Introduction

During the 20th century, European summer temperature depicts a warming trend during the first 40 years1, followed by a cooling trend until the late 1970s2. Since the 1980s, Europe’s temperature has risen rapidly, becoming the fastest-warming continent on Earth, as highlighted in the European State of the Climate 2023 report from Copernicus Climate Change Service (C3S) and the World Meteorological Organization (WMO). However, most of the state-of-the-art General Circulation Models (GCM) simulations from the Coupled Model Intercomparison Project Phase 6 (CMIP6) tend to underestimate the warming and heat extremes in Europe compared to recent observations3,4,5,6. As shown in Fig. 1a, b, recent trends in annual temperature over Europe are higher than the global average, and the observed temperature anomalies (compared to 1851–1900) clearly surpass the CMIP6 ensemble mean since the beginning of the last century (Fig. 1a, c). This is consistent with previous studies showing that CMIP6 GCM simulations tend to underestimate the observed warming over France7. Recent regional studies associated this fact either with poor representation in CMIP6 models of the recent observed trends in atmospheric circulation in western Europe8, or with prescribing constant aerosol forcing in EURO-CORDEX models over Europe9, or with a poor estimate of long-term aerosol changes in EURO-CORDEX simulations for western-central Europe10. Here, we highlight that larger warming over Europe as compared to the CMIP6 ensemble mean is also true in winter and is even larger than in summer (Fig. 1d).

Fig. 1: Time evolution of global and European surface temperature anomalies.
Fig. 1: Time evolution of global and European surface temperature anomalies.
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a Time evolution of global annual temperature (raw in dashed line and 31-year running mean in solid line) anomalies relative to the 1851–1900 baseline showing the spread (standard deviation) of CMIP6 General Circulation Models (GCM) simulations (grey; Supplementary Table S1 for a list of CMIP6 GCM models), the CMIP6 GCM ensemble mean (black), the Dynamically Consistent ENsemble of Temperature (DCENT69, in dark red), HadCRUT5 observations (HadCRUT571, in orange), and Berkeley Earth Surface Temperatures (Berkeley70, in red). b Same as panel (a), but focusing on Europe (10°W–50°E, 35°N–70°N). c Temperature difference between Berkeley Earth data and the CMIP6 ensemble simulations for the period 1993–2022, with geographical locations (yellow stars) and names of the five proxy records used in this study. d Boxplots showing the annual and seasonal (April to September: AMJJAS and October to March: ONDJFM) temperature differences between Berkeley Earth, DCENT, with HadCRUT5 data and the CMIP6 simulations for the period 1993–2022. We re-gridded all CMIP6 outputs and observational datasets to a common 1° × 1° latitude-longitude spatial resolution to calculate the CMIP6 multi-model mean values, and differences with observational products.

The role of internal climate variability in this greater warming over Europe has been poorly assessed so far. In this context, our study focuses on internal climate variability and its potential role in the pronounced European warming in recent decades. We focus on multi-centennial climate fluctuations, where research remains limited: the existence, magnitude, and mechanisms of such low-frequency variability are still poorly constrained, while there is still no clear consensus on the existence of such a low-frequency variability and its underlying drivers11,12,13. Using high-resolution proxy records and model simulations, we aim to quantify this slow variability and evaluate its contribution to regional warming.

Climate is actually influenced by internal variability, which stems from the complex, chaotic interactions among the various components of the climate system14. Internal variability interacts with the effects of anthropogenically-forced climate change, caused most notably by the increasing emissions of greenhouse gases since the Industrial Revolution. Although the global warming observed over the past century is primarily attributed to the increase in greenhouse gas concentration, historical and future simulations include a large uncertainty, especially at the continental scale15. For instance, it has been shown16 that over France, 50% of the uncertainty in the warming level by 2050 is due to internal climate variability, 38% to the uncertainties in the climate models used, and the remaining 12% to the greenhouse gas emission scenarios chosen by human societies. The latter, therefore, represents quite a small fraction of uncertainty within this time horizon. By 2100, these proportions move to 8, 22, and 70% for internal variability, climate models, and greenhouse gas emissions, respectively. At smaller spatial scales, where climate tends to be more variable, the contribution of internal variability to the uncertainty by 2100 can be dominant17. Understanding the magnitude and underlying mechanisms of internal variability is therefore essential for improving regional climate projections17.

In addition to the large uncertainty related to internal climate variability, recent modelling results have highlighted that atmospheric circulation might not sufficiently respond to changes in its boundary conditions, such as the ocean and sea ice (e.g. ref. 18). This important finding suggests that ocean variability could have a greater impact on the atmosphere than currently simulated by existing climate models. The variability over land related to the ocean could be therefore underestimated by climate models19, as a result of the so-called signal-to-noise paradox20. The Atlantic Meridional Overturning Circulation (AMOC), a key driver of heat transport in the North Atlantic, has shown internal centennial variability in some climate models that mirrors continental temperature shifts. This variability is reflected in the Atlantic Multi-decadal Variability (AMV), the dominant pattern of North Atlantic temperature fluctuations, highlighting a strong link between ocean circulation and regional climate patterns over Europe21,22. For example, Europe experiences widespread cooling when the AMOC is reduced23. Based on climate model simulations, ref. 13 suggested, that part of the global anthropogenic warming may have been obscured by a weakening of the AMOC during the second part of the 20th century24, which could be mainly associated with an internal multi-centennial variability mode. However, this variability was highly model-dependent, raising questions about its existence in the real world.

Given the short period of instrumental temperature data and the influence of the anthropogenic forcing during this period, it is not possible to provide an answer to these questions without longer observations of the past. To understand climate variability on multi-centennial timescales, long and high-resolution temperature reconstructions from palaeoclimate proxies and climate models are required. For this purpose, we focus here on the present interglacial period, the Holocene, over the last 6000 years. While other interglacial periods might also be relevant, the Holocene is well-documented in terms of temperature proxy data25, allowing for a more accurate reconstruction of past climates and providing a detailed backdrop for understanding low-frequency climate fluctuations. Additionally, advancements in climate modelling have allowed more refined models providing transient simulations over a large part of the Holocene26,27,28. While most proxy-model comparisons of palaeoclimate variability have been limited to the last millennium29, a too short period to estimate multi-centennial variability properly, a few recent studies have begun to use longer transient simulations11,30. Building on these advancements, we compare here various transient simulations, as well as available high-resolution (seasonal to decadal) palaeoclimate reconstructions of surface atmospheric temperature mainly over Europe25,31, covering the last 6000 years, and a recent proxy-based reanalysis covering the Holocene32 (see Methods). The aim of this study is to: (i) identify a common multi-centennial signal of natural climate variability across different palaeoclimate information sources and its origin; and (ii) deduce its potential impact on recent and near-future temperature trends in Europe.

Results and discussion

Multi-centennial climate variability: a consistent signal across models, reconstructions, and Holocene reanalysis

Figure 2 compares the spectral density, significantly different from a red noise33, of temperature variations since the mid-Holocene, in proxy-based reconstructions (individual sites in Europe and Greenland; Fig. 2a and see Methods), transient climate models simulations and Holocene reanalysis data32 (over Europe; Fig. 2b), and simulated AMOC (Fig. 2c). The spectral analysis of low-pass filtered temperature data (see Methods) reveals significant periodicities (above the 99% significance level from the red noise) at the multi-centennial scales (~100–200 years) in most direct proxy reconstructions from diverse European sites, including the UK, the southwestern Norwegian continental margin, Sweden, and Finland. Comparable significant periodicities are also observed at a site in Greenland, although they can exceed 200 years, consistent with the findings of ref. 34. Similar spectral analyses have been conducted in transient simulations and in the Holocene reanalysis over Europe (Fig. 2b), in its northern (10°W–50°E, 55°N–70°N), central (10°W–50°E, 45°N–55°N) and southern sectors (10°W–50°E, 35°N–45°N) (Supplementary Figs. 1–3) showing similar peaks at multi-centennial timescales. This confirms that the multi-centennial-scale periodicity has a spatial signature that extends far beyond the individual sites where reconstructions are available and can be found over most of Europe. The consistency of this pattern across various models and European regions, as confirmed by reconstructions, suggests that processes at the multi-centennial scale might be a key driver of long-term climate variability. There are also smaller peaks in the spectral density, indicating multi-decadal variability at frequencies around 70 years, which can be related to the AMV35 mode.

Fig. 2: Spectral density analysis of temperature from proxy-based temperature reconstructions, Holocene reanalysis data, and transient model simulations since the mid-Holocene.
Fig. 2: Spectral density analysis of temperature from proxy-based temperature reconstructions, Holocene reanalysis data, and transient model simulations since the mid-Holocene.
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a Normalised spectral density of temperature variability derived from proxy-based temperature reconstructions including Lapland (Norway), Torneträsk (Sweden), Diss Mere (UK), Nautajärvi (Finland), P1003 (Norway), and GISP2 (Greenland). b Normalized spectral density of temperature variability derived from the Holocene reanalysis32 data and transient climate model simulations over Europe (10°W–50°E, 35°N–70°N). c Normalized spectral density of the Atlantic Meridional Overturning Circulation (AMOC) strength at 26°N derived from transient climate model simulations (see Methods). Spectral densities are scaled by the standard deviation of each dataset, and only values exceeding the 99% red-noise significance level are displayed.

Wavelet analysis (see Methods) reveals that most proxy records (Supplementary Fig. 4) exhibit multi-centennial-scale variability (~70–300 years), though its occurrence and intensity vary across records and time periods. Some proxies, such as the one from Lapland (tree-ring width), display more persistent variability, whereas others, like the one from Nautajärvi (lake sediment) and Diss Mere (lake sediment), show more intermittent signals. Wavelet analysis in the Holocene reanalysis and transient simulations over Europe (Supplementary Fig. 5) reveals a similar multi-centennial variability (~70–300 years). Furthermore, significant coherent spectral power is concentrated at multi-decadal to centennial timescales (~60–200 years) across most proxy pairs (Supplementary Fig. 6). At longer periods (>200 years), coherence occurs intermittently and varies among proxy pairs. The reanalysis (Supplementary Fig. 7) and the IPSL-CM6A-LR transient simulations (Supplementary Fig. 8) show patterns broadly consistent with those observed in the proxy records. These results indicate coherent multi-decadal to centennial variability across sites and suggest that the proxy records are primarily linked through common variability at these timescales, supporting the interpretation that they respond to large-scale climate phenomenon during specific Holocene intervals. While the simulations reproduce the timing and dominant spatial scales of common variability reasonably well, the amplitude of coherent variability is generally weaker in the reanalysis than in both the model simulations and the proxy records. When quantified in temperature units, IPSL-CM6A-LR exhibits larger amplitudes than the reanalysis across all regions, with model-to-reanalysis standard deviation ratios of ~4–6 (Supplementary Table S2). In contrast, comparisons between IPSL-CM6A-LR simulations and proxy records yield lower ratios, mostly between ~1 and 4, indicating a more moderate model overestimation relative to proxies. This implies that IPSL-CM6A-LR provides an upper-end estimate of low-frequency temperature variability, rather than a conservative one. Indeed, the Holocene reanalysis itself also shows reduced variability compared to those proxy records (Supplementary Table S2). The reanalysis likely underestimates real variability owing to limitations in spatial coverage, seasonal proxy sensitivities, temporal resolution, covariance-based infilling32, and low signal-to-noise ratios in proxy records36. All those limitations might lead to a damping in the amplitude of the variations in the reanalysis.

Former studies13,37 have suggested that the multi-centennial temperature variability was linked to a low-frequency mode of the AMOC in climate models. Mehling et al.38, for instance, analysed AMOC variability in pre-industrial control simulations (piControl) from nine CMIP6 models and found that six models exhibited a statistically significant mode of multi-centennial variability. Similar multi-centennial variability was also evident in the piControl of the IPSL-CM6A-LR13 and EC-Earth39 climate models, indicating that this mode might be primarily driven by internal dynamics rather than external forcing over the Holocene. Here, we also identify a multi-centennial AMOC variability (~100–200 years) in the transient model simulations since the mid-Holocene (Fig. 2c), with periodicities (Supplementary Fig. 9) similar to those found in European temperature reconstructions (Supplementary Fig. 4) and transient simulations over Europe (Supplementary Fig. 5). Moreover, a wavelet coherence analysis of transient simulations reveals that the AMOC and European temperature are in phase (Supplementary Fig. 10), exhibiting persistent coherence in the multi-centennial variability mode during the last six thousand years. These results reinforce the hypothesis that multi-centennial variability is an inherent feature of the coupled ocean-atmosphere system driven primarily by the AMOC. While there is no consensus yet on a unique forcing mechanism for the internal multi‑centennial AMOC variability, several plausible mechanisms have been proposed in the literature. Those mechanisms are mainly implying either large salinity changes that accumulates in the Arctic or the propagation of salinity anomalies from the southern part of the Atlantic. Indeed, in a pre‑industrial control simulation from the IPSL‑CM6‑LR climate model, a pronounced multi‑centennial AMOC variability emerges, driven by a delayed accumulation and release of freshwater in the Arctic, which modulates surface and subsurface salinity and density, ultimately affecting deep‑water formation in the Labrador and Nordic Seas37. A recent multi‑model study confirms that Arctic-North Atlantic freshwater exchanges and sea‑ice/ocean interactions as a plausible driver across different models for the centennial-scale AMOC variability38. Similarly, in EC‑Earth3 piControl simulation, it has been shown that salinity anomalies from the Arctic, modulated by sea‑ice dynamics, accumulate there and are episodically released into the North Atlantic, altering water‑column stability and deep‑water formation, thereby driving AMOC oscillations on ~100–200 year timescales39. Another study40 using an Earth System of intermediate complexity, also highlights the existence of multi-centennial variability of the AMOC, which they also relate to a linkage between the North Atlantic and the Arctic through changes in Arctic freshwater fluxes (precipitation minus evaporation). Using also EC-Earth, it has been proposed that the salinity‑advection feedbacks for regions south of the subpolar gyre is also contributing to this variability. The mechanism proposed argues that perturbations in salinity gradients between subtropical and subpolar regions can be advected and later damped by mixing/convection, leading to a self‑sustained oscillatory mode41. Such a mechanism, highlighting a propagation of salinity anomalies from the Southern Ocean along the Atlantic until its northern part, was also proposed by ref. 42 and constitute an alternative or complementary mechanism that can explain multi-centennial variability in the North Atlantic.

This AMOC variability might play a crucial role in shaping low-frequency climate fluctuations over Europe. Within available reconstructions over the Holocene, the linkage between AMOC variability and European temperature is supported by significant correlations between AMOC strength and surface temperature (Supplementary Fig. 11) from two reconstructions: temperature from a Holocene reanalysis32 and an AMOC index43 based on multi-proxy North Atlantic sea surface temperature (SST) records44, which are not all used in the reanalysis. This result illustrates, using reconstructions over the Holocene, that AMOC variations exert a pronounced influence on European (in particular over Northern Europe) surface temperatures23, in line with model simulations’ results13 (Supplementary Fig. 11). The impacts of oceanic circulation changes are expected to be most pronounced in this region due to its proximity to the North Atlantic and the large influence of the heat transport from ocean currents in winter13. Given Northern Europe’s high sensitivity to AMOC variability45, the subsequent analysis will focus on this region.

Implications for the attribution of recent climate changes

Over the 1904–1944 period, refs. 1,46 found that long-lived greenhouse gas forcing played only a secondary role in global warming, with internal variability potentially being the primary driver. However, they do not suggest which variability mode is most likely to explain it. The multi-centennial variability highlighted here might also be capable of contributing to this warming phase. There is a cooling between 1940 and 1980, which is often attributed to the dominant influence of anthropogenic aerosols during this period47. Our findings suggest that these changes in external forcings may also co-vary with internal multi-centennial variability. The key aspect in supporting this hypothesis concerns the phase in time of the multi-centennial variability over the instrumental period.

To estimate what is this phase in time of the multi-centennial variability before the instrumental period, we use palaeoclimate reconstructions, which provide a longer-term context to study internal variability at this low-frequency timescale. Among the temperature proxies used in this study, the tree-ring width chronologies that include the Torneträsk record from Sweden48, and the Lapland record from Norway49, provide annually resolved records extending over the recent period. These records capture instrumental-era variability and extend further back in time, offering palaeoclimate evidence of earlier temperature fluctuations (Fig. 3a and Supplementary Fig. 12; see Methods). The temperature reconstruction from the Torneträsk tree-ring width chronology (red line in Fig. 3a) extends back to 7356 years before present (BP), offering palaeoclimate evidence of earlier temperature fluctuations. Those fluctuations in Torneträsk have quite a large amplitude before the industrial period, suggesting that some of the low-frequency variability observed since 1850 are not only due to external forcing, but also to internal variability. To further evaluate this hypothesis and better quantify the potential role of internal variability in recent changes over Northern Europe, we considered the CMIP6 multi-model large ensemble archive, version 2 (MMLEA-V2)50, which provides a valuable resource for assessing internal and forced variability across models over the historical era and beyond. Among the available ensembles, we analysed seven models that offer complete historical simulations since 1850 and a sufficient number of members: CanESM5, CESM2, CNRM-CM6-1, E3SM-2-1, IPSL-CM6A-LR, MIROC6, and MPI-ESM1-2-LR. Spectral analyses of the piControl simulations over Northern Europe (10°W–50°E, 55°N–70°N) show that IPSL-CM6A-LR exhibits pronounced centennial-scale variability, with peaks around 150 and 200 years, consistent with the reanalysis of ref. 32 (Supplementary Fig. 13). Although IPSL-CM6A-LR is not unique in exhibiting multi-centennial variability, it remains among the few models that closely reproduce reanalysis-based spectral features. Specifically, we used the IPSL-CM6A-LR large ensemble of extended historical simulations (IPSL-EHS), which consists of 32 members spanning the period 1850–2059, all sharing the same external forcings but differing in their initial conditions (see Methods).

Fig. 3: Multi-centennial temperature and AMOC variability in observations, proxies, and model simulations.
Fig. 3: Multi-centennial temperature and AMOC variability in observations, proxies, and model simulations.
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a 60-year low-pass filtered temperature anomalies relative to 1900–1997 (common period) from IPSL-EHS members (grey), Temp12k25 reconstruction (red), Hadley centre (HadCRUT5; pink), the Berkeley Earth Surface Temperatures (BEST; orange), and the Dynamically Consistent ENsemble of Temperature (DCENT; darkred) over Torneträsk in Sweden. b Same as (a) but over Northern Europe (10°W–50°E, 55°N–70°N). c same as (a) but for the IPSL-EHS AMOC at 50°N, with the AMOC reconstruction based on EN4 hydrographic data in the subpolar gyre56 (red). The black line represents the forced response (the ensemble mean of all IPSL-EHS members). The model member in blue is the one that aligns more closely with the observation-based estimates (Supplementary Fig. 14). The dashed line (darkblue) stands for the internal variability from the blue member (see Methods).

The IPSL-EHS large ensemble mean (black in Fig. 3) represents the forced signal due to external forcing because the effect of internal variability should average out when considering a sufficiently large number of ensemble members are considered51. This forced signal lacks the amplitude of several low-frequency fluctuations evident in the proxy and instrumental records and does not fully align with either the reconstruction or the observations (Fig. 3). While it is possible that the IPSL model underestimates aerosol radiative forcing13, ref. 52 instead suggests that CMIP6 models, in general, may overestimate aerosol forcing. Therefore, we argue that this discrepancy likely indicates that the observed centennial-scale variations cannot be explained solely by external forcing, but instead reflect an important contribution from internal variability. The internal variability of the real-world climate system can be possibly approached by a few individual simulations within a model ensemble51 if the simulated internal variability is representing reasonably well the real system. We argued before that the IPSL-CM6A-LR model is able to reproduce similar multi-centennial variability observed in a number of Holocene reconstructions over Europe. Within the IPSL-EHS framework, which provides a range of possible climate trajectories (see Methods), member 8 stands out because it exhibits the closest match to temperature observations in Lapland, Torneträsk, and Northern Europe (blue line; see Supplementary Figs. 14, 15 for a comparison of all IPSL-EHS members). It shows a steeper temperature increase over Northern Europe in recent decades (blue line in Fig. 3) compared to the forced signal (black line in Fig. 3a, b). The internal variability component is estimated as the time series of Member 8 with the forced signal, defined as the IPSL-EHS large-ensemble mean, removed (Fig. 3, dashed dark blue line). Comparable estimates of internal variability are obtained when using weighted means of the three top-ranked ensemble members (Supplementary Fig. 16). However, incorporating additional members into the mean does not necessarily provide a more realistic representation of the real world. Indeed, since each ensemble member represents a physically plausible realisation of the climate system, averaging across multiple members tends to reduce internal variability as compared to the externally forced signal. CNRM-CM6-1 also exhibits centennial-scale variability (Supplementary Fig. 13). Its best ensemble member closely reproduces the observed 20th-century temperature evolution over Northern Europe, similarly to IPSL-CM6A-LR (Fig. 3b), including early-century warming, mid-century cooling, and renewed warming after the 1980s (Supplementary Fig. 17).

Table 1 presents warming trends over 2000–2035 (°C dec⁻¹) for Lapland (Norway), Torneträsk (Sweden), Northern Europe, Europe, and the global scale, separating the externally forced signal (estimated by the CMIP6 ensemble) from the internal variability. This variability is estimated as the difference between Member 8 and the IPSL-EHS large ensemble mean and between observations and the CMIP6 ensemble mean. The estimate of the forced signal is actually different here because within the IPSL model “world”, a good estimation of the forced signal is based on the ensemble mean from this model (Fig. 3), while within the real world, a potentially better estimate of the forced signal is the ensemble mean of all the latest model simulations available from CMIP6. The amplitude of the internal variability is constrained by observations through the scaling of this IPSL-based internal variability onto the observed internal variability derived from the Berkeley Earth dataset (estimated as the time series of Berkeley Earth temperatures removed from the forced signal, defined as the CMIP6 ensemble (Supplementary Fig. 18). Over 2000–2035, internal variability contributes to regional warming, with magnitudes ranging from 0.05 to 0.14 °C dec⁻¹ over the regions considered in Table 1. The largest contributions occur over Lapland (0.14 °C dec⁻¹) and Northern Europe (0.11 °C dec⁻¹), highlighting the strong regional imprint of internal variability. When expressed as a percentage increase relative to the forced warming, the contribution of internal variability varies across regions and estimates of external forcing. When using the estimate of the forced signal from CMIP653, internal variability amplifies the forced warming by 15–37%, with the strongest amplification found over Lapland (37%) and Northern Europe (30%). The influence of internal variability over Northern Europe is already evident over 2000-2024 (Supplementary Table S3) and is projected to reach approximately 41% of the forced signal over 2025-2035 (Supplementary Table S4). At the global scale over land, internal variability contributes more modestly (15% over the period 2000–2035), demonstrating that the amplifying effect of internal variability on warming is considerably stronger over Europe than at the global scale.

Table 1 Rates of temperature change (in °C dec⁻¹ and estimated by the slope of a linear regression) over the period 2000–2035 at Lapland (Norway), Torneträsk (Sweden), Northern Europe (10°W–50°E, 55°N–70°N), Europe (10°W–50°E, 35°N–70°N), and the global scale over land
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These findings underscore the importance of considering both forced and internal variability when analysing future climate projections, as the influence of the latter may lead to more pronounced temperature changes than the forced signal would suggest, especially at the continental scale, but potentially even at the global scale (e.g. ref. 13). Evaluating centennial-scale internal variability remains challenging, but combining model simulations, instrumental observations, and Holocene constraints provides a robust framework for quantifying plausible ranges of amplification.

AMOC variability and its impact on climate dynamics

The question of the occurrence of an ongoing weakening of the AMOC since the 1950s, originally suggested by ref. 24, is still highly debated54. More fundamentally, a difficult point to understand is the potential cause of such a weakening. Indeed, an ensemble of climate models suggests that the effect of anthropogenic warming only started to weaken the AMOC in the late 1990s52. It has been suggested that natural AMOC variability might explain the weakening before the 1990s13, but this has not been fully demonstrated up to now. On the contrary, the impact of Greenland meltwater, when correctly accounted for (e.g. ref. 55), is unable to explain this trend starting as early as the 1950s, especially given that the acceleration of Greenland melting started in the 1990s. Thus, while the possibility of an AMOC weakening has now been supported by a number of other indices13, it remains unclear what exactly might have caused it as early as 1950.

Here, thanks to our identification of a multi-centennial variability in the temperature over Northern Europe, which might be closely related to AMOC internal fluctuation, we can try to estimate the phase in time of this multi-centennial variability in the AMOC over the instrumental period using the IPSL-EHS model. Consistent with temperature trends, the internally generated AMOC, in Fig. 3c, from IPSL-EHS member 8 (dashed dark blue line, after removing the forced signal), closely aligns with the Fraser & Cunningham observation-based AMOC reconstruction56 (Fig. 3c), except from 1990 to 2000, where the variations might be notably related to strong positive North Atlantic Oscillation (NAO) in the 1990s57,58, which we argue is of a different origin than the multi-centennial variability. Since 1900, observed and modelled changes in AMOC strength have shown periods of strengthening, which are largely attributable to the system’s intrinsic multi-centennial internal variability rather than solely to persistent external anthropogenic forcings59,60. The apparent agreement does not imply that internal variability alone explains the reconstruction, but rather that the amplitude and phase of the internal component in the model can strongly project onto the total (forced + internal) signal seen in observations. Indeed, ref. 57 shows that the total AMOC variations over 1960-2020 cannot be explained by external forcing alone, as the residual internal variability contributes substantially. For example, they found that half of the AMOC increase from 1960 to 1990 and much of the continued increase until 2000 were driven by internal variability, which also partly offsets the externally forced weakening after 2000. This highlights that reconstructions of the full AMOC signal inevitably reflect a combination of both forced and internal components, and the fact that our modelled internal variability aligns with the reconstructed AMOC underscores the large role of the internal component in shaping the observed record.

The phase in time of this internal mode is crucial. It highlights an initial AMOC increase during the early 20th century, followed by a weakening trend in the latter half, and a subsequent recovery since the 21st century. The effect of this internal variability allows explaining the reconstructed AMOC weakening observed in the second half of the 20th century, as highlighted by ref. 24. Furthermore, it helps to explain why recent direct observations do not show significant weakening, even though the forced signal from external forcing now clearly indicates a weakening trend. This interpretation is consistent with other studies, such as ref. 57, who linked the apparent stability of recent AMOC observations to the influence of a prolonged positive phase of the NAO, itself reflecting internal multi-decadal variability in the North Atlantic system. The interplay between forced and multi-centennial variability suggests a compensatory effect or destructive interference between this internal variability mode and the forced response during the beginning of the 21st century, likely leading to the very weak trend in the observations. Moreover, the phasing of the internal variability of the AMOC can also explain the warming over Europe during the early 20th century, its subsequent pause in the second part of the century and the rapid acceleration observed since the early 21st century.

To conclude, our study shows that the presence of multi-centennial internal variability in several CMIP6 models13,61,62 is confirmed by a number of palaeoclimate data since the mid-Holocene. The existence of such an internal mode of variability is able to explain a number of mismatches between the CMIP6 models ensemble mean and the observations (Fig. 1), suggesting that they can be largely responding to this internal mode of variability. This idea has a strong implication concerning the use of observational constraints based on recent trend and especially on the way internal variability is estimated (e.g. ref. 62). While there is no doubt that global warming is primarily caused by the increase in anthropogenic greenhouse gas emissions, quantifying precisely forced changes at the European scale is much more challenging, and future projections carry significant uncertainty, that can be largely driven by internal variability. In this context, our contribution is to bridge the gap between palaeoclimate and model-based perspectives at the European scale, using available high-resolution proxy records and an observational-constraint framework. This provides an independent line of evidence that multi-centennial internal variability is amplifying the recent and near-term future European warming signal. The existence and current phase of this variability mode are therefore crucial and should be considered systematically to provide more reliable information for future climate projections, particularly when discussing adaptation strategies for the coming multi-decadal timescale.

Methods

Proxy records

The temperature proxy-based reconstructions used in this study are sourced from the “Temperature 12k Database” (Temp12k) compiled by ref. 25 and recently developed Bayesian-based temperature reconstructions from varved European lake sediments produced by our research group31 (SCUBIDO reconstructions hereafter). The criteria for selecting the proxy records included in this study were based on the quality of their chronologies and the temporal resolution of the proxy reconstructions over the past 6000 years within the domain (40°W–50°E, 35°N–75°N). We selected records based on annual-layer counts (e.g. tree-rings, varved sediments) and quantitative temperature reconstructions with resolutions ranging from yearly to ~20 years. Applying these criteria to the Temperature 12k database and SCUBIDO reconstructions, we identified six temperature-sensitive proxy records (listed in Table 2). In the case of the Bayesian-based reconstruction, the quantification of the proxy data in degrees Celsius is based on a calibration period of instrumental climate data and overlapping X-ray fluorescence data (i.e. chemical element composition of the sediments) to learn about the direct relationship between each geochemical element and the covariant response between the elements and climate. The understanding of these relationships is then applied down core to transform the semi-quantitative proxy data into a posterior distribution of palaeoclimate with quantified uncertainties31.

Table 2 The distribution of the different types of proxy records represented by the proxy data
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It should be noted that the Scandinavian proxies (from tree-ring width and stable isotopes), primarily reflect summer season conditions and reconstruct summer temperatures. As a result, discrepancies may arise between the proxy data and model simulations, as the latter represent annual, rather than seasonal, temperature averages, potentially leading to differences in the amplitude of variability. Furthermore, when evaluating the phase of the main variability mode with respect to recent time, some challenges have emerged. Specifically, some records exhibited a notable loss of variance in recent centuries or contained a substantial number of missing data points approaching the present day. The loss of variance may arise from several factors, including inherent proxy limitations, as proxies often respond nonlinearly to environmental variables. The loss of variance, in Diss Mere, for instance, is due to the transition from annually laminated sediments to homogenous sediments with a higher sedimentation rate31. Consequently, we decided to focus on the Lapland and Torneträsk records, as they demonstrated both well-preserved variance over the recent period and minimal missing data.

In this study, age uncertainty is not expected to be a significant issue, as the proxy records are annually resolved and based on annually constrained chronologies (tree-rings and varved sediments). The reported age uncertainty primarily arises from cumulative counting errors and from uncertainties associated with other dating methods (e.g. radiocarbon or tephrochronology), when annual-layer chronologies are anchored to such dates. This uncertainty mainly affects the absolute age of a record or the dating of a specific event (e.g. a climate event occurring at 4.2 ± 0.3 kyr BP). Counting errors are typically quantified as the standard deviation among independent counts of annual layers (for example, in varve chronologies, at least three separate counts are commonly performed31. The annual resolution of these chronologies allows us to perform time series analyses without temporal uncertainty affecting the periodicities themselves. However, age uncertainty may slightly influence the absolute placement of these periodicities along the timescale. The only exception is the marine record included in this study, which has a temporal resolution of ~12 years according to its chronology. While this may introduce an uncertainty of ±12 years (on average)63 in the identified periodicities, such an error is negligible when considering variability at multi-centennial timescales.

Holocene simulations

To examine multi-centennial variability in climate models and allow a proper comparison with proxy data (contrary to e.g. pre-industrial simulations), we used temperature data from transient Holocene simulations that have been performed using six models (Table 3). These simulations incorporate evolving forcing conditions, such as varying greenhouse gas concentrations, solar irradiance, and orbital parameters, based on reconstructions from other studies. The minimum protocol for these simulations was provided by ref. 27 for insolation and trace gases. The other boundary conditions are left to the different groups, since their implementation depends on model complexity and they have large uncertainties that need to be accounted for.

Table 3 The six transient simulations used in the analysis
Full size table

We consider two simulations of the IPSL Earth System model. The first one, called IPSL-CM5 in this study, is run with the IPSL-CM5A model version used for the CMIP5 ensemble of past, present and future simulations64. The second simulation (called IPSL-CM6V in this study), is run with the IPSL-CM6A-LR model version used for the CMIP6 ensemble, but with the dynamical vegetation switch on and a different parameterisation of bare soil evaporation, revisited parameters for photosynthesis and boreal forest regeneration65. All the transient model simulations include interactive carbon cycles. They also all, except IPSL-CM566, include dynamic vegetation67,68 allowing them to simulate vegetation changes.

Holocene reanalysis

We utilise a reanalysis32 covering the whole Holocene to allow a comparison with proxy-based reconstructions and climate model simulations. Erb et al.32 used palaeoclimate data assimilation to reconstruct a comprehensive temperature record for the past 12,000 years. This reconstruction combines data from the Temperature 12k database with outputs from transient climate models. The data assimilation process begins by averaging outputs from the HadCM3 and TraCE-21ka simulations to a decadal resolution, which are then combined to form a multi-model ensemble prior. This prior provides an initial estimate of the climate state that is subsequently updated using a Bayesian approach, incorporating proxy information and its associated uncertainties. The result is a probabilistic estimate of the true climate state, referred to as the posterior.

Observational data

To consider the uncertainty in observations for the historical period, we used three datasets of observed monthly anomalies: (1) The Dynamically Consistent ENsemble of Temperature (DCENT), built by combining the NOAA GHCN v4 database for land (meteorological stations), and the ERSST v5 for ocean areas69; (2) Berkeley Earth Surface Temperatures (Berkeley), a gridded reconstruction of land surface air temperature records spanning 1850-present, obtained by combining the land air temperature with the HadSST3 sea surface temperature reconstruction70; and (3) Hadley Centre/Climatic Research Unit Temperature 5.0 (HadCRUT5), a global temperature dataset, obtained by merging the CRUTEM4 and HadSST3 for the land and ocean, respectively71.

AMOC reconstructions

We analyse two AMOC reconstructions: a paleo-data-based record spanning 2000–10,000 years BP43, and a recent in situ oceanographic reconstruction covering the period 1900–2019 CE56. Ayache et al.43 reconstructed AMOC variability based on a compilation of paleo-ocean SST data (HAMOC database)44, which are not yet included in the Temp12k database. Ayache et al.43 reconstructed AMOC variability with a temporal resolution of ~50 years, which might be hardly sufficient to fully study multi-centennial-scale variability. However, this is the highest-resolution AMOC reconstruction that is available to our knowledge. The study be ref. 56 presents a time series of AMOC strength over the past 120 years with an annual resolution, derived from observational data utilising the Bernoulli inverse method applied to hydrographic data, the authors reconstruct the general geostrophic circulation in the North Atlantic without relying on sea surface height information.

IPSL-CM6A-LR EHS

The Institut Pierre-Simon Laplace Climate Modelling Center has produced an ensemble of extended historical simulations72 using the IPSL-CM6A-LR climate model. This ensemble (referred to as IPSL-EHS) is composed of 32 members over the 1850–2059 period that share the same external forcings but differ in their initial conditions. In this study, we assess the air temperature and the AMOC simulations. The IPSL-CM6A-LR adheres to the CMIP6 protocol for historical simulations, covering the period 1850–2014. Initial conditions for these simulations were derived from various years of a long pre-industrial control simulation (piControl) that had reached a quasi-stationary state. Beyond 2014, the simulations were extended to 2059 under the SSP245 scenario, with all forcings included except for the ozone field, which was held constant at its 2014 climatology due to the unavailability of updated ozone forcing at the time.

Spectral analysis

The approach chosen to quantitatively assess the variability in climate time series from both proxies and models is spectral analysis. The goal of this analysis is to examine multi-centennial-scale variability, which requires filtering out high-frequency noise to ensure meaningful results. All records and model time series were interpolated to match the decadal resolution of reanalysis data using a univariate Akima interpolation method73 (Supplementary Figs. 19 and 20 for examples with proxy and model temperatures over Europe). By interpolating the data, a uniform and regular temporal resolution is established across all records, allowing for effective removal of high-frequency noise prior to spectral analysis. For this study, a low-pass Butterworth filter is applied, following the approach of ref. 74, as it provides an optimal balance between signal attenuation and phase response. It internally handles the treatment of the series edges by subtracting the mean of the input series and then padding the data at both ends by reflection to a length of twice the maximum. This reflection padding is designed to minimise edge effects and avoid artifacts that would arise from simpler approaches such as zero-padding. After filtering, the function removes the padding and adds back the series mean. The filter is configured with a 60-year cut-off frequency, following ref. 11. This approach preserves the upper part of the multi-decadal range and provides more detail in the centennial spectrum. Additionally, the time series were linearly detrended after interpolation and filtering.

Once the data were processed, spectral and wavelet analysis are conducted to identify cyclical patterns33. Spectral analysis examines the distribution of power or density across frequencies in a time series, allowing the detection of periodicities caused by cyclic or recurring processes. Spectral analysis was conducted using the ‘REDFIT’ programme33,75. To determine the significance of spectral peaks against red noise, the analysis compares the spectral density to the upper band of the 99th percentile of the χ2 distribution for red noise. Peaks exceeding this threshold are considered significant with 99% single-frequency false-alarm (e.g. ref. 76), indicating the presence of a meaningful cycle at that frequency. The spectrum values were normalised by dividing them by their standard deviation, thereby standardising variability across the data and making the results more interpretable and comparable.

The complex Morlet wavelet was chosen as the mother wavelet for the continuous wavelet transform of the time series. This wavelet is particularly well suited for analysing environmental signals due to its optimal balance between time and frequency resolution. To assess the significance of the wavelet spectra, a first-order autoregressive process (red noise) was used as the background spectrum with a 99% significance level applied against this background.

Simulated AMOC index

The AMOC strength is measured by the annual maximum of the overturning stream function below 500 m in the North Atlantic at 26°N from the transient simulations except EC-Earth, where it was obtained from ref. 77 at 30°N. For consistency with the AMOC reconstructions56 used in Fig. 3, AMOC was also computed at 50°N from the IPSL-EHS ensemble members.

Statistical information

The median of the boxplots is presented. Boxplots edges give the first and third quartiles. Boxplot “whiskers” give the full range, including outliers. Correlation is tested using a Student t-test for correlation, with correction in the degrees of freedom using time series autocorrelation78.

Constrained internal variability

The amplitude ratio in Table 1 is calculated over the 1930–2023 period as follows:

$$ {{\mathrm{Amplitude}}}\,{{\mathrm{ratio}}}=\\ \left(\frac{\sigma \left({{\mathrm{Berkeley}}}\,{{\mathrm{observations}}}-{{\mathrm{Forced}}}\left({{\mathrm{CMIP}}}6\,{{\mathrm{ensemble}}}\,{{\mathrm{mean}}}\right)\right)}{\sigma \left(\right.{{\mathrm{Member}}}\,8-{{\mathrm{Forced}}}({{\mathrm{IPSL}}}\,{{\mathrm{large}}}\,{{\mathrm{ensemble}}}\,{{\mathrm{mean}}})}\right)$$
(1)

where σ stands for standard deviation.

The contribution of internal variability to forced warming (\({R}_{{{\mathrm{forced}}}}\)) is expressed as:

$${{\mathrm{Increase}}}\,{{\mathrm{in}}}\,{{\mathrm{forced}}}\,{{\mathrm{warming}}}\,{{\mathrm{due}}}\,{{\mathrm{to}}}\,{{\mathrm{internal}}}\,{{\mathrm{variability}}}=\left(\frac{{R}_{{{\mathrm{int }}},{{\mathrm{constrained}}}}}{{R}_{{{\mathrm{forced}}}}}\right) \times 100$$
(2)

where:

Rint, Member 8 is the internal rate of temperature increase from Member 8;

\({R}_{{{\mathrm{forced}}}}\) i is the forced rate of temperature increase (CMIP6 ensemble mean); and

Rint, constrained is the internal rate of temperature increase constrained by observations, which accounts for potential overestimation or underestimation of the centennial-scale internal variability amplitude in the model compared to observations, estimated as follows:

Rint, constrained = Rint, Member 8 × amplitude ratio.