Most of the North Atlantic ocean has warmed over the last decades, except a region located over the subpolar gyre, known as the North Atlantic “warming hole” (WH), where sea surface temperature (SST) has in contrast decreased. Previous assessments have attributed part of this cooling to the anthropogenic forcings (ANT) – aerosols (AER) and greenhouse gases (GHGs) – modulated by decadal internal variability. Here, I use an innovative and proven statistical method which combines climate models and observations to confirm the anthropogenic role in the cooling of the warming hole. The impact of the aerosols is an increase in SST which is opposed to the effect of GHGs. The latter largely contribute to the cooling of the warming hole over the historical period. Yet, large uncertainties remain in the quantification of the impact of each anthropogenic forcing. The statistical method is able to reduce the model uncertainty in SST over the warming hole, both over the historical and future periods with a decrease of 65 % in the short term and up to 50 % in the long term. A model evaluation validates the reliability of the obtained projections. In particular, the projections associated with a strong temperature increase over the warming hole are now excluded from the likely range obtained after applying the method.

The increase of global surface air temperature (GSAT) over the 1850–2021 period is unequivocally attributed to human activities

So far, the impact of external forcings and internal variability on the observed WH over the historical period has been qualitatively estimated by using dedicated sensitivity model experiments

The SST observations from the HadSST4 (Hadley Centre's sea surface temperature, version 4) dataset

Historical and Scenario Model Intercomparison Project (ScenarioMIP) simulations from the CMIP6 ensemble

To assess past and future forced response of the WH, I use the KCC observational constraint method that has been previously applied to global mean warming

Implementing this methodology requires the computation of the values of

Historical simulations and single-forcing experiments from the DAMIP ensemble give a first characterization of the WH and an estimate of the contribution of each external forcing. Over the 1951–2014 period, anthropogenic aerosols have contributed to warming the subpolar gyre, with a mean increase of

The combination of CMIP6 models and observations via the KCC statistical method provides estimates of the SST forced responses to different external forcings with uncertainties that are consistent with the available observations and internal variability. Here, I apply the KCC method to the DAMIP ensemble by using the observed SST annual time series over the warming hole, defined as the spatial average over 48, 63

Figure

Changes induced by various subsets of external forcings over the historical period (1951–2020 with respect to (w.r.t.) 1870–1900) over the warming hole. Observed (Obs) changes (gray, left) are deduced from HadSST4 observations; uncertainty only includes observational uncertainty (i.e., measurement and processing; internal variability is ignored). For all other contributions, the bar and gray confidence interval on the left-hand side describe the DAMIP model range, assuming a Gaussian distribution. The bar and black confidence interval on the right-hand side correspond to results constrained by observations. All ranges shown are 5 % to 95 % confidence ranges. The SSP2-4.5 scenario is used to extend historical simulations after 2014.

The sensitivity of these attribution results to methodological factors is quantified by considering several aspects. First, to take into account the diversity of the CMIP6 models in the spatial structure of the simulated WH, the SST spatial average is defined for each model over a specific domain, to ensure a consistent comparison with observations. As done by

The second sensitivity test is to consider the full set of CMIP6 models available to estimate the forced responses, such that a sample of 27 models is considered instead of the only 12 models that contributed to the DAMIP ensemble, which may undersample internal variability and model uncertainty. Using the KCC method, hist-GHG-like simulations for the models that did not contribute to the DAMIP ensemble are reconstructed through the 1 %–CO

The KCC method is also used to constrain the SST projections associated with the CMIP6 SSPs simulations over the WH. Since DAMIP simulations are not required to perform the calculations based only on the ALL component, all available CMIP6 models are used to estimate the past and future forced responses, using a fixed WH domain as in Fig.

The observational constraint is applied to concatenated historical and SSP scenarios simulations (SSP1-2.6, SSP2-4.5, or SSP5-8.5). Annually observed values of SST over the warming hole (black points) are compared to the unconstrained (pink) and constrained (red) 5 % to 95 % confidence ranges of forced response as estimated from 27 CMIP6 models. All temperatures are anomalies with respect to the period 1870–1900.

In order to evaluate the confidence in these results, the KCC method is applied within a perfect model framework, following a leave-one-out cross-validation.

For a given model, a single member is considered as pseudo-observations

The other 26 models are used to derive the prior distribution

As done with the real observations, internal variability within the pseudo-observations is estimated from the difference between the time series of pseudo-observations and the forced temperature response estimated by the ensemble mean of the 26 other models. Then,

The KCC method is applied using the inputs

These four steps are repeated for each available member of the considered model and for all available models.

I use the confusion matrix to estimate the reliability of the method for the short- (2021–2040), mid- (2041–2060) and long-term (2081–2100) periods (Table

is included in both the constrained range

not included in both the constrained and unconstrained ranges (true negative rate),

is included in the constrained range but not in the unconstrained range (false positive rate),

is included in the unconstrained range but not in the constrained range (false negative rate).

The constrained distributions contain the true values from the pseudo-observations in 80 % up to 84 % of the cases, which is close to the expected value of 90 %. The significance of this result is assessed with a binomial test. Under the null hypothesis that the probability of success is equal to 90 %, the obtained coverage probabilities remain compatible with 90 % (

Confusion matrix relating the temperature projection constrained by the KCC method and the true value from pseudo-observations. Rates (in %) are computed from 249 members (from 27 models) for the SSP2-4.5 simulation. Each rate is normalized by the number of ensemble members for each model to avoid giving too much weight to models with a large ensemble.

As a second performance criterion to assess the error on the amplitude of the constrained SST projections, I use the continuous ranked probability skill score (CRPSS), defined as the relative error between the constrained distribution

CRPSS for the constrained SST projections over the WH within the perfect model framework. The red, green and blue boxplots indicate the CRPSS distributions for different lead times. Calculation is made for all CMIP6 ensemble members (see Table

The temperature response to external forcings on the North Atlantic warming hole (WH) over the past and future period is estimated by the KCC statistical method based on kriging techniques, which combines climate models and observations. Consistent with the observations, an anthropogenic cooling is diagnosed by the method over the last decades (1951–2021) compared to the preindustrial period. The impact of the aerosols is an increase in SST which is opposed to the effect of GHGs. The latter largely contribute to the cooling of the WH over the historical period. Although the anthropogenic response is clear, the respective contribution of each anthropogenic forcing is associated with large uncertainties, especially for the aerosols. The quantification is in line with previous studies

This result has important implications for the estimation of the future changes in terms of teleconnection processes between the North Atlantic and the continental climate, e.g., over Europe, North America or the Sahelian monsoon. It would be interesting to re-evaluate the climate impacts of the North Atlantic SST variability in light of the constrained temperature ranges obtained in this study, e.g., in terms of the occurrence of extreme events or changes in atmospheric circulation.

A relevant perspective of these results is the potential constraint of the Atlantic Meridional Overturning Circulation (AMOC). Using the same approach as in this paper and to directly constrain future AMOC changes is challenging due to the limited number of observations monitored via the RAPID program

List of the available CMIP6 Models and the associated number of members in the simulations used to constrain the temperature time series.

The observation operator

The DAMIP (or CMIP6) multimodel ensemble is used to derive a distribution of

In the Bayesian framework,

The matrix

I define

To compute

The initial estimate of

Hence, in order to ensure an accurate estimation of internal variability in the constraint procedure, an iterative algorithm is applied to find the MAR parameters that fit the residuals from the constrained forced response:

Initial-condition large ensembles and long piControl simulations provide a nice sampling of internal variability and could also be used to estimate this variability. However, I choose to not rely on it directly because of the huge discrepancies between models in terms of their simulated internal variability

The datasets generated and analyzed during the current study are available at

The supplement related to this article is available online at:

The contact author has declared that neither of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work was supported by the European Union's Horizon 2020 Research and Innovation Programme in the framework of the EUCP project (grant agreement 776613), the CONSTRAIN project (grant agreement 820829) and Météo-France. I thank Hervé Douville and Aurélien Ribes for fruitful discussions about this work. I thank the climate modeling groups involved in CMIP6 exercises for producing and making their simulations available. I thank the ETH Zurich for providing CMIP6 data through their CMIP6 next generation (CMIP6ng) interface (

This research has been supported by the H2020 Excellent Science (grant nos. 776613 and 820829).

This paper was edited by Jonathan Donges and reviewed by Jobst Heitzig and two anonymous referees.