2.1 Reference regional model configuration

We briefly describe the regional model configuration of reference used for the control run (with changes being made afterwards in the different sensitivity tests). Version 3.6 of NEMO is used. The geographical domain is shown in Fig. 1. It includes part of the Greenland Sea, the Denmark Strait, and a large part of the Irminger Sea. The reference NEMO setting has been designed to be representative of the solution that a global model would produce. Therefore, the configuration (geometry, numerical grid and schemes, physical parameterizations) has been extracted from an existing global ORCA12 configuration ($\mathrm{1}/\mathrm{12}{}^{\circ }$ resolution, 46 z levels) used in many simulations of the DRAKKAR Group (see Molines et al., 2014, for a description and namelist). This configuration, referred to as DSO12.L46 (for $\mathrm{1}/\mathrm{12}{}^{\circ }$ and 46 vertical levels) hereafter, is described with emphasis being given to the parameters chosen for the control simulation from which sensitivity tests are performed. Changes that are made in the sensitivity tests are also indicated.

• Bottom topography and coastlines are exactly those of the global $\mathrm{1}/\mathrm{12}{}^{\circ }$ ORCA12 configuration and are not changed in sensitivity experiments, except when grid refinement is used. In this latter case the refined topography is a bilinear interpolation of that at $\mathrm{1}/\mathrm{12}{}^{\circ }$, so the topographic slopes remain unchanged.

• The horizontal grid in the control run is a subset of the global tripolar grid at $\mathrm{1}/\mathrm{12}{}^{\circ }$ (the so-called ORCA12, ∼ 5 km at the latitudes of the Irminger Basin). The sensitivity to horizontal resolution is addressed by increasing the grid resolution to $\mathrm{1}/\mathrm{36}{}^{\circ }$ (∼ 2 km) and $\mathrm{1}/\mathrm{60}{}^{\circ }$ (∼ 1 km) over a small region that includes the Denmark Strait and a large part of the East Greenland shelf break (Fig. 1). The AGRIF two-way grid refinement software (Debreu et al., 2007) is used to connect the nested grids.

• Vertical resolution. The standard 46 fixed z levels used in many DRAKKAR simulations are used in the control simulation, with partial steps to adjust the thickness of the bottom level to the true ocean depth (Barnier et al., 2006). Sensitivity experiments also use 75, 150, and 300 z levels. The cell thickness as a function of depth is shown in Appendix A (Fig. A1), and the resolution of the Ekman layer in the different vertical resolution settings is discussed.

• Momentum advection scheme. A vector-invariant form of the momentum advection scheme (the energy- and enstrophy-conserving EEN scheme as in Sadourny et al., 1975, and Barnier et al., 2006, with the correction proposed in Ducousso et al., 2017) is used in the control and sensitivity experiments with an explicit biharmonic viscosity. Sensitivity tests used the upstream-biased third-order scheme (UBS scheme) available in NEMO. Since this scheme includes a built-in biharmonic-like viscosity term with an eddy coefficient proportional to the velocity, no explicit viscosity is used in the momentum equation.

• Isopycnal diffusivity on tracers. The TVD (total variance diminishing) scheme standard in NEMO is used with the Laplacian diffusive operator rotated along isopycnal surfaces. The slopes of the isopycnal surfaces are calculated with the standard NEMO algorithm. The diffusion coefficient remains the same in all sensitivity experiments. A sensitivity experiment was made that calculates the slope of the isopycnal using the Griffies triad algorithm (Griffies, 1998).

• Vertical mixing is treated with the standard NEMO TKE scheme (Madec et al., 2016; Reffray et al., 2015). Because the model uses hydrostatic pressure, the case of unstable stratification is treated with an enhanced vertical diffusivity (EVD) scheme that sets the value of the vertical diffusion coefficient to 10 m² s⁻¹ in the case of static instability of the water column. It is applied on tracers and momentum to represent the mixing induced by the sinking of the dense water. A few sensitivity experiments used the EVD scheme on tracers only. Other experiments used the K−ϵ closure scheme included in NEMO (Reffray et al., 2015).

• Bottom boundary layer (BBL) parameterization. The control run does not use the BBL scheme that is available in NEMO based on the parameterization of Beckmann and Döscher (1997). The scheme is tested in a sensitivity experiment.

• The free-surface (linear filtered) scheme, the LIM2 sea ice parameters, the scheme and data used at the lateral open boundaries, and the bulk formula and atmospheric forcing data that drive the model are identical in all experiments.

Figure 1Regional model domain with the ocean depth in colour. The 250, 500, 1000, 1500, and 2000 m depth isobaths are contoured in black. The grey box indicates the region where the two-way grid refinement (1∕36 and $\mathrm{1}/\mathrm{60}{}^{\circ }$) is applied in some simulations. The locations of the various sections used to monitor the model solution are shown by the red lines. Section 1 is the reference section chosen for the sill.

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2.2 Initial conditions, surface and open boundary forcing

Data used to initialize the simulation and to drive the flow at the prescribed open boundaries are obtained from an ORCA12 simulation. This global simulation was initialized with temperature and salinity values from a climatology (Levitus, 1998) and started from rest. The atmospheric forcing that was used is the daily mean climatology of the 6-hourly DFS4.4 atmospheric forcing (Brodeau et al., 2010). The forcing data of each day of the year are the climatological mean of that day calculated over the period 1958 to 2001 (see Penduff et al., 2018, for details). This global simulation was run for almost 9 decades with this climatological forcing being repeated every year. It has also been used in the studies of e.g. Sérazin et al. (2015) and Grégorio et al. (2015) to study the intrinsic inter-annual variability. Every DSO model simulation used in the present study (the control run and all sensitivity runs) is initialized with the state of the global run on 1 January of year 72 and is run for a period of 5 years (until year 76). The atmospheric forcing is the same as in the global run and is also repeated every year. The data used at the open boundaries of the DSO domain are extracted from years 72 to 76 of the global simulation (5 d mean outputs), so the open boundary forcing is fully consistent with the atmospheric forcing and the initial state.

We have chosen such a simulation scenario because several decades have passed from the initialization of the global run, and the model has reached a dynamical equilibrium and is close to thermodynamical equilibrium, which results in a negligible drift in the mass field. This allows us to undoubtedly attribute the changes seen in the sensitivity experiments to the changes made in the model setting. During this period the transport at the sill of the Denmark Strait is very stable and close to observed values (∼3 Sv, see Sect. 2.3).

In this scenario, the initial bottom stratification is expected to be particularly affected by biases introduced in the properties of the water masses by the unrealistic representation of the overflows in the z-coordinate framework, so any improvement achieved in the representation of the overflow should be rapidly identified. However, the presence of these model biases reduces the relevance of the comparison to observations.

2.3 Control simulation DSO12.L46

A control simulation (referred to as DSO12.L46) is performed with the characteristics described in Sect. 2.1 and the initial and forcing conditions described above. As expected from its design, the solution of the DSO12.L46 5-year-long control run very faithfully reproduces the solution of years 72 to 76 of the global ORCA12 run. This was verified in different aspects of the circulation. The large-scale circulation patterns are found to be very similar in both simulations, as illustrated with the surface and bottom currents shown in Fig. 2. The predominant currents such as the East Greenland Current (EGC), the Irminger Current (IC), and the DSO itself are very similar between the global and the regional model. This circulation scheme also compares well with that described from observations in Daniault et al. (2016) and from an ORCA12 model circulation simulation in Marzocchi et al. (2015). The correspondence between the global and control runs regarding the properties of abyssal waters was confirmed, especially at 29 different sections along the path of the overflow; the section locations are outlined in Appendix B, as is the correspondence in transport and bottom mean temperature across these sections (not shown). The bottom temperature in the Irminger Basin was found to be very similar in both simulations, with a diluted signature of the overflow waters as expected from a z-level model after a simulation of several decades. Therefore, this regional model appears to be a reliable simulator of what the global model produces in that region.

Figure 2Surface (a) and bottom (b) mean currents (year 76) in the global ORCA12 simulation. Vectors and colours indicate current direction and speed (m s⁻¹). Surface (c) and bottom (d) mean currents (year 76) in the regional DSO12.L46 regional simulation. Vectors indicate the direction of the current. Colours indicate the current speed difference between the global and the regional simulation (m s⁻¹). Blue and red indicate that the current speed is greater or smaller in the global or regional simulation.

Figure 3Time evolution of the volume transport of waters of potential density greater than σ₀=27.80 kg m⁻³ at the sill section (section 1 in Fig. 1) in the control (blue line) and the global (green line) simulations (the latter providing the open boundary conditions). Annual mean and SD (Sv) are indicated for every individual year of simulation. The depth-integrated (barotropic) transport is shown for the control simulation (purple line). 5 d mean values were used to produce this figure.

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Most important for the present study are the properties of the overflow “source waters”, i.e. the properties of the waters at the sill of the Denmark Strait. Figure 3 shows the volume transport at the sill of waters flowing below the 27.8 isopycnal. Both the global and the control runs show a very similar mean and variability as well as a transport that is very steady during the 5 years of simulation. The model mean (∼3 Sv) is comparable to but in the lower range of the values published in the work of Macrander et al. (2005) and Jochumsen et al. (2012). The standard deviation computed from 5 d outputs (∼0.3 Sv in the control run, increasing to ∼0.7 Sv when calculated from daily values) is rather small when compared to the 1.6 Sv of Macrander et al. (2005). The modelled flow of dense waters presents a marked seasonal cycle which is not present in observations (Jochumsen et al., 2012). This signal is the signature of the large seasonality of the barotropic flow (Fig. 3) that constrains the whole water column.

Figure 4 presents the characteristics of the mean flow across the sill. The model simulation is compared to the data of Mastropole et al. (2017), who processed over 110 shipboard hydrographic sections across the Denmark Strait (representing over 1000 temperature and salinity profiles) to estimate the mean conditions of the flow at the sill. Compared with the compilation of observations by Mastropole et al. (2017) (Fig. 4a) the model simulation (Fig. 4b) shows a consistent distribution of the isopycnals. However, the observations exhibit waters denser than 28.0 in the deepest part of the sill, which the model does not reproduce. Large flaws are noticed regarding the temperatures of the deepest waters, which are barely below 1 ^∘C when observations clearly show temperatures below 0 ^∘C (also seen in the observations presented in e.g. Jochumsen et al., 2012, 2015; Zhurbas et al., 2016). A bias toward greater salinity values (not shown) is also found in the control experiment, which shows a bottom salinity of 34.91 compared to 34.9 in the observations shown in Mastropole et al. (2017), but the resulting stratification in density shows patterns that are consistent with observations. The distribution of velocities (Fig. 4c) is also found to be realistic when compared with observations (i.e. Fig. 2b of Jochumsen et al., 2012), with a bottom-intensified flow of dense waters (up to 0.4 m s⁻¹) in the deepest part of the sill. Although the present set-up is designed to investigate model sensitivity in twin experiments and not for comparison with observational ends, the control run appears to provide a flow of dense waters at the sill that is stable over the 5-year period of integration and qualitatively reproduces the major patterns of the overflow source waters seen in the observations. Therefore, despite existing biases, the presence of a well-identified dense overflow at the sill confirms the adequacy of the configuration for the sensitivity studies.

Figure 4Mean flow characteristics (annual mean of year 76) in the global simulation for a section across the sill. Temperature (^∘C) is represented by colours and white contours for (a) the observations (Mastropole et al., 2017) and (b) the control simulation (DSO12L46 $\mathrm{1}/\mathrm{12}{}^{\circ }$ and 46 vertical levels). Potential density values (σ₀) are shown by the contour lines coloured in red (27.6), green (27.8), and black (27.85). (c) The velocity normal to the section in the control simulation (with southward velocity in blue being negative). White lines indicate the 0 m s⁻¹ contour (dashed–dotted line), the −0.1 m s⁻¹ contour (full line), and the −0.2 m s⁻¹ contour (dashed line).

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Figure 5Potential temperature (^∘C) at section 29 in (a) the observations (ASOF6 section; Quadfasel, 2010), (b) the $\mathrm{1}/\mathrm{60}{}^{\circ }$, 150-level simulation (annual mean), and (c) the $\mathrm{1}/\mathrm{12}{}^{\circ }$, 46-level simulation (annual mean). Red, green, and black full lines are isopycnals 27.6, 27.8, and 27.85. White lines are isotherms in 1^∘C intervals. In panel (b), section 29 is outside (100 km downstream) the $\mathrm{1}/\mathrm{60}{}^{\circ }$ AGRIF zoom, so the effective resolution is $\mathrm{1}/\mathrm{12}{}^{\circ }$, but the water masses acquired their properties upstream within the $\mathrm{1}/\mathrm{60}{}^{\circ }$ resolution zoom.

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Finally, in order to assess improvements in the sensitivity tests, the major flaws of the control simulation must be described. If similarities with observations are found at the sill, the evolution of the DSO plume in the Irminger Basin is shown to be unrealistic in the present set-up of the control simulation and presents the same flaws as in the global run. This is demonstrated by the analysis of the temperature and potential density profiles at the most downstream cross section (section 29), wherein the model solution is compared to observations (Fig. 5), and at the other cross sections along the path of the DSO in the control simulation (Figs. 6a, c and 7a, c). The evolution of the DSO plume as it flows southward along the East Greenland shelf break is represented by a well-marked bottom boundary current (e.g. the bottom currents in Fig. 2) carrying waters of greater density than the ambient waters. Far downstream of the sill (section 29), the observations show a well-defined plume of cold water confined below the 27.8 isopycnal under 1500 m of depth (Fig.  5a). The bottom temperature is still below 1 ^∘C. In the control simulation (Fig. 5c), one can clearly identify the core of the DSO plume by the 27.85 isopycnal, so it is clear that the plume has been sinking to greater depth as it moved southward. This evolution is only qualitatively consistent with the observations at this section. The modelled plume is significantly warmer and exhibits a core temperature of 3.5^∘ (against 2 ^∘C or less in the observations). The plume is also much wider than observed and exhibits much smaller temperature and salinity gradients separating the plume from the interior ocean, indicating a greater dilution with ambient waters. The plume is barely distinguishable from the ambient fluid below 2000 m, while it is still well-marked at that depth in the observations. The sinking and dilution of the plume as it flows southward along the slope of the Greenland shelf are well-illustrated in Figs. 6 and 7 (panels a and c), which display the potential temperature at the other sections. If the overflow waters are still well-marked at section 16 (Fig. 6a), they are barely distinguishable from the ambient water at section 29.

Figure 6Distribution with depth of the annual mean temperature (fifth year of model run) at section 16 (Dohrn Bank array) for (a) simulation DSO12.L46 and (b) simulation DSO60.L150 (in the refined grid), as well as at section 20 (Spill Jet section) for (c) simulation DSO12.L46 and (d) simulation DSO60.L150 (in the refined grid). Temperature (^∘C) is represented by colours with white contours. Potential density values (σ₀) are shown by the contour lines coloured in red (27.6), green (27.8), and black (27.85). The white-rimmed dot in (b) corresponds to the location of the profiles displayed in Fig. 15, and the red-rimmed and blue-rimmed dots in (d) correspond to the locations of the profiles displayed in Fig. 13.

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Figure 7As in Fig. 6 at section 24 (TTO array) for (a) simulation DSO12.L46 and (b) simulation DSO60.L150, as well as at section 29 (Angmagssalik array) for (c) simulation DSO12.L46 and (d) simulation DSO60.L150.

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The bottom temperature shown in Fig. 8a illustrates this excessive dilution of the overflow waters. Indeed, the cold water tongue seen at the bottom of the Denmark Strait at a temperature of about 2 ^∘C clearly sinks as it extends to the southwest and crosses the 1000 and 1500 m isobaths. But as it sinks, it is rapidly diluted, loses its “cold water” character, and is not distinguishable from the background waters beyond 64.5^∘ N. Such a plot of the bottom temperature summarizes rather well what we also learned in the analysis of the cross sections (e.g. Fig. 5). The same plot for the salinity (not shown) shows waters fresher than surrounding waters in the overflow path, with a salinity that increases from 34.91 at the sill to around 34.96 at 1000 m and reaches the background value (∼ 35.02) at 1500 m of depth. This demonstrates the large dilution by entrainment with the waters of the Irminger Current in the final solution.

3.1 Sensitivity to vertical resolution at $\mathrm{1}/\mathrm{12}{}^{\circ }$

The first set of tests that we present is for the sensitivity of the DSO representation to the vertical resolution at $\mathrm{1}/\mathrm{12}{}^{\circ }$ horizontal grid resolution. The DSO12.L46 control run (46 levels) is compared with simulations with 75, 150, and 300 vertical levels, with all other parameters being identical. The mean bottom temperature of the fifth year of these four simulations (Fig. 8) reveals that the increase in vertical resolution at $\mathrm{1}/\mathrm{12}{}^{\circ }$ works to the detriment of the representation of the overflow. In the 75-level case, the descent of the DSO plume stops at the 1500 m isobath, blocked by a westward flow of warm Irminger waters that invades the 1500 to 2000 m depth range. This yields a general warming of the bottom waters in the Irminger Basin and along the whole East Greenland shelf break. The overflow representation improves slightly in the 150-level case as the DSO plume still reaches the 2000 m isobath, feeding the deep basin, but with less efficiency than in the 46-level case. Finally, the representation of the DSO is even more degraded in the 300-level case, with this resolution exhibiting the greatest dilution of the DSO waters among all resolutions. This deterioration of the overflow properties was verified in all the other diagnostics (hydrographic sections, T–S diagrams, etc.).

To understand that behaviour, one recalls how the cascading of dense water is treated in the z-coordinate NEMO framework. In the case of static instability (i.e. when the fluid at a given level has a greater potential density than the fluid at the next level below), the vertical mixing coefficient, usually calculated with the TKE closure scheme, is assigned a very large value (usually 10 m² s⁻¹). This instantaneously (i.e. over one time step) mixes the properties (temperature, salinity, and optionally momentum) of the two cells, re-establishing the static stability of the stratification. This parameterization, referred to as EVD (enhanced vertical diffusion, already described in Sect. 2.1), is at work to simulate the sinking (convection) and the cascading (overflow) of dense waters. Note that when the EVD was not used in our experiments, we noticed that the TKE mixing scheme often produced values of the diffusion coefficient larger than 1 m² s⁻¹ and in very particular cases exceeding 10 m² s⁻¹.

Figure 9Vertical diffusivity coefficient (K_z, summer mean in the fifth year of simulation) along the path of the vein calculated for (a) simulation DSO12.L46 and (b) simulation DSO12.L300. Potential density values (σ₀) are shown by the contour lines.

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The vertical diffusivity along the path of the overflow is shown in Fig. 9 for the 46- and the 300-level cases (the definition and method of calculation of the overflow path are given in Appendix B). Compared to the 46-level case (Fig. 9a), the 300-level case (Fig. 9b) exhibits greater values of the diffusion coefficient near and above the bottom along the path of the overflow. This enhanced mixing affects the overflow plume, which 200 km after the sill does not contain waters denser than 27.85, while such waters are still found 300 km down the sill in the 46-level case. The 300-level case also exhibits large values of the diffusion coefficient at intermediate depth (between isopycnals 27.8 and 27.6). This is driven by the vertical shear existing between the northward surface current passing through the Denmark Strait (the NIIC), which is very variable in position and intensity, and the southward deep current carrying the overflow waters (e.g. Spall et al., 2019). We notice that the mixing is significantly greater in the high-resolution case, which indicates that this process could also contribute to the dilution of the overflow plume. However, it does not seem to affect the thickness of the 27.8 isopycnal. An explanation for this is searched for following the paradigm of Winton et al. (1998), which states that the horizontal and vertical resolutions should not be chosen independently: the slope of the grid (Δz∕Δx) has to equal the slope of the topography (α) to produce a proper descent of the dense fluid (see their Fig. 7). If this is not the case, the vein of dense fluid thickens by mixing with the ambient fluid at a rate proportional to the ratio of the slopes $\mathit{\alpha }/(\mathrm{\Delta }z/\mathrm{\Delta }x)$.

Figure 10Idealized experiment simulating the rationale explored in Fig. 7 of Winton et al. (1998). Cold water (10 ^∘C) descends a shelf break in a configuration with ambient water at 15 ^∘C after 9 d of simulation. Two vertical resolutions are used: (a) Δz=50 m, (b) Δz=10 m. Temperature (^∘C) is represented by colours. Vectors represent the velocity, with the vertical velocity being re-scaled according to the grid aspect ratio in the case in panel (a).

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To show how NEMO follows this concept, we simulate the descent of a continuous source of cold water down a shelf break in an idealized configuration (with no rotation). The configuration (Fig. 10) is as follows. A 20 km wide shelf of depth 500 m is located on the left side of the 2D domain. It is adjacent to a shelf break 250 km wide reaching the depth of 3000 m, and then the bottom is flat. Initial conditions are as follows: a blob of cold water is placed on the bottom of the shelf with a temperature of 10 ^∘C, with the temperature of the ambient fluid in the rest of the domain being 15 ^∘C and the salinity being constant (35) in the whole domain. During the simulation, the temperature is restored on the shelf to its initial value to maintain the source of cold water. A relaxation to the ambient temperature is applied over the whole water column in the last 50 km of the right side of the domain in order to evacuate the cold water. The horizontal grid resolution is 5 km (comparable to the $\mathrm{1}/\mathrm{12}{}^{\circ }$ resolution of our regional DSO configuration). Two simulations with different vertical resolutions are run. The first one uses 60 levels of equal thickness (50 m) such that the local grid slope always equals the slope of the bathymetry (Fig. 10a; Δz=50 m). In the second simulation, the vertical resolution is increased by a factor of 5 (300 vertical levels; Fig. 10b; Δz=10 m). In the absence of rotation, the pressure force pushes the blob over the shelf break and the EVD mixing scheme propagates the cold water down to the bottom as the blob moves toward deeper waters, generating an overflow plume. After about 5 d, the front of the plume has reached the end of the shelf break and entered the damping zone at the right side of the domain, reaching a quasi-stationary regime. In that regime, the overflow simulated in the 300 vertical levels run (i.e. with a local grid slope smaller than the topographic slope) presents warmer bottom waters (Fig. 10b) than in the 60-level run, in agreement with the results obtained with the realistic DSO12 configuration. Note that the vertical shear is more confined in the high-resolution case, which prevents the upward extent of the TKE-induced mixing of the upper part of the overflow that is seen in the low-resolution case. Note that when using a realistic bottom topography, the topographic slope will present large local variations and that it will be almost impossible to match the two slopes over the whole domain in a z-coordinate context. Therefore, increasing the number of vertical levels will not systematically degrade the overflow representation everywhere.

A set of simulations tested the effect of the different closure (i.e. vertical mixing) schemes available in NEMO (TKE with and without EVD; k−ϵ with and without EVD, constant diffusivity + EVD, Madec et al., 2016). It was found that the choice of the vertical mixing scheme has a very small (insignificant) impact on the final representation of the overflow at $\mathrm{1}/\mathrm{12}{}^{\circ }$.

Figure 11Annual mean of the bottom temperature of year 5 of simulations using grid refinement ($\mathrm{1}/\mathrm{36}{}^{\circ }$): (a) DSO36.L46, (b) DSO36.L75, (c) DSO36.L150, (d) DSO36.L300. Isobaths 500, 1000, 1500, and 2000 m are contoured in black.

3.2 Sensitivity to a local increase in horizontal resolution

3.2.2 The $\mathrm{1}/\mathrm{60}{}^{\circ }$ case

We now evaluate the representation of the DSO at $\mathrm{1}/\mathrm{60}{}^{\circ }$ (using a local refinement in the area shown in Fig. 1) with 46, 75, 150, and 300 vertical levels. At this resolution, the 46-level and 75-level cases show a solution very similar to that presented at the resolution of $\mathrm{1}/\mathrm{36}{}^{\circ }$ (no significant additional improvement, no figure shown). A significant change is again observed for 150 levels (Fig. 12a). The signature of the overflow waters at the bottom is even stronger in this case, with the cooling of the overflow plume being ∼ 1.1 ^∘C when compared to the $\mathrm{1}/\mathrm{12}{}^{\circ }$ solution (Fig. 8a) and ∼ 0.2 ^∘C compared to the $\mathrm{1}/\mathrm{36}{}^{\circ }$ case.

Figure 12Annual mean of the bottom temperature in the fifth year of simulations using a grid refinement of $\mathrm{1}/\mathrm{60}{}^{\circ }$ for (a) 150 vertical levels (DSO60.L150) and (b) 300 vertical levels (DSO60.L300). Isobaths 500, 1000, 1500, and 2000 m are contoured in black. The grey box indicates the area of refinement.

Figure 13Vertical profiles (annual mean) of the quasi-along-slope velocity (i.e. velocity normal to the section) at the two locations of section 20 indicated in Fig. 6d for simulations (a) DSO12.L150, (b) DSO36.L150, (c) DSO60.L150, and (d) DSO60.L300.

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The solution of the 300-level case at $\mathrm{1}/\mathrm{60}{}^{\circ }$ (Fig. 12b) represents an improvement compared to the $\mathrm{1}/\mathrm{36}{}^{\circ }$ case with the same vertical resolution. However, compared to the $\mathrm{1}/\mathrm{60}{}^{\circ }$ and 150-level solution (Fig. 12a), it shows a slightly greater dilution of the overflow and warmer temperatures at the bottom. Also, the propagation of the dense water away from the refinement area is clearly better with 150 levels. This should be taken into consideration when choosing the refinement region if used in global implementations. Improvements brought to the representation of the overflow by the resolution increase to $\mathrm{1}/\mathrm{60}{}^{\circ }$ and 150 levels can also be seen in Figs. 6 and 7, and they are quantitatively assessed in the following section (Sect. 4). At every section, the DSO60.L150 overflow (panel b and d) is clearly identified by a vein of cold waters well-confined along the slope with temperatures below 3 ^∘C and always at least 0.5 ^∘C colder than in the reference simulation (DSO12.L46; panels a and c). Temperature gradients between the core of the overflow and the interior ocean are also significantly increased, and the isopycnal 27.85 marks the limit of the vein of fluid very well. If a warm bias still exists compared to the observations of Quadfasel (2010) (bias in part due to the unrealistic properties of the interior entrained waters), the agreement of the overflow pattern with the observations is nevertheless greatly improved.

Figure 14Vertical diffusivity coefficient (K_z, hourly mean) at section 20 in simulations (a, c) DSO60.L150 (in the refined grid) and (b, d) DSO12.L150 in wintertime (with a 10 h difference). In black: contours of isopycnals 27.6, 27.80, and 27.85.

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