2), total heat content increase (HC; GJ m−2), and mean lateral heat flux (W m−2) in each model year at each level during restratification phase; the results are based on the ensemble mean of the three experiment cycles 3, 4, and 5.

Table 1.

6. Contributions by modeled Irminger rings

After the restratification begins in 2008, which is roughly at the end of March, there are 6, 5, and 8 IR-type eddies propagating south of 59.5°N for experiment cycles 3, 4, and 5, respectively. Among these propagating south of 59.5°N, 3, 2, and 4 eddies entered the convection area. The trajectories of those who entered the convection area in cycle 5 are shown in Fig. 12a. Eddies 1 to 4 have been found to enter the convection area (in Fig. 4b). The heat content of eddies 1 to 4 (HCE) are calculated, and their heat flux (fluxE) in the convection area is derived by taking the temporal derivative of their heat content across their lateral boundaries:
e5
e6
Fig. 12.
Fig. 12.

(a) The trajectories of eddies that propagate into the convection area after the lower level’s restratification starts in 2008. The heat content of eddies 1 to 4 for (b) 200–500 m and (c) 500–1000 m. The heat flux across the lateral boundary for eddies 1 to 4 in the (d) 200–500 m and (e) 500–1000 m.

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0198.1

The heat content of eddies 1 to 4 after entering the convection area is shown in Figs. 12b to 12c for both the 200- to 500-m layer and the 500- to 1000-m layer. The heat content in Figs. 12b and 12c has been spread over the convection area for cycle 5, which has an equivalent radius of 160 km in 2008. Upon the moment of entering the convection area, the heat content (spread over the convection area of 160-km equivalent radius) of eddies 1 to 4 and the concurrent convection area are documented in Table 2. Following the thermal contribution algorithm by Hátún et al. [2007, their Eq. (6.5)], the absolute contribution (AC) by each eddy at each level is calculated using the equation
e7
where r is the eddy radius, R is the convection area equivalent radius, HCE is the heat content of eddy, and HCC is the heat content of the convection area. The relative contribution compared to the total heat gain in 2008 (Table 1) is also calculated. The total observed 200–1000-m heat contribution of IR is 43 MJ m−2 (Hátún et al. 2007), while in Table 2, only the contributions by eddies 2 and 4 reach 37.6 and 39.5 MJ m−2. Heat contributions by eddies 1 and 3 are much smaller than the observation. It is possible for the model to underestimate the heat contributions by IRs because of their shorter lifespan and faster dissolution in the model; thus, before they reach the convection area, they already lost a certain amount of heat. Another cause of the difference is that the referenced Labrador Sea Water heat content is chosen differently. This study calculates the eddy heat content at the time when the eddy is entering the convection area, while Hátún et al. (2007) calculate the heat content when convection ceases. If the same assessing strategy is used, then the mean relative contribution by all the newly generated eddies will be about 5.3%, within the range from 3.6% to 8.3% estimated by Hátún et al. (2007). However, it is noted that the model has generally underestimated the number of eddies that can enter the convection area and their lifetime; thus, the modeled eddies will lose more heat before reaching the convection area even if they can. Given the underestimated eddy lifetime and enhanced eddy decay by the model, the model can still manage a reasonable heat balance compared to observations (Yashayaev and Loder 2009); the rest of the heat must have come from the boundary by other mechanisms, such as the BCEs. Although many of the IRs cannot reach the convection area, the modeled convection area may benefit from the BCEs activities artificially enhanced by the model because the short-lived IRs actually increased the stratification around the convection area and shortened its restratification time scale (Gelderloos11).
Table 2.

The heat content of eddies 1 to 4 in Fig. 12a (HCE; GJ m−2) and the heat content of the convection area (HCC; GJ m−2) when the eddy starts to propagate into it. The absolute and relative contributions (AC; MJ m−2 and RC; %) to that specific level are calculated. The date in 2008 when these eddies entered the convection area is also marked, and their radii and ages upon entering the convection area are also listed.

Table 2.

The direct eddy heat flux by IRs would be difficult to measure because of the high variability of the identified radius, hence the fluctuation of the heat flux cross the lateral boundary of the eddies (Figs. 12d,e). The strong fluctuation of the heat flux is likely to be related to the fluctuation of the radii of the eddies. Because of the vigorous eddy activity and corresponding stirring effect around the eddies, they are subject to frequent deformation, which will change their equivalent radius. Sometimes, the eddy can increase its radius and expand horizontally (Fig. 10b), so the heat content of the eddy will increase, resulting in a positive heat flux. The horizontal expansion or contraction of the IRs can also be observed from the altimetry data, for example, eddy 2 captured by Hátún et al. (2007) in their Fig. 2. On the other hand, the vertical extents of the IRs do not vary much between the depths of 200 and 1000 m. Although the rotation weakens at all depths toward the final dissipation, making it more difficult to quantify the vertical extents of the IRs, the IRs seem to be rather barotropic, given the covariant heat content in both layers (Figs. 12a,b).

7. Summary and discussion

This study simulates the 2007/08 winter deep convection events and subsequent restratification using ROMS. The results show that the general circulations and eddy activities are in line with the observations, except a relatively stronger boundary current and generally weaker EKE field. The model reproduced the 2008 winter deep convection event very well. The modeled mixed layer pattern resembles the Argo float–derived mixed layer in terms of both the depth and spatial distribution and thus may be able to reduce the activity of BCEs that is artificially enhanced to some extent. In general, the modeled restratification process in 2008 (Fig. 11c) has a similar pattern to the observations by Yashayaev and Loder (2009). In 2008, the heat regain during the restratification phase for 200–500 and 500–1000 m are 0.55 and 0.56 GJ m−2, respectively, and the modeled lateral heat inflow during a complete cycle for the whole water column is about 2.7 GJ m−2, which is very close to the observed 2.6 GJ m−2 (Yashayaev and Loder 2009). Moreover, the restratifications at different depths show a more or less harmonic seasonal cycle for the surface layer, while the lower layers’ heat content shows a steep decrease during convection season and a slow rise during restratification; the same trends have been observed by Straneo (2006) too.

The model simulated both the fast westward and southward pathways for IRs propagation. Yet, the direction of the modeled background current as a branch of the West Greenland Current did not turn southward immediately at the eddy-shedding zone, instead, it is diverted more toward west than the altimeter-derived currents (Fig. 3b). It is speculated that because of this error, the modeled eddies originating north of 61.5°N propagate fast toward the west, while those originating south of 61.5°N can drift southward, but the speed is much slower than indicated by observation (Lilly et al. 2003). As a result, there are only four eddies reaching the convection area in 2008 (Fig. 4b). During this slow and long journey before their arrival, they may have lost a considerable amount of heat; therefore, the modeled eddies 1 to 4 (Fig. 12a) did not carry as much heat as the observed one by Hátún et al. (2007). Equation (7) is used in this study to measure the absolute contribution by IRs, and it is similar to Eq. (6.5) used by Hátún et al. (2007). The only difference is that the equation by Hátún et al. (2007) calculates the IRs’ contribution over the unit area of the convection region, and our equation calculates the total contribution over the whole convection area. The contributions by IRs will be highly sensitive to the eddy radius and the eddy heat content, and these quantities vary a lot from eddy to eddy. On the other hand, the result is not as sensitive to the heat content of the convection region because it is averaged over a relatively large area.

One of the debates regarding the restratification mechanism is what is the relative importance of different eddies present in the convection area. Based on this model work, the lateral heat flux in two subsurface layers is about 1.1 GJ m−2, which should be mainly due to different eddy fluxes, if assuming no vertical exchange. Each mesoscale eddy in the convection area contributes about 1%–4% of the total heat influx (Table 2). Taking into account the significant underestimation of the number of IRs and their heat contribution, the model largely underestimates the total contribution, if there are instead 10 IRs [approximately the observed number by Lilly et al. (2003)] in the convection area during restratification, the contribution by IRs would correspondingly become 10%–40%.

Even though a single modeled IR in the convective region can bring similar heat to the observed one, the modeled IRs have a shorter lifespan, which results in its faster mixing into the background flow and a more homogeneous convection region than the real ocean. The modeled convection region has a restratification speed similar to observations, but more of the heat is brought in by smaller eddies, such as CEs, BCEs, or even smaller ones, due to the stirring of IRs, instead of the IRs. Although the model seems to be able to manage the heat balance and reproduce a reasonable end-of-restratification state (Straneo 2006; Yashayaev and Loder 2009) even without correct eddy fluxes in details, it should be noted that the real convection region may have more anticyclonic IRs presented and thus are much more patchy during convection, given the resistance to the disintegration of these anticyclonic IRs to winter cooling. The model needs better skill on mesoscale eddies and a more accurate and detailed heat balance scenario requires further investigation.

Acknowledgments

This study is partially supported by NASA Physical Oceanography Program, NASA EPSCoR Program, NASA Space Grant, and NOAA Sea Grant at the University of Delaware. We thank Emanuele Di Lorenzo for sharing his computational resource to the model preprocessing and his helpful comments on the configuration of the model. We thank Jonathan M. Lilly and Renske Gelderloos for their valuable explanations regarding their published work. We thank Federico Ienna for proofreading the manuscript. We thank the anonymous reviewers for their in-depth comments that largely improved this work.

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