2.1 Target resolution

In order to find an optimal mesh for the CMIP6 configuration and the associated endorsed Model Intercomparison Projects (MIPs), we performed a hierarchy of prototype pre-industrial CMIP6 simulations with AWI-CM, run at different ocean resolutions (Table 2). Ultimately, we will target coupled configurations with a globally eddy-resolving mesh, which implies “resolving the Rossby radius” almost everywhere with at least two grid intervals per Rossby radius (Hallberg, 2013). Using this criterion, we have recently reported on the development of such a frontier mesh (XR; see Fig. 2, right globe), with resolution capped at 4 km (7 km) in the Arctic (Antarctic) (Sein et al., 2017). Sein et al. (2017) note that an even finer resolution will be required locally to fully capture mesoscale eddies. A lot of engineering goes into the creation of such meshes, balancing computational resources and simulation quality, since the multi-resolution approach allows for a flexible distribution of the grid points. It is not clear a priori how best to distribute a fixed number of degrees of freedom over the globe, and Sein et al. (2016) have coined the term “mesh design” for this non-trivial task. The XR mesh has about 5 million surface nodes, which is roughly comparable to a $\mathrm{1}/\mathrm{10}{}^{\circ }$ quasi-Mercator mesh with about 5–6 million (wet) nodes. However, as of today, the XR mesh is still too computationally demanding for the multi-centennial simulations needed in a CMIP context. Therefore, here, the idea is to retain some of the beneficial properties of the XR ocean-only simulation analyzed by Sein et al. (2017) by keeping higher resolution only in hotspots of high eddy activity. This reduces the computational cost to a level that is suitable for multi-centennial coupled climate simulations and ensemble simulations.

Table 2Model settings for the different AWI-CM configurations.

^* More details on the AWI-CM CMIP6 configurations can be found at https://github.com/WCRP-CMIP/CMIP6_CVs/blob/master/CMIP6_source_id.json (last access: July 2019).

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2.2 Hierarchy of ocean meshes

The hierarchy of different ocean grid resolutions that are used in this study is shown in Fig. 2. The number of surface grid points increases from left to right and, specifically, the spatial resolution in the North Atlantic Ocean systematically increases from “REF” (reference or “benchmark” mesh) up to “HR” (high resolution). In order to isolate the impact of horizontal resolution, the vertical levels were left unchanged: there are in total 46 levels with vertical resolution ranging from 10 m at the surface to 250 m below 2150 m. Certainly, going to even higher resolutions beyond the XR mesh, a higher number with different placement of levels might need to be considered, but we kept the standard levels in all meshes for consistency. The bathymetry in the different grids is based on a blend of the IBCAO (Jakobsson et al., 2008) and GEBCO (2008) bottom topography data sets, as detailed by Q. Wang et al. (2014).

“REF” and “LR” (low-resolution) use CMIP5-type spatial resolution (∼1–0.7^∘) with moderate isotropic refinement to about 25 km in the tropics and in the Arctic. The LR mesh was used for ocean-only simulations within the CORE-II intercomparison project (Danabasoglu et al., 2014; Wang et al., 2016a, b), while REF was used as a “benchmark” mesh for the coupled AWI-CM (Rackow et al., 2018a). Although all prototype simulations except REF use a T127 atmosphere (Table 2), we still include the REF/T63 benchmark configuration here for better comparability with previous studies (Sidorenko et al., 2015; Rackow et al., 2018a).

The medium-resolution “MR0” and “MR” meshes as well as the high-resolution “HR” mesh follow the new mesh design strategy introduced by Sein et al. (2016). The main approach is to increase resolution locally over areas of high observed eddy variability. While the number of grid points for MR0 and MR is kept at a similar level, MR0 focuses more grid points in the Agulhas region than MR, which in turn focuses them into the North Atlantic Current region (Fig. 2). The HR grid is more balanced in this respect and further increases the size of the areas that use locally increased resolution, resulting in an increase of the number of surface grid points by more than 60 %.

It is worth mentioning that HR uses 1.3 million surface grid points (Table 2), similar to traditional $\mathrm{1}/\mathrm{4}{}^{\circ }$ quasi-Mercator grids (about 1.5 million nodes of which about 1 million are wet). However, the degrees of freedom on HR are differently distributed, focusing resolution on hotspots of high eddy activity such as the Western Boundary Currents and the Southern Ocean. In fact, this configuration reaches ocean resolutions as high as 1 km locally, e.g., in the Bosporus or over the Danish Straits – but still runs at a competitive throughput of 5–6 simulated years per day due to the excellent nearly linear scalability of the FESOM model (e.g., Biastoch et al., 2018). For a spatial map of the eddy-permitting and eddy-resolving regions on the HR grid, please refer to Fig. 4c in Sein et al. (2016).

3.1 Atlantic meridional overturning circulation (AMOC) and ocean transports

The Atlantic meridional overturning circulation (AMOC) pattern is similarly simulated between the model experiments (Fig. 3a). However, it appears that the change of the atmospheric resolution from REF/T63 to T127 (used in all other configurations) reduces the maximum AMOC strength significantly, which fits to the earlier result by Sein et al. (2018). In contrast, with increasing ocean resolution in the North Atlantic, the AMOC maximum slightly increases to more than 18 Sv in MR and HR (Fig. 3a). The ocean heat transport (Fig. 3b) reflects the behavior of the AMOC: a stronger poleward ocean heat transport is seen in REF, while LR, MR0, MR, and HR differ only in details. Concerning the transport of the Antarctic Circumpolar Current (ACC) at the Drake Passage (Table 3), REF/T63 somewhat stands out, while the other configurations with T127 atmosphere are in closer agreement. REF is close to an observational estimate for the ACC transport, which is 136.7±7.8 Sv (Cunningham et al., 2003). The mean ACC transport of current CMIP5 models is however 155±51 Sv after Meijers et al. (2012), with a range from 90 Sv up to 264 Sv. This means that all analyzed configurations simulate an ACC transport within the typical model spread.

Figure 3(a) AMOC streamfunction [1 Sv =10⁶ m³ s⁻¹] and (b) meridional ocean heat transport [1 PW =10¹⁵ W] in the five pre-industrial experiments (years 71–100). The black contour in panel (a) denotes the 18 Sv streamline.

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Table 3Transport of the ACC at Drake Passage [1 Sv =10⁶ m³ s⁻¹].

^a Meijers et al. (2012). ^b Cunningham et al. (2003)

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We conclude that all five experiments, with vastly different spatial ocean resolution and computational demand, depict a canonical overturning circulation and very similar northward ocean heat transport. These large-scale transport patterns, however, do not necessarily reflect possible differences in the hydrography of the deep ocean. In the following, we will therefore analyze temperature and salinity in more detail.

3.2 Vertical profiles of temperature and salinity

Temperature and salinity show major improvements for medium- and high-resolution configurations, as seen from horizontally averaged temperature and salinity profiles for years 71–100 of the pre-industrial simulations (Fig. 4). Differences in the simulated potential temperature and salinity compared to the PHC peak at a depth of around 1000 m. The North Atlantic deep biases, identified both in CMIP5 models (Fig. 1) and in the benchmark REF/T63 and LR/T127 versions of AWI-CM, successively decrease with increasing ocean resolution, both for potential temperature and for salinity (Fig. 4). Although the changes are not strictly monotonic when moving from REF to HR, this highlights the benefit of enhanced spatial resolution. The simultaneous change of the ocean and atmospheric resolution from REF/T63 to LR/T127 leads to a clear improvement of the salinity profiles below 1500 m, and all configurations with T127 atmosphere (LR, MR0, MR, and HR) share a very similar salinity bias in this range. While it is difficult to say what the relative influence is between the atmospheric resolution change (T63 vs. T127) and the switch of the ocean grid (REF vs. LR), it appears that surface conditions can significantly impact deep ocean biases. Note that the slight drift in HR towards colder temperatures in the 3000–5000 m range is due to a production of denser waters around Antarctica, coinciding with a stronger deep overturning cell in this model configuration.

Figure 4Profiles of potential temperature (a) and salinity (b) in the North Atlantic Ocean for years 71–100 of the pre-industrial simulations. Shown is the mean difference to PHC (PHC 3.0, updated from Steele et al., 2001). With the medium- and high-resolution meshes, the biases around 1000 m depth decrease strongly for both temperature and salinity.

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3.3 Hovmöller diagrams for temperature and salinity drift

In addition to considering biases at the end of the 100-year simulations discussed above, it is instructive to study the transient development of the biases over time. To this end, time–depth Hovmöller diagrams (Griffies et al., 2015; von Storch et al., 2016; Hewitt et al., 2017) have been computed for both potential temperature and salinity. The REF and LR configurations show a strong erroneous initial warming at a depth of around 1000 m, together with a cooling in the upper ocean above about 400 m (Fig. 5). In the medium- and high-resolution configurations, both the erroneous deep ocean warming and upper-ocean cooling are reduced. Consistent with the study by von Storch et al. (2016), a similar pattern holds for salinity, with freshening in the upper ocean and salinization in the deep ocean. The improvement of the salinity field with increased spatial resolution is similar to the potential temperature case (Fig. 6).

Figure 5Time–depth Hovmöller diagram of the potential temperature drift [K] in the North Atlantic for (a–e) the five pre-industrial simulations. (f) Definition of the North Atlantic mask that was used in the Hovmöller analysis.

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Figure 6Time–depth Hovmöller diagram of the salinity drift [psu] in the North Atlantic for (a–e) the five pre-industrial simulations. The definition of the North Atlantic mask is identical to the one used in Fig. 5.

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3.4 Spatial patterns of temperature and salinity biases

3.4.1 Deep ocean (1000 m)

When considering horizontal maps of potential temperature and salinity biases in the deep ocean, the REF and LR configurations show an erroneous warming in the deep Atlantic Ocean (Fig. 7a), similar to the pattern identified for the CMIP5 models (Fig. 1a). With increasing resolution in the North Atlantic, there is a very consistent improvement in deep ocean hydrography (Fig. 7), making the remaining biases in MR and HR comparable in magnitude to smaller biases in the other ocean basins. Compared to the changes in the Atlantic, the other basins remain largely unchanged, suggesting that resolution changes in distant regions play a minor role for the bias reduction in the Atlantic.

Figure 7(a) Potential temperature [K] and (b) salinity [psu] biases with respect to PHC (PHC 3.0, updated from Steele et al., 2001) at 1000 m depth, plotted on the observational grid. A systematic decrease of the temperature and salinity biases in the North Atlantic with increasing resolution (top to bottom) is evident.

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Figure 8(a) Spatial discretization of the Strait of Gibraltar and the Gulf of Cádiz in the five different model grids. The thick black line shows the true coastline as implemented in the Basemap plotting toolbox, using data from GSHHS (http://www.soest.hawaii.edu/pwessel/gshhs/index.html, last access: 17 May 2019). Triangular elements are shown with thin black lines; colors depict the local ocean depth in meters. (b, c) Vertical profiles of regionally averaged potential temperature and salinity in the vicinity of the Strait of Gibraltar (20–40^∘ N, 5–30^∘ W; red box in the insets). The horizontal dashed line highlights the depth of 1000 m.

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It appears as if the resolution increase of MR and HR leads to overshooting close to the Strait of Gibraltar since both MR and HR change the sign of the potential temperature and salinity biases at 1000 m. We hypothesize that at these resolutions, smaller issues become relatively more apparent; that is, other processes might need to be included for a proper simulation of the Strait of Gibraltar outflow and spreading of Mediterranean waters into the North Atlantic. Also, resolving the overflow processes at the Strait of Gibraltar would require resolutions on the order of tens of meters in the horizontal (Izquierdo and Mikolajewicz, 2018) and meters in the vertical direction, which is still far from the resolutions applied in this study. Two possible solutions are therefore the use of an overflow parameterization (e.g., Wu et al., 2007), which is currently not implemented in the model, or systematic changes to the bottom (and lateral) topography at the outflow of the Strait of Gibraltar (Fig. 8a) to minimize spurious entrainment. Vertical profiles of regionally averaged potential temperature (Fig. 8b) and salinity (Fig. 8c) in the vicinity of the Strait of Gibraltar show that REF/LR (and MR0) generate too much Mediterranean outflow waters at 1000 m depth, while MR and HR lack these at a depth of 1000 m. Since the simulated model profiles envelop the observed profiles from PHC (at 1000 m), there is potential for much better agreement by systematically adjusting the representation of the local bathymetry and the width of the strait. In order to simulate the correct spreading of Mediterranean waters from the Gulf of Cádiz into the North Atlantic, another approach could be to add additional physics like the effect of tides (Izquierdo et al., 2016), which are usually not included in current climate models. Without tides, ocean models often simulate erroneous southwestward spreading, leading to stronger biases when compared to climatology than in simulations with active tides (Izquierdo and Mikolajewicz, 2018).

3.4.2 Surface conditions

Since there are no heat sources or sinks in the interior ocean, the observed deep bias cannot develop in situ. Furthermore, since there is no sizable cold (fresh) bias above 1000 m, it cannot be entirely explained by a vertical redistribution of heat (salt). Instead, the surface has to be a major origin of the simulated deep ocean warming, and improvements in the deep ocean hydrography with higher resolution should be caused by improved surface fields.

Focusing on the SST bias in the last 30 years of the REF, MR0, and HR pre-industrial simulations (years 71–100) in detail (Fig. 9), systematic differences between the simulations are evident (for the discussion of LR and MR, see Appendix A). The surface is consistently colder than PHC in all simulations, which is expected, since pre-industrial (PI) runs are compared with a climatology representing present-day conditions. However, in the whole Labrador Sea, REF, MR0, and HR are on the warmer side for years 71–100. When overlaying their SST bias with simulated surface isopycnals (gray and black contours in Fig. 9b–d), which represent the mapping to the deep ocean in 600–1000 m depth (see details in the sections below), it is evident that warm SSTs over these critical regions are systematically reduced when going to the higher resolutions (Fig. 9b–d). Consistent with uncoupled ocean-only results for LR and HR (Sein et al., 2016, their Fig. 7), which show a much better simulation of the position and separation of the Gulf Stream further south at higher resolutions, the coupled simulations analyzed here also show a successively reduced meridional warm/cold bias pattern along the east coast of North America.

Figure 9(a) The North Atlantic sea surface temperature and (e) σ₁–density structure at the ocean surface, as determined from PHC (PHC 3.0, updated from Steele et al., 2001). Black and gray contours indicate outcropping areas for typical isopycnal surfaces found in the deep ocean around 1000 m (e.g., σ₁=31.8). (f–h) Same for the simulated density structure in REF, MR0, and HR (years 71–100). (b–d) Sea surface temperature (SST) biases in the three simulations (years 71–100) with respect to PHC in panel (a). Three simulated σ₁–density contours that represent the “mapping” to deeper ocean layers are overlaid with black and gray contours (identical to the contour levels in panels (f)–(h). To highlight the SST improvements in the areas encircled by these contours, hatching grays out regions that are not in contact with the deep ocean around 600–1000 m (based on the 30-year annual means).

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Despite these clear improvements over the deep convection sites and over the Gulf Stream region, the cold temperature spot in the Northwest Corner is a persistent bias and is visible even better in the medium- and high-resolution coupled simulations, since the surrounding warm biases are much reduced. Note that also uncoupled ocean-only models still struggle to properly simulate the Northwest Corner of the North Atlantic (Sein et al., 2017), and presumably much higher resolution along with a more detailed representation of the bathymetry is needed for the Gulf Stream to reach this area. Although the Gulf Stream and its extension could impact the location of the outcropping regions, the strong cold temperature spot (hatched in Fig. 9b–d) is, however, not in direct contact with the deep ocean around 600–1000 m depth via outcropping isopycnals (as diagnosed from 30-year annual means). Despite possible seasonal excursions, we therefore do not expect a major impact on the analysis of the present study, which is focused on the deep ocean.

We conclude that the deeper ocean is connected to less-warm surface conditions (non-hatched regions in Fig. 9b–d) in the higher-resolution model versions, and in the next section we will study how this translates to the improvements seen in the deep ocean.

3.5 Along-isopycnal bias propagation in the Atlantic

By focusing on surfaces of constant potential density (isopycnals), it is possible to trace the development of the biases from the surface to the deep ocean around 1000 m depth, where our lower-resolution simulations and the CMIP5 models show the strong anomalous warming (Fig. 1). We compute running 10-year means for the temperature bias along the σ₁=31.8 isopycnal (σ₁ denotes potential density, referenced to 1000 m depth). We chose this specific isopycnal, because it coincides with a depth of 800–1000 m in the North Atlantic area (Fig. 10). It also lies in the middle of the envelope formed by the 31.6 and 32.0 contours that were already shown in Fig. 9 (gray contours).

Figure 10Meridional section at 30.5^∘ W through the Atlantic Ocean for the potential temperature bias in the five simulations. The difference compared to PHC is shown with colors for years 21–30 (left column) and years 91–100 (right column), illustrating the North Atlantic bias development along isopycnal layers (see animations S3 and S4 for LR and HR with a 10-year running window in the Supplement videos; Rackow et al., 2018c). The contours show σ₁ density contours that are representative for the deep ocean between 600 and 1000 m (gray and black; σ₁=31.6, 31.8, 32.0) and for the surface ocean until a maximum depth of about 300 m (red; σ₁=30.5, 30.8). The average (maximum) mixed layer depth in the 10-year windows is overlaid with a green line (green shading).

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To isolate the influence of the chosen ocean grid using the same atmospheric T127 configuration, we will focus on the LR and HR configurations here as examples. When looking at the bias development in LR (see animation S1 in the Supplement videos; Rackow et al., 2018c), there are two major surface source regions for the deep bias in the Atlantic – the Strait of Gibraltar and the northeastern North Atlantic. The first source of the warm bias in 1000 m is likely to be of geometric nature, since the very narrow Strait of Gibraltar cannot be properly discretized at coarse resolutions. However, simply increasing the resolution in the Strait of Gibraltar does not automatically remove the bias; instead, climatological T/S profiles in the vicinity of Gibraltar lie between the according REF/LR/MR0 and MR/HR profiles (Fig. 8b, c). As mentioned before, a systematic geometric tuning of the ocean bathymetry in this area was not attempted (Fig. 8a), and there is thus potential for closer agreement with climatological potential temperature and salinity profiles in this region by adjusting the spatial resolution within (and in the vicinity) of the strait.

The source in the northeastern North Atlantic is related to enhanced downwelling and an erroneously deep mixed layer (≥500 m; green contours in the Supplement videos) in this area. This is a feature that has already been identified in uncoupled FESOM simulations using the LR grid as part of the CORE-II intercomparison project (Danabasoglu et al., 2014, their Fig. 13). Since the Gulf Stream in the LR (and REF) simulations is too zonal and reaches the northeastern North Atlantic, part of the flow has to become downwelling here, which we suspect could explain part of this deficiency by entraining waters and deepening the mixed layer. Other factors influencing the mixed layer depth could be biased buoyancy fluxes or the restratification process via eddy activity. By comparing the years 21–30 to the years 91–100 of LR (second row in Fig. 10), the advective nature of the bias signal propagation from the surface in high latitudes to the deep ocean at lower latitudes is evident, which coincides with the mean currents of the subtropical gyre that go into the same direction.

The mixed layer (green line and shading in Fig. 10) is deep enough so that surface biases can reach the 31.8 and neighboring isopycnals, from where the signal is further advected towards the south. Eventually, the signal is advected towards the Equator, from where it propagates to the east as a Kelvin wave (Supplement video S1; Rackow et al., 2018c).

In contrast, all abovementioned issues are almost absent in the HR configuration (see last row in Fig. 10 or Supplement video S2; Rackow et al., 2018c), which is a major improvement compared to the previous AWI-CM-LR configuration. This strongly suggests that also in the CMIP5 models the lack of spatial resolution is favoring biases in the deep ocean. Higher spatial resolution is needed to properly resolve the very narrow geometry of the Strait of Gibraltar and it is one way to better simulate the position of the Gulf Stream, although other factors also play an important role. The latter improvement reduces warm SST biases over North Atlantic areas that are in contact with the deeper ocean (Fig. 9b–d), which in turn reduces the warming in the deep ocean. While a strong resolution dependence was also shown by Marzocchi et al. (2015), there are additional ways for getting a more realistic Gulf Stream separation. These include details of the numerical scheme that can affect current–topography interactions (Penduff et al., 2007) or the representation of non-local dynamics that impact the formation of a northern recirculation gyre along the North American coast, such as the Deep Western Boundary Current downstream of Cape Hatteras (Zhang and Vallis, 2007) and the cold Labrador Current northward of the Gulf Stream front (Sein et al., 2017).

3.6 Displacement and tilt of simulated isopycnals

There is a third source of biases, which is responsible for the deep ocean warming in the Southern Ocean. It is related to the fact that the eddy parameterization (GM) has difficulties in representing the slope of the isopycnals, which is determined by the counteracting effects of Ekman pumping and eddy transport (Farneti et al., 2015). As an example, meridional sections along 10.5^∘ E reveal that the strong deep ocean warming in LR seen in Fig. 7a to the west of Cape Agulhas is linked to too-steep simulated isopycnals between 40 and 45^∘ S (black and gray contours in Fig. 11b, left) compared to the much flatter observed tilt of the isopycnals (as in PHC; magenta contours). Already at MR, the simulated isopycnal slope is about halved compared to LR and much closer to the observed slope (Fig. 11, right) with strongly reduced temperature biases, suggesting that the explicitly resolved eddies outperform the eddy parameterization as applied in the prototype simulations with AWI-CM (using a default K_GM).

Figure 11(a) Right: the Southern Ocean σ₁–density structure at the ocean surface in LR and MR (years 71–100). Black and gray contours indicate outcropping areas for typical isopycnal surfaces found in the deep ocean around 1000 m; red contours represent shallower isopycnal surfaces with a maximum depth of about 200 m. Left: sea surface temperature (SST) biases in the two simulations (years 71–100) with respect to PHC. Simulated σ₁–density contours are overlaid (identical to the contour levels in the right panels). A meridional section at 10.5^∘ E is highlighted with a vertical red line. (b) Meridional section at 10.5^∘ E, to the west of Cape Agulhas, showing the potential temperature bias with respect to PHC in (left) LR and (right) MR (years 71–100). Contours show simulated σ₁–density contours that are representative for the deep ocean between ≈600 and 1000 m (gray and black; 31.6, 31.8, 32.0) and for the surface ocean until a maximum depth of about 200 m (red; 30.5, 30.8). In contrast to LR, the tilt of the isopycnals in MR is a close fit to the “target” σ₁ contours from PHC (given in magenta). The average (maximum) mixed layer depth in the 30-year window is overlaid with a green line (green shading).

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Isopycnals in the upper ocean above 200–300 m in MR (${\mathit{\sigma }}_{\mathrm{1}}=\mathrm{30.5},\mathrm{30.8}$) are also much closer to the observed state from PHC than in LR (compare red contours to magenta contours in Fig. 11b), associated with an interior bias dipole of warmer/colder temperatures in LR (left panel) and a more homogeneous (cold) bias pattern in MR (right panel). Interestingly, the surface representation (SST bias) of this warm/cold interior bias to the west of Cape Agulhas and a similar dipole-like bias in the Brazil–Malvinas Confluence region are cleanly separated into their warm and cold parts by the σ₁=30.5 isopycnal surface contour (red contour in Fig. 11a, left) in LR. This suggests that these biases could be caused by shifted water masses as indicated by the erroneous northward shift of the σ₁=30.5 contour, leading to a warm bias on its northern side and to a cold bias on its southern side. Flattening the slope would result in a southward shift with potentially reduced biases. Indeed, the surface biases are strongly diminished in MR (Fig. 11a) with better-resolved eddies and the associated flatter isopycnals, which are a close fit to the target contours from PHC (Fig. 11b).