Presently in the real ocean, Antarctic Bottom Water is primarily formed in several locations (including the Weddell Sea, the Ross Sea, and by Adélie Land) as water is cooled, made saltier, and becomes denser on the continental shelves and then cascades down the continental slopes, entraining deep waters on its way to the sea floor (visible as the densest areas in Fig. ). The CMIP6 models' bottom density bias on the shelves suggests that 19 out of 35 models may form dense water on the shelf: ACCESS-CM2 (Weddell and Ross), ACCESS-ESM1-5 (Ross), CAMS-CSM1-0 (Ross), the four CESM2 (Ross), CanESM5 (Weddell and Ross), GFDL-ESM4 (Weddell and Ross), the three GISS (Ross mainly), HadGEM3-GC31-LL (Weddell and Ross), INM-CM5 (Weddell and Ross), IPSL-CM6A-LR (Weddell and Ross), the two NorESM2 (Ross mainly), SAM0-UNICON (Ross mainly), and UKESM1-0-LL (Weddell and Ross). The other 16 models are too light (strong negative bias in Fig. ). Mean biases over 30 years are not enough to determine whether the dense shelf water flows into the deep ocean; we instead created movies of the monthly bottom density over the entire historical run for these 19 models, of which 2 are available as a video supplement.

The movies let us split these 19 models into the following three groups.

INM-CM5 and NorESM2-LM show overflowing from the Ross shelf to the deep basin (as does NorESM2-MM) and in the Amery sector (see video).

If up to 8 models may export dense water from the shelf, how do the other 27 models of our study form their AABW? Deep convection, so far observed only once in the real ocean, in response to the 1974–1976 Weddell Polynya , is the next obvious process to investigate. Mixed-layer depths exceeding 2000 m are most prevalent in the Weddell sector (black contours in Fig. , DMVs in Table , MLD in Table ). Of our 35 models, 24 exhibit deep convection in the Weddell Sea, of which 19 do so for most years of our study period. Most of these models also have a too large and too frequent Weddell Polynya , except for GFDL-CM4 and IPSL-CM6A-LR, which may be convecting under sea ice cover, and the two MIROC, which are ice-free . In the Amery and Ross sectors, we need to distinguish between the models that have non-zero DMV because of open-ocean deep convection and those with coastal polynyas. In the Amery sector, aside from MCM-UA-1-0, whose deep convection area is just a continuation of the Weddell one, we have 10 out of 35 models with open-ocean deep convection: the two CNRM, the two EC-Earth3, GISS-E2-1-H, MIROC6, MPI-ESM-1-2-HAM, MPI-ESM1-2-LR, and the two NorESM2. In the Ross sector, we have 15 models with open-ocean deep convection: 14 in the Ross Sea and 1 (NESM3) in the Amundsen Sea. In the Amery and Ross sectors, there is no link anymore between DMVs and the polynya activity in , suggesting that bottom water formation occurs under ice cover. There is, however, a strong correlation of +0.47 between DMV in the Ross sector and DMV in the Weddell sector, i.e., models that convect a lot do it in both sectors. suggests that a strong DMV is associated with a strong Antarctic Circumpolar Current (ACC), while find that strong DMV would weaken the westerly winds, i.e. may weaken the ACC. Here the only relationship between DMV and ACC, using the values from , is in agreement with : the more deep convection in the Amery sector, the weaker the ACC (correlation of -0.54, significant at 95 % level). We find no relationship with DMV in the Weddell or Ross sectors.

Up to now, there are still seven models that have no open-ocean deep convection and no shelf overflow: the four CESM2, GISS-E2-1-G and GISS-E2-G-CC, and NorCPM1. GISS-E2-1-G and GISS-E2-G-CC have non-zero DMV when considering the entire historical run (1850–2014, not shown), with GISS-E2-1-G convecting once in the Weddell sector and once in the Ross sector, and GISS-E2-1-G-CC thrice in the Weddell sector. The four CESM2 models do not, but they have an overflow parameterisation that artificially moves dense water from the shelf to the deep basins . If the water on the shelf exceeds a critical density, a pipe artificially transports this dense water from the shelves to the deep basin. Without having to cascade, the dense shelf water keeps its properties. Consequently, the absence of cascade means that we cannot detect it on the overflow movies. For NorCPM1 though, we could not determine how its AABW is formed; maybe it formed before 1850. In conclusion, most models form their AABW via open-ocean deep convection. Even the models that seem to represent shelf processes accurately exhibit open-ocean deep convection. Somewhat surprisingly, the only relationship between the DMV and the climate sensitivities of is in the Weddell sector (correlation of -0.36): models that convect a lot there have a low sensitivity, which is to be expected as heat and CO2 are sent to the deep ocean. What is surprising is that the relationship holds only in the Weddell sector. Hence, the sensitivity might be more linked to polynya activity, which is linked to deep convection only in the Weddell sector.

Does the way CMIP6 models form their AABW impact its characteristics, as it did in CMIP5 ? Only density biases are shown in Fig. , but salinity and temperature biases are provided in Figs.  and , respectively. A total of 10 models have a negligible bottom density bias (root-mean-square error, RMSE, lower than 0.05 kgm-3, white numbers in Fig. ): UKESM1-0-LL, CanESM5, IPSL-CM6A-LR, CESM2-WACCM-FV2, CESM2-FV2, CESM2, CESM2-WACCM, GISS-E2-1-H, CNRM-CM6, and HadGEM3-GC31-LL. A total of 12 more models have an acceptable bottom density bias (RMSE lower than 0.1 kgm-3), including all the other models that are based on NEMO. That means that 22 of 35 models have acceptable biases. Let us investigate rather what may be common to the 13 models that are performing poorly.

INM-CM5 is the only model that is biased dense. Its bottom salinity is extremely high (RMSE of 0.42, Fig. ) while its bottom temperature is rather accurate (RMSE of 0.8 ∘C, Fig. ). Its predecessor INM-CM4 had a similar issue, although whether this was caused by a too short spin-up or non-conservation of salt could not be determined (Alexander Gusev, personal communication, July 2014). All the other 12 models are biased light (Fig. ). For BCC-CSM2-MR, BCC-ESM1, MCM-UA-1-0, MIROC-ES2L, MIROC6 and MRI-ESM2-0, it is because of a fresh bias (Fig. ). The other 6 models have relatively accurate bottom salinity, but are biased warm (Fig. ). CMIP6 models are overall biased light or biased dense in the entire deep Southern Ocean (excluding the shelves).

Finally, the multi-model mean bottom water is too light (mean bias of 0.06 kgm-3), too warm (0.85 ∘C), and too fresh (0.02 psu) throughout the entire Southern Ocean (Fig. ). Technically, as the multi-model mean bottom temperature is 0.57 ∘C, we can even say that on average CMIP6 models do not have AABW (defined as having a temperature below 0 ∘C) at the bottom of the Southern Ocean. The multi-model mean biases in mixed-layer depth exceed 2000 m in all sectors, especially in the Weddell Sea, but they do so over a small region so that the average bias over the entire deep Southern Ocean is low (151 m). As mentioned before, the biases in properties are moderate in the open ocean but exceed 0.1 kgm-3 or 0.1 psu on the shelves: the multi-model mean shelves are too light and too fresh as many models do not form high-salinity shelf water. This is also the reason why the standard deviation (Fig.  rightmost column) is largest on the shelves. In the open ocean, the standard deviation is larger in the Weddell Sea than in other sectors for the temperature, salinity and MLD, as it is where DMVs differ most (Table ).

The models with low biases in bottom density also tend to have zero to low DMVs in the Weddell Sea, but the relationship does not hold for maximum DMVs larger than 200 1013m3 (Table ). NorESM2-LM and NorESM2-MM notably have low biases but very high DMVs, but they also do shelf overflows. Open-ocean deep convection leads to a warming and salinification of bottom waters ; one hypothesis is then that models that hardly convect stay closer to the bottom density value they were initialised with. In the case of the CESM2 suite, the overflow parameterisation may help form accurate bottom water. Biases are not the whole story though. As expected, we do find a significant relationship (95 % level) between the actual temperature and salinity of AABW and the DMV: in the Amery and Ross sectors, more deep convection leads to warmer AABW (correlation of +0.33 and +0.29, respectively) as in . In the Weddell sector, however, more deep convection leads to fresher AABW (correlation of -0.35), which in fact is consistent with the short-term response of the Southern Ocean to deep convection in . The multi-model mean AABW salinity is 34.606±0.154; the reference value from is 34.641. The multi-model mean AABW temperature is -0.45±0.73 ∘C; the reference value from is -0.88 ∘C. Therefore, the multi-model mean AABW is warmer and fresher than the reference, and more DMV worsens these biases. Note that the values of the individual models are given in Table .

To summarise, in the Southern Ocean most models form their AABW by open-ocean deep convection. In the Weddell Sea, this convection seems tied to the Weddell Polynya activity and impacts the AABW salinity most: more deep convection means fresher bottom salinity. In the Amery and Ross sectors, it is linked more to the bottom temperature: more deep convection means warmer bottom salinity. Models that seem to form dense water via shelf processes also exhibit deep convection, so we cannot determine whether overflows alone would make the Southern Ocean more accurate. The models that convect the least or not at all tend to be the most accurate. For the CESM2 family, accurate bottom properties and lack of deep convection may both be the result of their overflow parameterisation . For another model, NorCPM1, the accuracy in all properties may come from its observation assimilation rather than accurate model physics .

We will study the impact of these biases on the global transport of AABW in Sect. , but as we cannot do so without investigating the AABW–NADW balance in the Atlantic basin, let us first evaluate the representation of NADW in CMIP6 models.

In the North Atlantic, all 35 CMIP6 models of our study exhibit deep convection in the subpolar gyre (black contours in Fig.  and Table ). As in CMIP5 , a large proportion of them convect not only in the Labrador Sea as the reference but also intensely south of Iceland (Irminger Sea):

6 of the 35 models convect only in the Labrador Sea (Fig. ): CNRM-CM6-1, CNRM-ESM2-1, EC-Earth3-Veg, IPSL-CM6A-LR, NorCPM1, and NorESM2-LM;

As in , the higher-resolution NorESM2-MM and MPI-ESM1-2-HR have larger deep convection areas than their corresponding lower-resolution NorESM2-LM and MPI-ESM1-2-LR. Note that the difference between NorESM2-MM and NorESM2-LM is in the atmospheric component resolution. There is, however, no robust relationship across models between the horizontal resolution and the DMV. There is a relationship with the climate sensitivities of though: the larger the DMV in SPG, the less sensitive the model (correlation of -0.36), which as already discussed in the Southern Ocean part is not surprising. Consequently, there is also a strong correlation between the DMV in the Weddell Sea and in SPG (+0.57): models that convect a lot in the Weddell Sea convect a lot in SPG as well. As already mentioned, no causation can be inferred: deciphering whether global biases in DMV are responsible for the models' sensitivities or sensitivities are set by other processes and impact the DMV is beyond the scope of this analysis.

All models except INM-CM5-0 and NorCPM have deep convection in the GIN seas as well. Moreover, in GIN models convect most years, with a minimum as high as 24 of 30 years (Table ). There is more variability in the SPG, but likewise the majority of models convect all years. Besides, they convect too deep. While in the Southern Ocean, deep convection to the sea floor can happen , in the North Atlantic it should not go much beyond 1000 m e.g.. In the SPG, only the three models CanESM5, INM-CM5, and NorCPM1 have maximum mixed-layer depths just exceeding 1000 m (Table ). An extra four models, ACCESS-CM2, CESM2, CESM2-WACCM, and MIROC-ES2L, have tolerable depths up to 2500 m. However, the vast majority convects too deep, often to the sea floor. It is the same in GIN, albeit with different models: this time, the four models CESM2, MPI-ESM1-2-LR, and NESM3 have MLDs up to 2000 m, and all the other models go to 3000 m or even the sea floor. There is no significant correlation between the DMV in SPG and that in GIN. In summary, CMIP6 models exhibit deep convection in the North Atlantic too often, too deep, and over too large an area. It is not possible to determine the single most accurate model in the North Atlantic or even in each subregion; model users must choose a compromise between correct representation of the variability, location, depth, or extent.

CMIP6 water property biases at the bottom of the North Atlantic are of the same order of magnitude as those at the bottom of the Southern Ocean (shading in Fig. ). Three models have bottom density biases resulting in an RMSE lower than 0.05 kgm-3 in both SPG and GIN: CESM2-WACCM, HadGEM3-GC31-LL, and UKESM1-0-LL. An additional nine models have an RMSE lower than 0.1 kgm-3 in both SPG and GIN: CESM2, CESM2-FV2, CNRM-CM6-1, EC-Earth3-Veg, GFDL-CM4, GFDL-ESM4, IPSL-CM6A-LR, MRI-ESM2-0, and SAM0-UNICON. As for the other 23 models, it depends on the region.

INM-CM5, NorCPM1, NorESM2-M, and NorESM2-MM are biased dense in both regions because they are biased salty (Fig. ). The magnitude of the bottom cell biases in INM-CM5 is very grid cell dependent, maybe because of faulty regularisation of the sigma grid (even though it did not have this problem in the Southern Ocean).

The multi-model mean biases reflect the individual model biases that we just described (Fig. ): in the deep ocean, in both GIN and SPG, the multi-model mean is biased salty (0.07 in GIN, 0.15 in SPG) but warm (1.68 and 1.91 ∘C respectively), and hence slightly light (0.04 and 0.07 kgm-3). The across-model spread, given by the standard deviation (right column in Fig. ), is on the order of 0.1 kgm-3 or psu and 1 ∘C in both regions, similar to what we found for the Southern Ocean. The multi-model mean MLD is too deep over too large an area compared to the reference (bottom row in Fig. ), corresponding to a bias of nearly 800 m on average in both regions. The standard deviation is relatively high though, also reaching 800 m on average, indicative of model disagreement over the location of the deep MLD. The largest bias in standard deviation, i.e. the location where the across-model agreement is lowest, is in the Greenland Sea, probably a consequence of the across-model differences in sea ice representation .

In the SPG, there is a strong relationship between the bottom temperature RMSE and the climate sensitivity of : the more sensitive the model, the less biased the temperature in SPG (correlation of -0.68). There is a somewhat significant (at the 90 % level) relationship between the DMV and the bottom density bias in SPG only: the more the model convects, the less biased it is (correlation of -0.29). There is, however, no relationship with the location of deep convection itself, e.g. MIROC-ES2L that convects only in the Irminger Sea has a similar bias (magnitude and sign) as MPI-ESM1-2-LR that convects only in the Labrador Sea; MPI-ESM1-LR in turns has a large bias and convects at the same location as UKESM1-0-LL, which has a low bias. The four CESM2 models and their overflow parameterisation by the Denmark Strait are again among the most accurate, which was in fact the original motivation for that parameterisation . NorCPM1 is somewhat disappointing; it is built on NorESM2-LM and is supposed to have improved performance thanks to data assimilation . Its bottom density is indeed better than NorESM2-LM's in SPG but is biased even denser (saltier) in GIN. There is no across-model relationship between the sensitivity or the DMV and the salinity or GIN though, so the cause of NorCPM's and other models' bottom density bias in the GIN seas remains unknown. It may be linked to their respective biases in the representation of the Atlantic Multidecadal Oscillation, as suggested by . There is, however, a strong interhemispheric correlation: the more biased the bottom density in the Southern Ocean, the more biased it is in SPG (+0.81).

Finally, looking at the NADW properties instead of the biases (individual values in Table ), we find that the multi-model mean NADWSPG, which refers to as upper NADW (UNADW) or Labrador Sea Water (LSW) is too warm and too salty: 4.86±0.81 ∘C and 35.163±0.143 in CMIP6, instead of 3.32 ∘C and 34.894 in . The multi-model mean NADWGIN in contrast is accurate: 0.77±0.99 ∘C and 35.001±0.169 compared to 1.30 ∘C and 34.878 for the water mass called lower NADW (LNADW) or Iceland–Scotland Overflow Water (ISOW) in , despite five models having a temperature below 0 ∘C. Again in SPG, models with a high sensitivity have a lower salinity and temperature (correlations of -0.31 and -0.45 respectively), which is consistent with the links previously found with the DMV. But again no relationship can be found in GIN. In GIN, we found no relationship between the biases or properties and the horizontal or vertical resolution or between the grid type and ocean model component. In CMIP5, had found strong across-model biases in the inflow to the Nordic seas caused by the large-scale oceanic and atmospheric circulations, as well as the bathymetry, while showed that GIN property biases can be linked to the representation of multidecadal variability. Investigating the exact cause of the biases in GIN is beyond the scope of this paper, not least because in the next section we will show that NADWGIN does not contribute to the global NADW in CMIP6 models. For now, we can conclude that the bottom property biases in GIN are not related to deep water formation in the region.