We use the global coupled climate model EC-Earth3P , a version of the model specifically developed within the PRIMAVERA project, to contribute to the first phase of HighResMIP , as part of the CMIP6 initiative. This model version uses the atmospheric IFS cy36r4 model, the ocean NEMO model in its version 3.6, and the sea ice model LIM3. To investigate the role of fine-scale processes in the deep water formation in the North Atlantic, we compare simulations of eddy-parameterised (standard resolution, SR), eddy-permitting (high resolution, HR), and eddy-rich (very high resolution, VHR) configurations of the model with approximate grid spacings in the ocean of about 100, 25, and 8 km, respectively. (Table  shows more information about each configuration; detailed information regarding the models can be found in and ). Their atmospheric components also feature gradual enhancements in resolution, from about 80 to 40 and 16 km, respectively. Because our interest is in comparing internal variability in the North Atlantic, we focus on the HighResMIP 1950-control simulations (i.e. with perpetual radiative forcing conditions from 1950) with one member per resolution.

The HighResMIP protocol sets a minimum duration of 100 years for the 1950-control experiment . Although the lower-resolution experiments extend much longer, due to the high computational costs of the VHR version, the corresponding 1950-control could be run for only a total of 106 years. Therefore, the VHR experiment limits the number of years we consider for all the model configurations, as we prefer to keep comparable setups. Moreover, we discard the first 30 years of all simulations to avoid the effects of a drift that lingers after the relatively short spin-up period. The 50 years recommended by the HighResMIP protocol are insufficient for the model to reach a trend-free state on the ocean surface . We therefore analyse 76 years of each simulation. Also, for all the experiments, we use a second-order polynomial detrending to remove residual model drifts that all the models preserve in the deep ocean layers (not shown).

We use oceanic temperature and salinity observations to compare the vertical density profiles and MLD variability. In particular, we use the EN.4.2.2 g10 EN4; version based on mechanical bathythermograph and expendable bathythermograph corrections. To produce variables that are comparable for both experiments and observations, we compute in both cases the sigma0 and sigma2 potential density anomalies from monthly means of potential temperature and practical salinity using the TEOS-10 equation . Then, we use the monthly sigma0 outputs thus derived to compute the MLD following the density threshold of 0.03 kgm-3, setting the reference depth at 10 m . In addition, to maximise comparability with the simulations, we select different time ranges in the observations, depending on the target analysis. We take the 21 years centred around 1950 (1940–1960) to compute all climatological values to stay close to the 1950 radiative forcing conditions. When assessing variability (e.g. with standard deviations and correlations), we instead consider the last 76 years available (1948–2023) so that both observations and simulations cover comparable timescales. Because observations include forced signals, which are not present in the simulations, a second-order polynomial is previously removed from the data to focus on the interannual variations, which are mostly internally driven. Sea ice concentration has been taken from the March 1940–1960 average from HadISST2 .

To characterise the AMOC, we compute the meridional overturning streamfunction for the Atlantic basin in the native grid's y axis. Note that ORCA grids are almost regular in the 90° S–45° N range, which means that the computed transport at those latitudes will be virtually meridional. We define the transport as the cumulative sum, from bottom to top, of the return flow; see Eq. (). 1ψz(t,y,z)=-∫z′=-Hz∫x′=xWxEv(t,x′,y,z′)dx′dz′ Here, xW and xE are the west and east boundaries of the basin, respectively, and H is the basin depth.

In the subpolar region, the density profile changes sharply in the longitudinal direction due to the multiple processes occurring in the area (e.g. Arctic outflows, deep convection, western boundary current, subpolar gyre circulation). For this reason, we also analyse the overturning streamfunction in sigma-space (see Eq. ), which is more suitable to capture the contributions from deep water formation in the subpolar North Atlantic region : 2ψσ(t,y,σ)=-∫x′=xWxE∫z′=zσmaxzσv(t,x′,y,z′)dz′dx′, where zσmax is the depth at which σ is maximum; in a stable ocean, this will be -H, as in Eq. (). zσ is the depth at which the density is equal to σ. Note that while integrals can be rearranged in Eq. (), in Eq. (), the integral in z′ should be done first, as there is a change in the system of reference.

To study the AMOC signal driven by thermohaline changes in vertical ocean mixing, we remove the Ekman transport from the overturning streamfunction. We compute the total Ekman transport as the west-east integral of the surface wind stress divided by the Coriolis parameter and the reference density; see Eq. (). Note that, as the net transport should be equal to 0, the resulting transport V in the Ekman layer (approximately the first 30m) should be compensated by an equal and opposite transport, which is assumed to happen uniformly throughout the whole water column. 3V(t,x′,y)=-1ρ0∫x′=xWxE1f(x′,y)τx(t,x′,y) Here, ρ0=1025kgm-3 is the reference density, f is the Coriolis parameter, and τx is the zonal wind stress. The transport should be divided by the cross-section x–z area to recover the average speed, which is integrated as in Eqs. ()–() to get the streamfunction in both the z and sigma spaces.

All the scientific analyses are performed using well-established open-source scientific programming languages and tools. Most of the analyses are performed directly with Python and ESMValTool v2.11.0 , a software package specifically created to facilitate a rigorous evaluation of CMIP simulation outputs that is especially useful for comparing multiple models with observational datasets.

We use Pearson's correlation coefficient, r, to assess the interrelation between variables in several analyses. The effective number of degrees of freedom, Neff, of a correlation of N-length series is computed using the approach proposed by to take into account the temporal autocorrelation of the data; see Eq. (). 4Neff=N1+2∑k=1N-1N-kNrXX,krYY,k-1 Here, rXX,k and rYY,k are the autocorrelations of each series at lag k. Their statistical significance is computed according to a Student's t distribution setting a p value of 0.05 (i.e. 95 % confidence level) to determine if the correlation is statistically different from 0.

We first look at the climatology of the MLD in March, the month in which it reaches its yearly maximum. In the three model versions (Fig. a–c), the Labrador and Irminger seas appear to have a stronger mixing than the Nordic Seas (Fig.  shows the locations of all geographical regions referenced in the results). The models show qualitative and quantitative differences with each other in the areas with active mixing around the Labrador Sea. The MLD in the subpolar gyre is much more intense in HR (Fig. b), where it exceeds 2000 m in a broad region covering both the Irminger and Labrador seas. By contrast, VHR (Fig. c) has a thinner mixed layer climatology, which can locally reach up to 1500 m deep in the Labrador Sea interior. In addition, VHR has a comparatively shallower mixing south of Cape Farewell and the Irminger Sea. SR (Fig. a) shows an even smaller MLD of about 1000 m, concentrated in a small region south of Cape Farewell. This model configuration has, in fact, a positive bias in the sea ice concentration covering the western Labrador Sea (see the contour lines in Fig. ), which dampens the local air–sea interactions and, subsequently, the mixing. For similar reasons, due to the positive bias in sea ice concentrations in the Nordic Seas, all the model configurations simulate very little mixing in that region.

By contrast, EN4 (Fig. d) shows very intense mixing in the Nordic Seas region, with much stronger values than in the models, which can locally exceed 2000 m in depth. Some of these differences, however, might derive from the large uncertainties in EN4 during the considered period (1940–1960), in which observations in the subsurface were very scarce . It could also happen that the way of generating this observation-based product affected the estimated MLD values. EN4 uses spatial and temporal interpolations of different observational sources, including instantaneous profiles, to produce a monthly regularly gridded dataset. This process may artificially reduce the vertical stratification, resulting in a higher MLD . Nonetheless, EN4 still gives useful qualitative information about the spatial extent and the key regions of deep water mixing, allowing us to conclude that all model configurations underestimate the mixing in the Norwegian Sea, with values that are consistently shallower than in the Labrador Sea, unlike in observations.

When looking at the variability of the MLD, as represented by the standard deviation in time, this is generally greater in the regions where the climatological mean values are also large (Fig. ). In the case of SR and HR, Fig. a and b, the standard deviation in the western subpolar gyre is of similar magnitude, reaching maximum values of around 1000 m, although differences are found in the Nordic Seas, where SR shows higher variability. Compared to SR and HR, VHR shows lower variability in the Labrador Sea, with values of around 400 m and even lower in the Nordic Seas (Fig. c). In EN4, for the 1948–2023 period (Fig. d), we see consistently stronger variability than in the models (i.e. values above 1300 m) in all regions. The substantially higher observational uncertainty in the early part of EN4 compared to the present period may affect the associated MLD variability. We also note that EN4-derived data might include forced signals that have not been properly removed by the polynomial detrending. These include low-frequency modulations not present in the (unforced) control simulations, as well as some additional interannual variability linked to the response to the three major volcanic eruptions that occurred in 1963, 1982, and 1991.

We now focus on the Labrador Sea, where the models show important MLD differences and where MLD has extensively been linked to changes in the AMOC . To understand the differences in the MLD mean state and variability across the three model configurations and observations, we examine their vertical density stratification, which is a key preconditioner for mixing. Figure a shows the climatological vertical profiles of density in March for the Labrador Sea, computed as area-weighted averages in the box 60–35°W 50–65°N from, also shown with a black box in Fig. a. The Labrador Sea density is found to be more stratified in SR than in EN4 and less stratified in HR and VHR. We use two different complementary metrics to measure the degree of agreement of the simulations with the observed profile, namely, the root-mean-square-error (RMSE) and the correlation, both estimated in the vertical dimension. SR is the model configuration with the best agreement with EN4 in terms of RMSE, while VHR has the best agreement in terms of correlation, followed closely by SR (Table ). Overall, HR shows the poorest agreement with EN4, and it is also the model configuration that represents the weakest vertical stratification, which can explain why its MLD climatology is overly strong, as the threshold it has to overcome is smaller. This can also be seen in Fig. d, which shows the linear regression coefficients of the MLD time series with the vertical density profile, as an additional diagnostic to compare the models with the observations. The density anomaly needed in the top ocean to generate one metre of MLD is much smaller in HR compared to the other two model configurations, although, interestingly, it stays closer to the observed regressed value. Somehow, surprisingly, the largest differences with respect to the observed regressions happen for VHR, which had the most realistic climatological profile.

To gain further insights, the analysis is expanded to the temperature and salinity profiles. Even if the vertical density profile may suggest that SR is the model configuration in best agreement with the observational dataset near the surface, we can see that it happens for the wrong reasons, as there is a strong error compensation between the biases in the salinity (Fig. b) and temperature (Fig. c). When looking at those variables, VHR is consistently the model configuration in best agreement with EN4 regarding both temperature and salinity profiles, also reflected in the correlation coefficients and RMSEs shown in Table . Interestingly, for all three model configurations, the density profile is clearly dominated by salinity, as inferred by the vertical profiles of the haline and thermal contributions to the Labrador Sea densities (Fig. ), in which temperature has a minor influence and opposes the contribution from salinity. The better representation of the vertical profile in VHR may be due to several factors. Although VHR does not have the resolution required to explicitly resolve eddies in the Labrador Sea (a resolution of 1/16° would be necessary; ), it has a fine-enough resolution to do so in the Gulf Stream and the North Atlantic Current. These currents play a key role in transporting heat and salinity to northern latitudes, which can improve the climatological conditions in the subpolar gyre, including in the Labrador Sea. Additionally, better topography, improved resolution of boundary currents, and enhanced air–sea interaction, among other processes, may also contribute to correcting these biases.

Salinity regressions against MLD time series show that, overall, HR has the best agreement with EN4 (see Fig. e), with VHR being the second best, with overly salty regression values in the upper ocean. By contrast, SR overestimates the regression values at the surface by a factor of 2, which might be related to the large negative bias in the corresponding climatological profile (Fig. b). The temperature regression against the MLD shows the largest qualitative discrepancies between models and observations (Fig. f). While observations show a moderate negative link between the mixing and local temperatures that is maximum at the surface and decreases monotonically with depth, both HR and VHR do show a negative link, but stronger in the subsurface (∼200m). It is also worth noting that regression values for VHR are almost 1 order of magnitude higher than for HR and the observations. However, the largest discrepancies with respect to EN4 occur for SR, for which the regression values near the surface are of the opposite sign (i.e. positive instead of negative). This change in sign can be explained by the particularly strong local bias in sea ice, which is associated with both cold ocean conditions and reduced mixing. The inter-model differences revealed by the regression patterns for the mixed layer depth point to potential differences in the drivers of Labrador Sea mixing, which are investigated in the following.

We first compare the local atmospheric forcing exerted by the zonal wind across resolutions, which in winter generally brings cold air masses from the continent. Figure a–c shows the correlation in time between December–March (DJFM) wind stress in the x-grid direction (zonal in mid-latitudes) over the North Atlantic and the time series of the Labrador Sea MLD in March. All the model configurations show a dipole-like pattern, with some qualitative and quantitative differences. In the HR and VHR configurations, the pattern shows a strong positive correlation band going from approximately 40 to 65°N and a negative correlation band south of 40° N. This dipolar wind structure has typically been associated with a positive North Atlantic Oscillation (NAO) phase e.g. and also matches the one from the first EOF of the zonal wind stress (not shown). This means that, for both experiments, positive NAO phases tend to increase the mixing, while negative NAO phases tend to reduce it, as already shown in other studies . To corroborate this, Fig. a–c also includes (in contours) the correlation of Labrador Sea MLD in March with the mean sea level pressure in DJFM, which shows a clear NAO-like dipole, with positive correlations over the Azores High and negative correlations over the Icelandic Low. Following the increase in the zonal wind, both HR and VHR show a cooling of the surface water masses through enhanced heat loss to the atmosphere (Fig. e and f), which makes them denser and thus promotes local mixing as shown by . In the case of SR, we observe a similar pattern for the wind stress to that in HR and VHR, but with weaker correlation coefficients that are also more confined to the basin's western side. The weaker correlations for the wind also result in weaker correlations for the surface heat fluxes, which are not significant in the western part of the Labrador Sea, where the presence of sea ice precludes the local interactions with the atmosphere on the western side of the sea. This results in the impact of the NAO being less strong and widespread as for the other two model configurations. In all cases, the impact of atmospheric forcing through the zonal wind stress happens on a year-to-year scale. The next considered driver is associated with longer-time-scale advective processes.

At all three model configurations, salinity has been shown to have an important role in explaining the surface density profiles as well as the changes in the MLD in the Labrador Sea. We will now explore the origin of those salinity signals and how they are linked to changes in the mixing by computing correlations between the annual surface salinity fields and the March MLD index in the Labrador Sea (Fig. ). When both variables are in phase, that is, at lag 0, all three experiments show strong positive correlations with salinity in the Irminger and the eastern Labrador seas, extending farther east in SR and HR, and westward into the Labrador Sea in VHR (Fig. j–l).

The subsequent lagged correlations allow us to track down the origin of the surface salinity signals. When lagging the MLD by 1 year (Fig. g–i), SR and HR still show positive significant correlations in the same area, which suggests that they build up over the years, probably due to positive feedback linked to the local salinity stratification conditions. VHR no longer shows significant correlations in the Labrador Sea, but it does a bit further north near the Irminger Sea, where the other two model configurations also show slightly higher correlation values than at lag 0, which suggests some salinity propagation. When the MLD index lags by 2 years (Fig. d–f), the three experiments show a positive significant correlation in the northeastern part of the Irminger Sea, south of the Denmark Strait, further supporting the aforementioned propagation. Likewise, when the MLD index lags by 3 years (Fig. a–c), we still see significant correlations in the same area for HR, and in the case of VHR, the area of significant correlations is displaced to the east, extending from Iceland all the way to the British Islands. By contrast, no significant correlations are found for SR in those regions. The propagation of salinity anomalies, more evident in VHR, is probably explained by the mean transport of the subpolar gyre circulation. Similar correlation patterns have been produced against the surface temperature fields (Fig. ), but they do not show any clear advection of temperature signals into the Labrador Sea for any experiment, which excludes temperature propagation as a key driver of Labrador Sea mixing.

Our results so far have shown differences across the three model configurations of EC-Earth3P in terms of vertical mixing, preconditioners, and drivers of its variability, which could result in major differences regarding their link with the ocean circulation. In the next section, we will therefore study this link with the AMOC.

The mean state of the AMOC also varies with resolution. All analyses in this section are based on the volume streamfunction in density space, which is more adequate to represent the contributions of deep water formation in the subpolar North Atlantic than in depth space . Furthermore, the Ekman transport has been removed from the volume streamfunction to focus on its thermohaline component, which is more directly linked to the vertical mixing. When computing the volume overturning streamfunction without the Ekman transport in sigma2 space, all the models show the maximum value of the climatology around 55° N and 36.8 kgm-3 (Fig. , contour lines) but with different magnitudes. HR and VHR show the strongest AMOC, with values greater than 20 Sv in both cases, although slightly higher in HR. Meanwhile, in SR, the highest value is lower than 20 Sv. The three model configurations have the strongest variability of the AMOC situated at the same latitude as the maximum but at a slightly higher density level (Fig. ). Interestingly, despite having the weakest mean AMOC state of the three experiments, SR shows higher variability than the rest, with HR and VHR exhibiting similar values. Therefore, the AMOC mean state and variability are largely comparable between HR and VHR but differ in SR.

Newly formed dense waters in the Labrador Sea are usually propagated southward along the DWBC . As these dense waters resulting from the vertical mixing move southward, they change the zonal density gradient, triggering a thermal wind balance response that leads to a general intensification of the AMOC. To explore whether this link is affected by resolution, Fig.  compares the response of the AMOC to changes in the Labrador Sea MLD in March across the three model configurations, using lagged correlations in which the Labrador Sea mixing always leads the AMOC. For the SR model, the lagged correlations of the overturning streamfunction in density space with the MLD show how, over lead times from 0 to 4 years, the significant correlations at the densest levels (≥36.7 kgm-3, i.e. those formed by the deep mixing) progressively move southward, reaching 20° N. However, the propagation pattern is different at finer resolutions. At lag 0, HR and VHR show much stronger correlations than SR in the subpolar latitudes (i.e. north of 45° N), where deep water mixing occurs. The main differences between HR and VHR emerge at subsequent lead times, when significant correlations progressively reach more southern latitudes, in line with a southward propagation of the AMOC signals. In the case of HR, a very slow propagation is hinted, with the area of significant correlations reaching the 35° N latitude by the fourth lead year. Meanwhile, VHR shows a very quick drop of the correlation values already in the first lead year, with significant correlations limited to the 40–50° N latitudinal band. Interestingly, at lag 2, we observe a wide range of densities (i.e. 35–37 kgm-3) showing significant correlations south of 25° N, although the lack of coherence with the previous subpolar signals raises the question of whether they have propagated from the subpolar region, represent a local response, or are simply a spurious correlation.

The southward propagation of the AMOC response to changes in the Labrador Sea deep mixing can be better captured if the density level is fixed, as this allows the temporal evolution to be visualised in a single plot. Figure a–c shows the correlation of Labrador Sea MLD in March with the annual AMOC at the 36.73 kgm-3 sigma2 level, as a function of lead time with MLD leading. The largest correlations between AMOC and MLD happen at lag 0 and between 50 and 65°N. Subsequent lead times show how the significant positive correlations move southward, although with notable differences across resolutions regarding the timescales and the southward extent of the AMOC propagation. The SR shows a relatively slow propagation to about 45° N in about 2 to 3 years, with correlations becoming insignificant beyond that lead time and latitude. This slow propagation appears to be consistent with the advective propagation regime described by , although they found it to reach 34° N. The propagation in HR shows two distinct timescales; there is a fast propagation within the first year to approximately 40° N, followed by a much slower one that reaches 35° N over 8 years. The fast one could be linked to fast wave propagation, as enhancing resolution enables the representation of boundary waves, such as Kelvin waves . Even if the propagation pattern found in HR does not match the one described by , it is consistent with recent results by . In the VHR model case, a much weaker cross-latitudinal link between the MLD and the AMOC is seen. Only a fast propagation such as the one seen in HR occurs in this experiment, although with weaker correlations that also remain significant for a shorter period.

To further inspect the cross-latitudinal coherence of AMOC changes, which might not be necessarily driven by changes in the Labrador Sea mixed layer, we have recomputed the same lagged correlations but between the AMOC fixed at 55° N (where it exhibits the strongest climatological values) and the basin-wide AMOC streamfunction, both defined again at the 36.73 kgm-3 sigma2 level (Fig. d–f). As expected, this version has systematically higher correlation values than the previous one, which helps to better illustrate the gradual southward propagation of the AMOC changes. For SR, we now see that the subpolar AMOC is connected with the AMOC at 20° N with a delay of 2–3 years. For HR, the main results are very similar to those previously described for the correlations with the mixing, with a very clear fast propagation from the northern latitudes to 45° N, followed by a slowly paced propagation to 30° N over the next 6 years. In VHR, we can now see that the strength of the correlations is comparable to that in HR and SR, in contrast with the correlations against the mixing. We also note for VHR an almost continuous band of significant correlations from the subpolar to the tropical latitudes, with a 1–2 year lag between 55–37°N and an almost instantaneous connection between 35–20°N. This plot suggests that, for VHR, other influences than the Labrador Sea mixing are responsible for the southward propagation of AMOC changes, which is consistent with some recent studies suggesting that Labrador Sea water formation may not be a crucial driver of AMOC .

The lagged correlations of the large-scale density field with the Labrador Sea MLD index give further information on how the signal produced by the mixing propagates along the western boundary, subsequently impacting the AMOC (Fig. ). For each grid point, we extract the maximum correlation in the depth range from 400 to 1400 m, which is where the highest change in density related to mixing happens (Fig. ). To better examine the structure of the boundary current, we also computed the lagged correlations between the Labrador Sea MLD index and the ocean densities along a zonal cross-section located at 45° N off the coast of Newfoundland (Fig. ). Other cross-sections have also been considered, yielding similar results (not shown). At lag 0, all simulations show significant positive correlations in the interior Labrador Sea but with differences across model configurations in their location (more central in SR, flanked to the east in HR, and to the west in VHR). Inter-model differences are also found along the boundary currents. In SR, only the Greenland Current shows clear and significant correlations, and in HR, significant values (stronger than for the Labrador Sea interior) extend from the Greenland Current to the Labrador Current and around the Grand Banks area down to 40° N, remaining significant until Cape Hatteras. In VHR, a distinct band of significant correlations extends from the Labrador Current all the way to Florida (∼30° N). These results thus describe a very rapid (subyearly) propagation occurring both at HR and VHR, with the final latitude reached likely determined by the location where density anomalies in the interior Labrador Sea are formed. In VHR, significant correlations are also found further south, but they are stronger and span a much wider zonal extent, suggesting that they originate from a different process than the boundary propagation (e.g. a wind effect not accounted for when Ekman transport is removed).

At subsequent lags, further differences across experiments are revealed. For SR, a slow propagation is hinted at, with significant correlations gradually reaching 40° N at lag 1, 35° N at lag 2, and 25° N at lag 3. As expected from the coarser grid spacing and higher viscosity in SR, the DWBC is also wider and more zonally coherent than at higher resolutions. However, significant correlations in SR tend to remain more constrained to the coast and occur at shallower levels than in HR and VHR (Fig. ). For HR, correlations remain significant along the boundary at all lags considered, reaching the southernmost tip of Florida at lag 3. This contrasts with the results of VHR, for which significant correlations are no longer found along the boundary by lag 3. The greater persistence of significant correlations in HR, along with the gradual southward displacement of the latitudes with the strongest correlation values, is consistent with the slow propagation of AMOC signals found for this simulation in Fig. .