Given our primary interest, which is the implications of MLD in the deep-water formation in the MH North Atlantic, we focus here on changes in MLD during winter (January–March). The MH simulations from the PMIP4 and PMIP3 models show markedly different changes in winter MLD relative to the PI, both in terms of spatial pattern and amplitude (Figs. 1 and 2). Among the PMIP4 models, ACCESS-ESM1.5 shows the largest winter MLD anomalies, whereas INM-CM4-8 displays the smallest anomalies, especially in the North Atlantic. Compared to the PMIP4 ensemble, more models from the PMIP3 ensemble show widespread anomalies of very large magnitude (over 500 m), such as FGOALS-s2, GISS-E2-R, and KCM1.2.2.

In the North Atlantic, a recurring pattern is revealed in ACCESS-ESM1.5, EC-Earth3-Veg, GISS-E2.1G, MPI-ESM1.2-LR, and MRI-ESM2.0 from the PMIP4 ensemble: increased winter MLD in the Labrador Sea (and sometimes the Irminger Sea) concurrent with a northwestward shift in the location of MLD deepening in the Nordic Seas. The increase in MLD in the Labrador and Irminger Seas is also seen in several other models, such as CESM2, FGOALS-g3, and NorESM2-LM; on the contrary, IPSL-CM6A-LR and NESM3 are the only models that show a pronounced decrease in MLD in this area. The northwestward shift in the MLD deepening area in the Nordic Seas is also found in EC-Earth3, EC-Earth3-LR, MIROC-ES2L, and NESM3; however, FGOALS-f3-L and IPSL-CM6A-LR instead show a shift in the opposite direction. Finally, CESM2 and NorESM2-LM seem to exhibit a dipole pattern, with increased MLD in the Labrador and Irminger Seas but decreased MLD in some areas of the Nordic Seas. The anomaly pattern of increased MLD in the Labrador Sea and northwestward shift in the Nordic Seas is also found in the PMIP3 ensemble (CNRM-CM5, HadGEM2-CC, HadGEM2-ES, MPI-ESM-P).

We further analysed the seasonal cycle of MLD averaged over three deep-water formation regions as defined by Treguier et al. (2023): the Labrador Sea, Irminger Sea, and Greenland Sea (see also Fig. S1 in the Supplement). Most models simulate a seasonal cycle of the MLD comparable to that observed today: the MLD slowly deepens starting from late autumn and rapidly shoals in spring (Figs. 3 and 4). However, there is a large spread in simulated MLD values across the models in both MH and PI, with some models producing excessively deep mixed layers in some regions. In the three regions where deep convection occurs, the models seem to have their own “preference”: notable wintertime MLD deepening would generally be simulated in one or two of the three regions. In the PMIP4 ensemble, NorESM2-LM is the only model to show significant winter MLD deepening across all three regions. The other exception is EC-Earth3-LR, from which MLD deepening is not simulated in any of the three regions in MH or PI, but rather in the area extending across the Norwegian Sea, the eastern North Atlantic shelf, and the Iceland Basin (see Fig. 1). Compared to the PMIP4 ensemble, more models in the PMIP3 ensemble show significant winter MLD deepening in all three regions and all models simulate a deeper winter MLD in at least one of the regions.

The winter MLD reconstruction from dinocyst records, despite their sporadic distribution, reveals some spatially coherent patterns (Fig. 5a, c). All four sites in the Labrador Sea show shallower winter MLD during the MH. In the Nordic Seas, increased winter MLD is reconstructed at most sites from the west and southeast, while decreased winter MLD is reconstructed at the sites from the east. The PMIP4 ensemble mean MLD anomaly in the North Atlantic largely captures the recurring pattern of increase in the Labrador Sea and northwestward shift in the Nordic Seas found in individual models, and aligns broadly with reconstructions in the Nordic Seas (Fig. 5a). However, in the Labrador Sea, both the PMIP3 and PMIP4 ensembles show contrasting signals of MH anomalies compared to the reconstructions.

As models often simulate MLD anomalies of the opposite sign to the reconstructions, differences in RMSE between models largely reflect differences in simulated amplitude rather than in agreement with the reconstructions. Consequently, a low RMSE may reflect a weak simulated response rather than better agreement (Sect. 2). We therefore do not use RMSE to rank model performance. The RMSE remains informative in absolute terms: for every model, it exceeds the RMSEP of the reconstruction itself, indicating that the proxy-model disagreement is larger than can be attributed to reconstruction uncertainty alone. The standard deviation across the ensemble is comparable to the ensemble-mean signal of the MLD anomaly for PMIP4, but larger for PMIP3 (Fig. 5b, d).

The PMIP4 model simulations' RMSE relative to proxy reconstructions ranges from 75.79 m of EC-Earth3 to 355.66 m of FGOALS-g3 (see Fig. 1). The ensemble mean field has an RMSE of 100.58 m. Testing the models' ability to predict the direction of change, MRI-ESM2.0 is the only model that shows statistically significant agreement with the proxy data, with a Cohen's κ coefficient of 0.44 and a 95 % confidence interval of 0.15–0.73. For the other models and the ensemble mean, the κ coefficient is generally low or negative, suggesting slight or no agreement between the proxy and the models. The confidence interval for these models and the ensemble mean includes zero (see Table S1), implying that the true κ coefficient could be zero and that the true agreement could be the same as would be expected by chance despite a positive κ value; hence, the calculated degree of agreement is not statistically significant. Among the models, ACCESS-ESM1.5 (κ=0.35) and GISS-E2.1G (κ=0.27) have the highest potential proxy-model agreement; however, this agreement may not be significant as discussed above.

None of the PMIP3 models or the ensemble mean has a statistically significant agreement with the proxy data, and the calculated Cohen's κ coefficients are generally low and sometimes very negative (see Fig. 2 and Table S1). Due to the stronger signals of simulated winter MLD anomaly in the models, the RMSE reaches up to 668.71 m for GISS-E2-R and 639.89 m for KCM1.2.2, while the PMIP3 ensemble mean field has an RMSE of 112.51 m, comparable to that of the PMIP4 ensemble. Some models contributed to both the PMIP3 and PMIP4 MH experience with different model versions. Substantially improved agreement with proxy data from PMIP3 to PMIP4 is found for the GISS and the MRI models.

The comparison of Holocene (the last 12 ka) time series shows little agreement among the models and between the models and the reconstruction (Fig. 6). The distribution of meltwater flux, either global and uniform as in HadCM3_uniform or routed to individual outlets as in HadCM3_routed, appears to have little influence on North Atlantic deep convection. TraCE-21ka remains nearly constant throughout the Holocene in deep-water formation regions and only shows a long-term trend in an area that is not a major deep-water formation site (the central subpolar North Atlantic). The MPI modelling group tested two ice-sheet reconstructions, Glac1D and Ice6G, with three model versions (P1, P2, P3). The results suggest that different ice-sheet evolutions generally lead to changes in timing and magnitude of MLD variations at the sub-millennial scale, without affecting the longer-term trends. In contrast, different tuning of the same model strongly affects the MLD response, as P1 differs substantially from the otherwise similar P2 and P3. This is expected given that P1 is an older version of MPI-ESM-CR and that P2 and P3 are equivalent to each other with a slight change in the threshold between cloud water and ice (Text S1 by Kapsch et al., 2022).

Cohen's κ coefficients calculated from the MH anomalies suggest that none of the models has a significant agreement with proxy reconstructions of annual MLD anomaly (Fig. 7 and Table S1). The RMSE relative to the reconstructions is very low for HadCM3_uniform, HadCM3_routed and TraCE-21ka, primarily because they simulate little variation over the last several millennia and hence very small anomalies.

The inter-model spread of the North Atlantic MLD is significantly reduced across the PMIP4 ensemble compared to the PMIP3 ensemble (Fig. 5b, d). The PMIP3 ensemble mean field shows large anomalies and uncertainty in the central and eastern subpolar North Atlantic, which are not key areas of present-day deep-water formation. This suggests that the difference between the PMIP4 and PMIP3 ensembles is likely due to improved model physics, such as vertical mixing schemes and vertical grid resolution near the surface, which lead to more accurately simulated locations of deep convection in the new generation of Earth system models. In fact, improved mixing parameterisation is among the most important updates to the CMIP6-PMIP4 models (Xu et al., 2025; see also their Table 1). In this section, we will focus on differences among the PMIP4 models, which represent the current state of the art.

An important part of the changes in winter MLD simulated by the PMIP4 models seems to be tightly related to changes in winter sea ice concentration in MH relative to PI. Increased winter MLD is usually found at locations of reduced winter sea ice concentration (see Figs. 1 and S2), probably as a result of the two-way feedback between sea ice and open-ocean convection. A consistent reduction in Arctic sea ice minimum extent is found in the MH experiment across the PMIP4 models, primarily due to enhanced summer melt in response to higher insolation in Northern Hemisphere summer (Brierley et al., 2020). This leads to reduced export of Arctic sea ice in winter and reduced sea ice concentration in the subpolar North Atlantic, thus enhancing the ocean buoyancy flux to the atmosphere and promoting vertical mixing, which deepens the MLD. A more vigorous vertical mixing also allows warm and salty subsurface water of subtropical Atlantic origin to be mixed upward, which counteracts sea surface cooling and limits local sea ice formation, hence further strengthening the buoyancy flux and convection (Gelderloos et al., 2012).

Most models simulate a decrease in winter sea ice in different parts of the subpolar North Atlantic. In the Nordic Seas, this generally drives convection toward higher latitudes and the new sea ice edge (when sea ice extent exhibits a clear change). In the Labrador and Irminger Seas, the inter-model spread is large as the area ranges from entirely ice-covered to ice-free in the PI control experiment (Fig. S3). Consequently, when forced by the MH boundary conditions, the models produce remarkably different responses in the sea ice cover of this area. The initial state of sea ice concentration in PI can affect how its changes relate to the MLD. Unlike the previously mentioned negative correlation between MLD and sea ice concentration, when an increase in sea ice takes place in already densely sea ice-covered areas, there is no evident change in MLD since deep convection was already inhibited in PI and MLD remains very shallow (e.g., EC-Earth3, EC-Earth3-LR, INM-CM4.8, MIROC-ES2L). In contrast, in areas that are ice-free in PI, the MLD generally increases in response to enhanced ocean heat loss under reduced winter insolation, with no accompanying change in sea ice (e.g., CESM2, GISS-E2.1G, MPI-ESM1.2-LR, MRI-ESM2.0, NorESM2-LM). The intensified deep convection reduces stratification, so conditions there remain unfavourable for local sea ice formation.

Inter-model differences in sea ice and its transport seem to account for part of the large spread in MLD anomalies across the PMIP4 models. The models not only simulate considerably different pre-industrial sea ice extent as a baseline, but they also exhibit divergent responses to the MH forcings. The analysis of North Atlantic deep-water formation in the CMIP5 historical simulations (same generation as the PMIP3) suggests that deep convection is most realistic in models with realistic sea ice extent (Heuzé, 2017). Uncertainties in the PI sea ice extent are likely a more important source of the inter-model spread in MLD than uncertainties in the response of sea ice concentration. Our statistical analyses on winter sea ice concentration (Table S1) show no universal correlation between model performance in simulating MLD anomaly and sea ice anomaly: significant agreement on sea ice concentration anomaly does not guarantee agreement on MLD anomaly (e.g., FGOALS-g3, MPI-ESM1.2-LR), although the model with the best performance for MLD anomaly (MRI-ESM2.0) does have significant agreement for sea ice anomaly. This highlights the importance of other mechanisms affecting simulated MLD.

The sea ice model itself is affected by other model components. In some cases, differences in simulated sea ice and MLD may result from other model components. For example, by comparing the three versions of the EC-Earth3 model (EC-Earth3, EC-Earth3-LR, EC-Earth3-Veg), we find that using a lower-resolution atmospheric grid can cause a change in the amplitude of MLD and sea ice anomalies but preserves the spatial pattern, whereas incorporating a dynamic vegetation module instead of using prescribed modern vegetation leads to a marked change in the Labrador Sea and the Southern Ocean. Dynamic vegetation feedbacks enhance warming in the Sahara under MH forcings and increase rainfall in the Sahel region (Berntell and Zhang, 2024). This increased precipitation over northern Africa would be compensated by decreased precipitation over the western subtropical North Atlantic, creating a high salinity anomaly that is advected toward the subpolar North Atlantic (e.g., Zhang et al., 2021). In the EC-Earth simulations, this high salinity anomaly appears to affect the Labrador Sea the most, reducing stratification and sea ice formation, promoting convection and deep-water formation, and possibly enhancing the AMOC, which further strengthens the feedback loop. Vegetation can also increase warming in the Arctic through albedo feedback, leading to amplified Arctic sea ice retreat and reduced sea ice export in winter (e.g., O'ishi and Abe-Ouchi, 2011), which reinforce the stronger wintertime convection in the Labrador Sea. As another example, IPSL-CM6A-LR shares the same ocean and sea ice models as the EC-Earth3 suite, with a similar grid resolution but coupled to different atmosphere and land models. The simulated changes in MLD and sea ice are in opposite directions across the Nordic Seas between EC-Earth3 and IPSL-CM6A-LR. Similarly, FGOALS-f3-L and FGOALS-g3 produce considerably different MLD change and MH sea ice extent despite having the same ocean and sea ice models, implying the governing role of the atmosphere component in a coupled model as the primary driver of open-ocean convection and sea ice formation.

These findings highlight the importance of air-sea-ice interactions in modulating convection in the subpolar North Atlantic and the need to resolve both oceanic and atmospheric processes, as well as sea ice dynamics, to correctly represent the ocean mixed layer. In addition, the difference between HadGEM2-CC and HadGEM2-ES suggests that the implementation of tropospheric chemistry might mitigate the model's response to MH orbital forcing (see Fig. 2). However, with only 35 years available for HadGEM2-CC, we cannot establish whether this difference exceeds internal variability, and we note this as a potential direction for future work. Models differ substantially in the North Atlantic deep-water formation areas (Fig. 5b), indicating that accurately simulating the strength of deep convection and the MLD remains challenging. The situation is similar for simulated AMOC strength, with a large spread across the PMIP4 models (Brierley et al., 2020; Jiang et al., 2023). Although many models simulate little change in AMOC strength, the direction of change is generally consistent with the relative proportion of increase and decrease in winter MLD. For example, EC-Earth3-LR simulates a stronger AMOC in the MH relative to PI while IPSL-CM6A-LR simulates a slightly reduced one (Jiang et al., 2023).

While most PMIP3 and PMIP4 models agree that winter convection in the MH is stronger than PI in the Labrador Sea because of the deeper MLDs, proxy data suggest the opposite (Fig. 5a, c). Differences between simulated and reconstructed sea ice change might explain the discrepancy at the proxy record site in the west and the other two sites in the south, but not in the northern Labrador Sea (Fig. 5e). In the northern Labrador Sea, both proxy records and numerical simulations indicate reduced winter sea ice concentration relative to the PI; the reconstructed and simulated sea ice concentrations are both below 50 % in the MH (Fig. S4). However, while models simulate increased MLD straightforwardly in this case, reconstructed MLD decreases.

This leads to the hypothesis that during the Holocene, meltwater influx played a key role in modulating deep convection and deep-water formation in the Labrador Sea. The MH experiment is an equilibrium simulation designed to examine the impact of changes in orbital forcing at times when greenhouse gas levels were similar to those of the preindustrial period, and the continental configurations were close to modern ones (Otto-Bliesner et al., 2017). Hence, the modern configuration of ice sheets is prescribed in the MH simulation, and the ice sheets are in equilibrium with other components of the Earth system in the final outputs, which is a known source of uncertainty (Otto-Bliesner et al., 2017). In the real world, the MH Labrador Sea likely remained under a superimposed effect of rapid ice-sheet melting before the Middle Holocene and ongoing ice-sheet melting, thus far from an equilibrium state. Geomorphological evidence indicates a final disappearance of residual ice caps and glaciers in eastern North America as late as 6–5.5 ka BP (e.g., Clark et al., 2000; Dyke, 2004; Dalton et al., 2023), and glaciological, ice cores, as well as paleoecological records from coastal areas agree that the Greenland Ice Sheet reached a minimum extent around 4000 years ago (Briner et al., 2016 and references therein, including Vinther et al., 2009). Marine proxy records indicate highly variable sea surface salinity in the Labrador Sea during the Early to Middle Holocene (e.g., de Vernal and Hillaire-Marcel, 2006; Gibb et al., 2014), with lower sea-surface salinity until the Late Holocene at some locations (e.g., Allan et al., 2021; Solignac et al., 2004), which could be attributed to meltwater discharge. Proxy data of surface and subsurface waters in the Labrador Sea suggest the presence of a buoyant surface layer unfavourable for deep-water formation until the Middle Holocene (Hillaire-Marcel et al., 2001; de Vernal and Hillaire-Marcel, 2006), suggesting possible changes in the routing and rate of meltwater input. Together, the proxy evidence indicates that the Labrador Sea was under prolonged influence of meltwater influx throughout the Middle Holocene, which likely inhibited deep convection. Such transient effects and the continued meltwater flux into the North Atlantic are missing in the MH equilibrium simulation.

In contrast to the Labrador Sea, there is relatively good proxy-model agreement in the Nordic Seas despite the missing meltwater forcing, suggesting that the northwestern North Atlantic may be the most affected deep-water formation region under a future scenario of global warming and ice-sheet melting. This is consistent with modelling studies of meltwater pathways in the present-day North Atlantic that suggest generally limited exchange from the East Greenland Current into the Nordic or Irminger Seas, with most of the meltwater ending up in the Labrador Sea or Baffin Bay (e.g., Dukhovskoy et al., 2019; Pennelly et al., 2019).

In the last deglaciation simulations, models generally do not overestimate MLD in the Labrador Sea as much as in the MH equilibrium simulations (Fig. 6), which could provide evidence for the influence of meltwater fluxes. However, the models do not show better overall agreement with the proxy records or with each other, raising questions about the robustness of this evidence. The models' sensitivity to meltwater forcing appears highly variable, as simulations run with the same ice sheet reconstruction (e.g., HadCM3_routed versus the MPI_Ice6G ensemble) yield very different evolutions of MLD, with some remaining nearly constant and others showing large fluctuations. While reconstructions in the Labrador Sea reveal an increase of MLD toward modern-like conditions over the Late Holocene, none of the models reproduces this trend. This implies that the memory of the ocean in long transient simulations might be too long compared to what proxy records suggest, especially in the Labrador Sea. In the Nordic Seas, the MPI ensemble largely overestimate the MLD, which is consistent with the previously mentioned fact that meltwater affects the Labrador Sea more than the Nordic Seas; the HadCM3 simulations are the closest to the proxy records in the Nordic Seas; TraCE-21ka shows lower annual MLD than proxy records, and the results further indicate that this model is probably not resolving the correct locations of deep convection. The divergence between transient simulations and proxy data in North Atlantic deep convection could be one of the reasons behind the `Holocene temperature conundrum' discussed by Liu et al. (2014).

Unfortunately, the robustness of the statistical analyses in this study is limited by the small sample size. The estimated statistical metrics, notably the Cohen's κ coefficient, may not accurately reflect the true performance of the models and should therefore be interpreted with caution. Nevertheless, it is interesting to note that the ensemble average does not always align better with proxy data than individual models, and that models capable of, or nearly capable of, reproducing the direction of MLD change do not necessarily have a smaller RMSE. The response of MLD to MH forcing could be dampened in some models due to the apparent deep bias in some deep-water formation regions (Figs. 3 and 4). The model biases could be due to the various parameterisations, such as those for mesoscale eddies or vertical mixing scheme. The coarse resolution of the models could also introduce bias, as low-resolution models tend to exhibit larger deep biases in winter MLD in some eddy-rich regions than their high-resolution counterparts (Treguier et al., 2023). For transient simulations of the last deglaciation where a meltwater flux is applied, the coarse resolution models struggle to simulate the narrow, fast boundary currents, in addition to the model biases discussed above. The slower boundary advection would cause freshwater to be trapped within the ocean basins for much longer time. The biases could also be related to uncertainties in boundary conditions, such as the ice-sheet reconstruction and the associated timing, volume, and routing of meltwater, changes in vegetation cover, etc. For the PMIP MH simulations, using monthly rather than higher-frequency model output to recompute MLD would likely yield smoothed signals of density profiles and extreme events such as storms (Treguier et al., 2023), further adding to the uncertainty.

The model biases are challenging to analyse here as there is uncertainty in the reconstructed MLD data as well (see Wu et al., 2025). The main sources of proxy-related uncertainties are errors in sediment sample age estimation and errors in the reconstruction method. The errors in sediment core age modelling vary from core to core and depend on the number of ¹⁴C dating points in each core and the accuracy of the estimated ocean reservoir-age correction. This error can be as high as a few hundred years, affecting the actual 6.5–5.5 ka BP time window used to represent the MH in sediment cores. Its impact on the results, however, is difficult to analyse and core-specific. The reconstruction error (RMSEP) is estimated from leave-one-out cross-validation to be 40.9 m for winter MLD, 16.0 m for annual MLD, and 17.6 % for winter sea ice concentration. Finally, we found that the reconstruction method can exhibit regional biases, as discussed in Wu et al. (2025), which we attempt to mitigate using the MH minus PI anomaly approach. For example, the reconstruction method tends to underestimate the MLD in the southern Labrador Sea and the Iceland Basin (see Fig. S12 in Wu et al., 2025). Overall, the proxy-related uncertainties are probably comparable to, or slightly less than, the uncertainty of the multi-model mean. Systematic benchmarking of the previous generation of PMIP MH experiment shows that differences in model performance are only weakly related to modern-day biases (Harrison et al., 2015). Greater availability of quantitative reconstruction data based on different proxies is therefore necessary to improve climate model evaluation.