The model selection was based on three criteria: (1) both the HIST and DCPP experiments were available via the Earth System Grid Federation (ESGF) portal for each model; (2) both the HIST and DCPP experiments were driven with the CMIP6 external forcings to ensure complete consistency in the forced signals; and (3), in both sets of experiments, the relevant output variables for our analyses, such as 3D salinity (so in CMIP convention), 3D potential ocean temperature (thetao), 2D sea level pressure (psl), downward surface heat fluxes (hfds), and sea ice concentration (siconc), were available at monthly frequency for the period 1960–2014 (which is their overlap period). Also, except for two justified exceptions (details below), models with fewer than 10 ensemble members for HIST and/or DCPP were excluded. A total of 8 AOGCMs were retained based on the selection criteria. For models that provided more than 10 ensemble members, in either the HIST or DCPP experiments, only 10 members were retained to maximize the consistency across models. By default, we took members r1–10, except for EC-Earth3 historical simulations, for which we used 10 members performed at the BSC (i.e. r2, r7, r12, r17–22, r24). This ensemble size is the minimum that is recommended for the DCPP-A protocol in and is the most common ensemble size across the models considered. Both HadGEM3-GC31-MM and MPI-ESM1-2-HR contributed with fewer than 10 ensemble members (4 HIST members and 5 DCPP members, respectively), but, since both have comparatively higher horizontal resolution (0.25° and 0.4°, respectively), they were included to assess if there is any added value, either in process representation or predictive skill, when horizontal resolution is increased. More details on the models considered in this analysis and their characteristics can be seen in Table .

We used the EN4 version 2.2 ocean temperature and salinity objective analysis dataset based on optimal interpolation to evaluate the predicted OHC700 and the ocean stratification. Three ocean reanalyses (ECDA3.1 , ORAS4 , ORAS5 ), the same used in , were additionally considered and compared with EN4 to identify the regions with high and low OHC700 observational uncertainty (Fig. ).

To understand the processes driving local OHC700 skill, we analysed additional variables, such as sea level pressure, surface heat fluxes, and sea ice concentration. To determine how realistically the systems simulate these variables, we compared them with other observationally based datasets. For the atmospheric variables, we used the global atmospheric reanalysis ERA5 , as it provides a complete and physically coherent description of recent atmospheric variability that is constrained by observations. These include monthly sea level pressure fields (necessary to compute the NAO) and net surface heat fluxes (derived from thermal radiation, surface solar radiation, surface sensible heat flux, and surface latent heat flux). Finally, to evaluate the sea ice concentration, we used the monthly fields of HadISST.2.2.0.0 , hereinafter simply HadISST.

Data from both models and verification products were regridded to a common regular 1°×1° resolution grid. All model outputs were regridded using the Earth System Model Evaluation Tool ESMValTool; versions 2.4.0 to 2.7.0, which was particularly useful for its ability to process all models, experiments, start dates, and variables in a consistent way. For other pre-processing tasks that were less computationally intensive, such as the calculation of yearly averages or the regridding of the ERA5 reference data, the Climate Data Operators tool version 1.9.10 (https://mpimet.mpg.de/cdo, last access: 9 July 2025) was preferred. Additionally, we used ESMValTool to compute the OHC700 and potential density anomaly (σ; computed for the reference level of 1000 m). The post-processed outputs were then analysed with the s2dverification/s2dv package for R software and Python scripts that were developed purposely for this research. Both the NAO and the linear regression analysis were also computed with s2dverification/s2dv.

To evaluate the forecast quality of the models, we used the anomaly correlation coefficient (ACC). The statistical significance of ACC differences was assessed following the methodology proposed by , a statistical test developed for cases where competing forecasting systems are strongly correlated with one another.

An important aspect to consider when comparing predictive skill between a DCPP experiment and its HIST counterpart is the selection of a common period for forecast evaluation, to ensure that differences in skill only arise from the effect of initialization (as prediction skill can be sensitive to the evaluation period). Our evaluation period is fixed and starts in 1970 – the first year for which the DCPP ensemble provides predictions for the full forecast range (1st to 10th year) – and finishes in 2014, which is the last year covered by the HIST ensemble. Linear trends in our analysis were also computed for this same period.

Not all models in this analysis were initialized in the same month. One model was initialized on 1 October (NorCPM1), several were initialized on 1 November (CMCC-CM2-SR5, EC-Earth3, HadGEM3-GC31-MM, MPI-ESM1-2-HR, and MRI-ESM2-0), and the others were initialized on 1 January (CanESM5 and IPSL-CM6A-LR). Therefore, for practical reasons, in all models, we computed all forecast years (FY1–10) from January through December, discarding the first months from those models initialized in October and November. Additionally, we computed the boreal winter mean (defined from December to February, referred to as DJF hereafter), which is important for some of the processes and drivers investigated (such as the NAO). The forecast winters were numbered according to their January and February forecast years, which means that, for example, DJF2 refers to the winter that includes the December month of FY1 but months January and February of FY2. We discarded DJF1 from all analyses, since some systems do not fully predict the first winter (as it requires December of FY0).

We firstly evaluate the ACC for OHC700 in all the prediction systems for three different forecast times (years 2, 5, and 10) and in all the historical ensembles. Overall, all decadal prediction systems show positive correlations for most of the NA at all the different forecast ranges (Fig. , columns 1–3), with higher correlations typically taking place in the Labrador Sea and along the eastern flank of the basin and negative correlations developing in a region located east of the Grand Banks (EGB; approx. 40–55° N and 40–25° W, with small regional differences across models). We note that, over the EGB region, the ocean reanalyses and EN4 show the highest discrepancies in terms of OHC variability (Fig. ); therefore the associated skill scores are expected to be more uncertain and should be interpreted with caution. We also note that no systematic overall improvement at any forecast time is observed for systems based on full-field initialization compared to those using anomaly initialization, and vice versa (first 4 rows vs. last 4 rows in Fig. ). The ACC patterns for HIST are generally close to those in the predictions, although with a tendency for more widespread negative correlations and lower positive correlation values than in the predictions. The largest added value of initialization, as indicated by the ACC differences between the DCPP and HIST ensembles, is found predominantly in the subpolar gyre region (Fig. ). Residual correlations, introduced by , help to more clearly identify regions where initialization is beneficial for prediction. These correlations (Fig. ) reveal another area with a strong added value of initialization in the eastern North Atlantic. However, this result should be interpreted with caution, as residual correlations assume that models accurately represent the forced signals in observations – an assumption that may not hold in regions where the HIST ensemble exhibits high inter-model differences.

We now turn our attention to some specific cases of distinct individual model behaviour in Fig. . While, in most models, ACC values tend to be highest in FY2 and usually decrease as the FY progresses, as expected due to the effect of initialization, this is not the case for IPSL-CM6A-LR and CanESM5. In both models, ACC is higher in FY5 and even FY10 than in FY2 over the Labrador Sea (LS) and the EGB region. The comparatively lower skill in FY2 than in subsequent forecast years for IPSL-CM6A-LR and CanESM5 might be caused by a strong initialization adjustment, as their historical ensembles show comparatively higher ACC values than the DCPP at FY2. Another system showing a rapid loss of skill in the LS and EGB regions is NorCPM1, where negative correlations emerge by FY5 and FY10. In this case, it might reflect a deficiency in the representation of the forced signals, which could be related to a reported problem in the transient land-use specification in North America, with downstream impacts in the subpolar North Atlantic area . Its HIST ensemble has a large area of negative skill values over the LS and its surroundings. Interestingly, in this same region, NorCPM1 predictions show the highest levels of skill at FY2, which suggests that initialization can temporarily correct the errors in the land-use forcing.

Figure  describes the inter-model differences in ACC shown in Fig. , as diagnosed by the standard deviation of the ACC values across models. The HIST experiments have higher ACC spread than the DCPP experiments over most of the NA at all forecast years. The largest standard deviation values (and thereby inter-model differences) are found for HIST along the eastern North Atlantic (up to 0.6) and in the LS (up to 0.4). In the DCPP experiments, the inter-model spread tends to change with forecast year, without much spatial consistency in terms of the regions with the largest standard deviations. The LS (red rectangle in Fig. ; 45–65° N and 60–30° W.) emerges as a region in which inter-model differences in skill are prominent at all forecast times. We note that the selected box extends into the Irminger Sea, which also shows important inter-model spread. We also note that this is a characteristic region of deep vertical mixing, with common precursors and drivers whose representation may vary across models, and could explain the inter-model spread. Hence, in the rest of the study, we will focus on this region to understand its inter-model differences in OHC skill.

To better understand the differences in skill, the predicted and observed evolutions of LS OHC700 anomalies are shown in Fig. . At FY2 and FY5, all systems but CanESM5 predict the observed evolution reasonably well, characterized by a very weak cooling trend until the mid-90s, after which a warming trend starts to unfold. CanESM5's long-term trend is characterized by a cooling, completely failing to represent the warming after the 90s. This could be related to the use of ORAS5 for initialization , which has been reported to have non-stationary trends in the region . At longer forecast times (FY10), all models except CanESM5 and NorCPM1 simulate a long-term warming trend of similar amplitude to the observed one, although none of the models capture the relative cooling well between 1990–1995.

Interestingly, in the HIST ensemble, only two models, IPSL-CM6A-LR and CanESM5, simulate a clear warming trend consistent with the observed one. The other models show a rather flat evolution, and NorCMP1 shows a cooling trend. We also note that none of the HIST ensembles simulate the cooling until the mid-90s or the subsequent rapid warming partly captured by the DCPP experiments, supporting a key role of initialization in the decadal variability around the trend.

Figure  shows that the relationship between the OHC700 trends (as derived for the period 1970–2014; see Sect. ) and the OHC700 skill in the LS is largely linear across models. In other words, models with stronger OHC700 trends in the LS tend to have higher OHC700 skill in this region, which is particularly evident in the HIST ensemble and in the first forecast years of the DCPP ensemble, although with some notable differences. While, for HIST, all the models show a wide range in the magnitudes of the simulated trends, in the first forecast years of the DCPP ensemble, all models predict similar trends to the observed one, except for CanESM5, which has previously been mentioned as an outlier. This clear correction of the predicted trend via initialization can imply that (1) the observed LS trend is only driven by internal variability processes or that (2) external forcings contribute to the trend but require realistic background climate conditions – achieved through initialization – to represent it accurately. Interestingly, predicting the trend well does not always lead to high levels of OHC700 skill, as noted for IPSL-CM6A-LR at FY2 in Fig. .

To further investigate the impact of the long-term trends on the OHC700 skill in the LS, Fig.  portrays the ACC values as a function of FY when both DCPP and the observed data are linearly detrended (dashed blue line) and compares them with the skill for the original time series (solid blue line). In all models, except for CanESM5, the forecast skill systematically decreases when the trend is removed, even though the drop in skill is not always significant with respect to the un-detrended ACC values (red crosses in Fig. ). This confirms that an important part of the skill comes from the representation of the trend. Figure  also shows the forecast skill of the HIST ensemble, which, compared with the DCPP skill, can inform us about the predictive role of the forcings. The results are largely model-dependent. In some systems, HIST and DCPP have similar ACC values that are only significantly different in the first FYs, which suggests a predominantly forced origin of the skill. Other models, like MRI-ESM2-0, HadGEM3-GC31-MM, and CMCC-CM2-SR5, show high and significant ACC values for DCPP, while, for HIST, the ACC values are indistinguishable from zero. The interpretation of these latter systems is more complex, as the high predictive value of initialization could imply that internal variability is the dominant factor leading to the OHC700 skill, but it is also possible that the corresponding HIST ensembles simulate an unrealistic, externally forced variability that is largely corrected via initialization. It is also possible that external forcings exert only a prominent role in OHC predictability for some specific areas within the wide Labrador Sea box considered. Indeed, all models but NorCPM1 show positive skill for their historical ensemble in the westernmost part of the region and poorer skill on its easternmost side (Fig. ).

Figure  thus illustrates how the large uncertainties in the representation of the forced signals, together with the initialization shocks in some of the systems (CanESM5, EC-Earth3, IPSL-CM6A-LR), prevent us from learning about the true origin of the LS OHC700 predictability. The underlying problem is that we do not know how much of the observed variability is actually driven by the forcings. In the next two sections ( and ), we will explore (i) how different precursors and drivers of LS decadal variability are represented across models and experiments to ultimately investigate (ii) whether they can explain some of the inter-model differences in the forced LS OHC700 predictive skill.

In this section, we explore the underlying differences across models of two important factors controlling Labrador Sea temperature variability: (1) LS stratification and (2) surface atmospheric forcing. The former is a preconditioning factor for the occurrence of deep convection in the region, whereas the latter is a direct driver of convection and OHC variability via its influence on local air–sea heat fluxes. We note, however, that these factors can also interact with each other. For instance, in strongly stratified models where deep convection is suppressed, atmospheric forcing may instead lead to sea ice formation. In the following, we will evaluate how models simulate these important processes and whether they are improved via initialization.

An accurate characterization of the externally forced component of North Atlantic OHC variability is fundamental to understanding decadal predictability and evaluating model performance, as it is possible that some models show higher predictive skill for the wrong reasons. This last section seeks to narrow down the large uncertainties identified in the LS OHC700 externally forced signal, which is unknown for the real world, as observations include both internal and forced variability. We can, however, contrast the HIST simulations against observationally based climatological values for the previously analysed key physical properties (i.e. stratification, NAO regression, surface heat fluxes, and sea ice concentration), as these are largely determined by the background forcing conditions. To this end, a set of scatter plots was assembled in Fig. .

We find a strong linear relationship between the forced OHC700 skill and the stratification index, with stronger stratification linked to higher skill. This result is robust for different definitions of the stratification index considered (not shown). A possible interpretation of this linear relationship is that stronger mean stratification limits the occurrence of deep convection events, especially those triggered by internal climate variability processes (which in HIST runs cannot be in phase with the observations), allowing better capture of the long-term trends. This would be consistent with the fact that ACC values for Labrador OHC700 are shown in Fig.  to be strongly related with its associated long-term trends. However, it is important to note that the models with the largest forced OHC700 skill also largely overestimate the local stratification when compared to an observational reference, which raises questions about their realism.

The relationship between the OHC700 skill and the climatological winter surface heat fluxes (hfds) in the LS (Fig. c) is also highly linear. In this case, however, both variables exhibit an inverse relationship: models like NorCPM1 or MRI-ESM2-0 that have stronger climatological surface heat fluxes in the LS (i.e. that lose more heat to the atmosphere) tend to have lower ACC values for OHC700, and vice versa. One potential explanation for this relationship is that, with stronger heat fluxes, the local stratification can be overcome more easily, which therefore allows a higher presence of spurious unforced signals that degrade the agreement with the observations (i.e. lower the ACC value). Interestingly, even though higher ACC values are linked to weaker surface heat forcings, the observed ERA5 climatologies suggest that the models with the highest forced skill are not particularly realistic. It should be noted, however, that ERA5 does not include all of the air–sea ice fluxes that are included in the HIST fluxes and might be important at the western side of the Labrador Sea.

For the two other preconditioners identified in Sect.  (i.e. the local NAO surface forcing and the climatological sea ice conditions), we do not find a clear linear relationship with the forced OHC700 LS skill. Despite this, CanESM (the model with the highest ACC values) is identified in both cases as a clear outlier when compared with observation-based references.

All the above results thus suggest that high ACC values in some of the historical ensembles are not necessarily indicative of good model performance. The underlying issue is that the true split between the forced and the internally generated variability in the real world is unknown, which hinders the identification of the models that simulate the forced signal better. Interestingly, the observation-based references included in the scatter plots are generally close to the multi-model mean value, supporting its standard use to derive our best estimate of the real forced signal. This multi-model mean has a forced OHC700 skill in the LS of ∼0.4, which would imply a significant but not dominant contribution of the external forcings to Labrador Sea OHC700 variability (as it would explain around 16 % of the total variance).