https://orcid.org/0009-0007-5166-4850
Figures
Abstract
The upward trend of observed global surface air temperature anomalies exhibits a well-known multidecadal undulation, largely muted in the state-of-the-art climate models. We provide a comprehensive spatiotemporal description of these differences in the estimated unforced residuals representing the internal climate variability between a multi-model ensemble of historical simulations and two different reanalysis data sets, using optimal filtering. The signal identification was carried out within a limited set of observed and model simulated Northern Hemisphere’s climate indices, but full two-dimensional spatial patterns of this signal, in the global gridded surface air temperature (SAT) and sea-level pressure (SLP) fields were also obtained. We then compared the magnitudes, spatial patterns, and characteristic time scales of the observed and simulated dominant low-frequency variability so defined. The observed variability is characterized by a hemispheric-to-global scale multidecadal signal exhibiting coherent anomalies over the North Atlantic, North Pacific and Southern Oceans. The simulated signals have time scales similar to observed, but different spatial patterns, and are weaker, with substantial sampling variability between different models and between simulations of each individual model. Few outlier models produce multidecadal signals with magnitudes comparable or exceeding those observed yet with vastly different spatial patterns dominated by the North Atlantic SAT variations. In the ensemble average, the simulated SLP pattern is negatively correlated with the observed pattern, which hints at root cause of the observed vs. simulated multidecadal-signal differences, with the former likely reflecting internal ocean dynamics and the latter largely consistent with the ultra-low-frequency atmospheric noise.
Citation: Westgate A, Kravtsov S (2025) Comparison of multidecadal variability in climate reanalyses and global models. PLOS Clim 4(10): e0000519. https://doi.org/10.1371/journal.pclm.0000519
Editor: Valerio Lembo,, CNR: Consiglio Nazionale delle Ricerche, ITALY
Received: July 23, 2024; Accepted: September 10, 2025; Published: October 7, 2025
Copyright: © 2025 Westgate, Kravtsov. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data and scripts are publically accessible through figshare. The following are the links to the data files and scripts. Data Link: dx.doi.org/10.6084/m9.figshare.27859269 Script Link: dx.doi.org/10.6084/m9.figshare.27871488 Figure Link: dx.doi.org/10.6084/m9.figshare.27868437.
Funding: The author(s) received no specific funding for this work.
Competing interests: The authors have declared that no competing interests exist.
Introduction
In addition to the striking positive trend in global surface air temperature (SAT) anomalies across the globe due to anthropogenic forcings, there exist naturally occurring, spatially non-uniform, coherent oscillatory-like fluctuations not only in SAT but also in sea level pressure (SLP). These climate modes can have time scales from a few years to several decades, with the latter representing the decadal climate variability [DCV: 1–4]. The DCV modes exhibit teleconnections on a range of spatial scales too, thus greatly affecting global weather and climate. Many studies have been published detailing regional manifestations of DCV in SAT, such as the Atlantic Multidecadal Oscillation [AMO: 5,6], the Pacific Multidecadal Oscillation [PMO: 7], and, possibly connected to these modes signatures of DCV in the North Atlantic Oscillation [NAO: [8,9], and the Aleutian Low Pressure [ALPI: 10] SLP indices. A northern-hemispheric version of the AMO and PMO indices is referred to as NMO index [7].
Many climate simulations included in the Coupled Model Intercomparison Project, Phases 5 [CMIP5: 11] and 6 [CMIP6: 12] have been successful in replicating patterns of some of the key regional modes mentioned above in their historical simulations [13]. Historical simulations produced by these models are representations of the twentieth century climate; they are driven by the observed time series of natural and anthropogenic external forcings, with the former including solar and volcanic processes and the latter emissions from human activity. By contrast, the external forcings in preindustrial control runs of these models are held constant so that these simulations only include internal variability by construction; they are also used to generate the initial conditions for the historical simulations.
Hence, the mixture of the forced signal (response of the climate to variable external forcing) and the internal variability in historical simulations is further complicating the analysis of DCV there, due to the presence of the DCV components in both. Using many historical simulations from a single model whose runs are started from statistically independent initial conditions allows one to isolate this model’s forced signal [14,15]. In particular, averaging these simulations across the ensemble members tends to zero out the internal variability, leaving behind the forced signal. Estimating forced signals from multiple climate models with different physical parameterizations in this way also provides an estimate of the forced-signal uncertainty.
With only one “realization” of the observed climate evolution available, the forced signal component of this evolution cannot easily be estimated through ensemble averaging, and one has no other choice than to use climate models to do so, by either utilizing model estimated forced signals directly or using them to develop statistical techniques to optimally infer the forced signal from a single climate realization [16–18]. One way of coming up with the most likely estimate of the forced signal would be based on computing a multi-model ensemble mean of simulated forced signals [e.g., 19]. By contrast, single-model ensemble means from different models [15] produce multiple forced signal estimates, whose spread represents model uncertainty of these estimates. In either case, each model’s estimate of the forced signal (perhaps additionally rescaled using linear regression to best match a given historical time series [7]) can then be subtracted from the observed (or simulated) climate data to obtain multiple approximations of the observed or simulated internal variability; this is the methodology we will use in this study (see section 2 for further details).
Through various methods of isolating the internal variability, numerous studies have analyzed the influence regional internal climatic dynamics can have on the global temperature trend [see, for example, 20]. A particular issue discussed extensively is whether the internal variability is a contributing factor to the global warming “hiatus” periods [21,22]. Some have speculated that such hiatuses may be caused by basin-specific internal dynamics, such as the Interdecadal Pacific Oscillation [IPO: 19, 23], while others have speculated it is the result of the variability in the global ocean heat uptake [24,25] or a top-of-the-atmosphere energy imbalance [26].
Many of these studies further compared observed internal variability with that found in CMIP5 or CMIP6 simulations. Consistently, a weaker-than observed DCV variability and teleconnections [15,21,27–32] diagnosed in the differences between historical model simulations and reanalysis-based gridded proxies of climatic time series include distinctive twentieth century climate features, such as the global warming hiatus [33,34]. These differences may in part be due to model deficiencies in representing the processes dependent on internal ocean dynamics [15,19–23,27,32,35,36], such as those that drive the IPO. Kravtsov et al. (2018) argued that such differences in gridded SAT time series at multidecadal time scales — rather than being a global manifestation of regional climate modes — have a truly global character and can be succinctly described in terms of an oscillatory-looking signal of a fixed temporal undulation but a different phase in different geographical locations; they referred to this signal as the global stadium wave [GSW: 37, 38], which, they argued, dominates the observed internal multidecadal variability. This DCV structure — when decomposed into regional contributions — is characterized by globally connected patterns [39], which prompts an alternative explanation of this variability as the one associated itself with the climate system’s forced response, rather than with its internal dynamics [e.g., 40]. However, no matter what its source is, state-of-the-art climate models seem to underestimate the amplitude of this DCV variability and misrepresent its regional patterns and global teleconnections [15,27,36,41–44]. Kravtsov (2017) found that the SLP component of the multidecadal signal found in the observed NAO index is essentially non-existent in its simulated counterpart, suggesting that the multidecadal discrepancies between observations and climate model simulations lie in weaker or distorted atmospheric teleconnections. In a mechanistic study utilizing observed and CMIP simulated climate data, Kravtsov (2020) further attributed these discrepancies to a higher level of interaction between the deep ocean and surface processes in the reanalysis data, leading in turn to a lack of substantial atmospheric response to the weaker-than-observed ocean-induced sea-surface temperature (SST) anomalies in climate models.
Leaning on these earlier findings, we seek to extend the Kravtsov et al.’s GSW analysis [15,27,36] to the newest reanalysis datasets: NOAA’s Twentieth Century Reanalysis Version 3 [20CRv3: 45] and the European Centre for Medium-Range Weather Forecasts (ECMWF) twentieth century reanalysis [ERA-20C: 46]. Further, in addition to the CMIP5, the present analysis will also include members of the newest generation of climate models, CMIP6, and will be consistently applied to the combination of SAT and SLP data. Although the forced-signal removal and multidecadal filtering methodologies we employ here are the same as in our previous work, the novel focus of the analysis here is on systematic comparison of the time scales, magnitudes, and spatial patterns of these — observed and simulated — dominant multidecadal signals through principal component analysis [PCA: 47]. We thus provide, in a novel and systematic way, a comprehensive spatiotemporal description of the differences between the observed and model simulated multidecadal variability over the historical period, which is suggestive of dynamical causes underlying these discrepancies. In further presentation, the data and methods are described in detail in the Data and methods section, the Results section discusses the results, while the Summary and conclusion section provides a summary, conclusions, and our future plans regarding this line of research inquiry into multidecadal climate variability.
Data and methods
Data
We analyzed the annual-mean SAT and SLP time series based on 20CRv2c, 20CRv3, and ERA-20C reanalysis datasets (with the exception of the SLP regional indices based on monthly data; see Estimation of forced signal and internal variability section). However, we only discuss here the results from the latter two products; the 20CRv2c results (not shown) are qualitatively similar to those in 20CRv3 but are characterized by spurious multidecadal trends in some high-latitude regions and some other regions over land [cf. 36]. Both the 20CRv3 and ERA-20C datasets generate first-guess fields with monthly SST and sea-ice concentration data from HadISST2 [48] and are based on atmospheric general circulation models (AGCMs), with the National Centers for Environmental Prediction’s General Forecasting System (GFS) for 20CRv3 and the European Centre for Medium-Range Weather Forecasts’ Integrated Forecasting System (IFS cy38r1) for ERA-20C. Key limitations of both are that each exclusively assimilate surface observations, with pressure data coming from the International Surface Pressure Databank, and use AGCMs that neglect human-induced changes like land use and irrigation [49].
Some key distinctions between the two reanalysis datasets are 1) 20CRv3 possessing a 80-member ensemble relative to ERA-20C being deterministic, 2) the IFS used for the ERA-20C contains a higher spatial and temporal resolution than the GFS used for the 20CRv3, 3) ERA-20C assimilates surface winds in addition to SLP, which is assimilated in both datasets, and 4) 20CRv3 dataset utilizes the Ensemble Kalman Filter data assimilation system [50] to generate first-guess fields while ERA-20C utilizes a 24-hour four-dimensional variational [4D-Var: 51].
In general, the errors, particularly due to a decreased number of observations assimilated to generate these reanalyses, pre-1950 fall within the spread of uncertainty of realizations for 20CRv3. However, errors increase as one moves back in time in the dataset [52] due to the spatially heterogeneous coverage of assimilated data, as well as uncertainties in the SST/sea ice fields, which are also strongly extrapolated during early periods or in remote high-latitude regions. ERA-20C has a temporally consistent cold bias [46], weakening SLP trend over the Arctic [53], and weak interannual midlatitude flow, which connects the Pacific climate indices to the Atlantic’s [54]. However, despite these known biases, our results, evaluated on multidecadal timescales, are consistent between both reanalyses (see Results section). The historical model simulations we used alongside the reanalysis data are listed in Table 1 and Table 2 for CMIP5 and CMIP6 multi-model ensembles, respectively. We only used the first ten ensemble members from the individual-model ensembles that contained more than ten runs (such as, for example, the EC-Earth3 model) to prevent those models from dominating any ensemble-based estimates. We found that three of the CMIP6 models, namely EC_Earth3, EC-Earth3-Veg [55], and CNRM-CM6-1 [56], are characterized by a relatively large multidecadal SAT variability, i.e., a longer period and larger magnitude, predominantly in the North Atlantic region; these models, highlighted in Table 2, are hereafter referred to as the outlier models. These outlier models are the same as those whose Atlantic Meridional Overturning Circulation (AMOC) variability have a period of approximately 150 years, much larger than CMIP5 and nonoutlier CMIP6 members [57–59]. In EC-Earth3 models, Arctic salinity anomalies released into the northern Atlantic regions seem to be at the heart of the resulting centennial-scale variability [58, see their Fig 11]. These salinity anomalies are driven by sea ice formation and melting due to the strengthening and weakening of AMOC [59]. Interestingly, similarly driven — albeit weaker — AMOC variability is also a feature of the IPSL-CM6A-LR model [60,61]; this model is not included in our outlier model group.
Time series of SAT and SLP based climate indices (see text for details). a) AMO; b) PMO; c) NMO; d) NAO; and e) ALPI. Red curves show raw annual ensemble-mean time series from the 20CRv3 reanalysis. Light gray curves show rescaled forced-signal estimates from the 17 CMIP5 models considered; their average is shown in black.
M-SSA spectra of internal variability — that is, variances of M-SSA modes ranked in the order of decreasing variance — from (a, b) 20CRv3 and (c, d) ERA-20C reanalysis (blue) and (a, c) CMIP5 and (b, d) nonoutlier CMIP6 simulations (red). Green bars show variances associated with projections of CMIP5 simulated internal variability onto the 20CRv3-based space-time EOFs. Error bars represent the 25th and 75th percentiles about the ensemble mean for each ensemble of spectral estimates shown.
Same as Fig 2, but for CMIP6 outlier runs. Observed internal variability is still based on all 21 forced signal estimates from CMIP6 members, not solely the outlier models.
Observed reconstructed components for a) 20CRv3 (based on rescaled CMIP5 forced signals); b) ERA20c (based on rescaled CMIP5 forced signals); c) 20CRv3 (based on rescaled CMIP6 forced signals); and d) ERA20c (based on rescaled CMIP6 forced signals). For visual convenience, the indices are normalized to unit standard deviation and offset by 2 in the vertical to avoid overlap and the NAO and ALPI indices have been inverted. The error bars show the standard spread of the multidecadal signal across its entire set of estimates associated with all available combinations of multiple reanalysis samples and CMIP estimated forced signals.
Taylor diagrams comparing the observed (crosses) and model simulated (circles) multidecadal patterns in the effective space of climate indices. Taylor diagrams are plotted in polar coordinates. The distance from the origin indicates the pattern’s standard deviation (denoted by the dotted arches radiating away from the origin, labeled by the axes) and the cosine of the angle between the diagrams’ horizontal axis and a ray emanating from the origin and passing through the point associated with this pattern gives the value of the spatial correlation between this pattern and the reference pattern (these dotted rays emanating from the origin are labeled with magenta numbers, spanning from a correlation of 0 to 1). The reference pattern (positioned at (0,1) is denoted by the large dot. The distance of each estimate or model run from the reference pattern measures the dissimilarity between the two (RMSE, denoted by the half circles radiating from the reference pattern dot). The results are shown for: CMIP5 runs in the first row (a, b); CMIP6 nonoutliers in the second row (c, d); 20CRv3 in the first column (a, c); and ERA20c in the second column (b, d). The reference patterns are computed as the ensemble-mean reanalysis patterns in each case.
Same as in Fig 5, but only including CMIP6 outlier runs.
Same as in Fig 5, but with the multi-model ensemble-mean reference pattern.
Same as in Fig 6 (for outlier runs), but with the outlier runs’ multi-model ensemble mean as the reference pattern.
Regression of SAT (°C) on the leading PC of five M-SSA filtered climate indices of SAT (°C). (Please note that, despite not being the leading EOF, they are referred to as such in the figure titles for brevity). The EOF patterns were computed by regressing the time series of the estimated SAT internal variability at each grid node onto the normalized leading PC of the corresponding M-SSA filtered set of the internal variability in the five climate indices considered (section 2.4). Color shading represents the ensemble-mean EOF pattern based on (a) 20CRv3; (b) ERA-20C; (c) CMIP5; and (d) nonoutlier CMIP6 based internal variability estimates. In (a), stippling indicates grid nodes where at least 95% (out of 80x17=1360) of the 20CRv3 ensemble members have the pattern of the same sign; in (b) stippling marks the regions over which at least 13 out of 17 ERA20c based patterns have the same sign at a given grid node, which corresponds to the 95th percentile of the binomial distribution with p=0.5 and N=17, in (c, d) stippling has been changed to represent grid nodes where at least 80% of the ensemble of patterns have the same sign. Coastline data were obtained and plotted using The MathWorks, Inc.’s Mapping Toolbox.
Same as Fig 9, but for SLP. Coastline data were obtained and plotted using The MathWorks, Inc.’s Mapping Toolbox.
Note that not all models in Table 1 and Table 2, even those from different modeling groups, are entirely independent in terms of their physical parameterizations. Models stemming from the same “family” often produce similar climate characteristics, thus reducing the effective number of ‘dynamical’ degrees of freedom in multi-model ensembles [62]. Our subsample of 17 CMIP5 models stems from 8 parent atmospheric models, while the subsample of 21 CMIP6 models stems from 7 parent atmospheric models.
Prior to further analysis, all (annual SAT and SLP) data were interpolated onto a regular 2.5°x2.5° longitude/latitude grid, restricted to the 1880–2005 range (1900–2005 range for ERA20C data) and smoothed with the 11-year boxcar running-mean filter to focus on multidecadal variability. The smoothing aids in the isolation of the multidecadal signal, as it does not greatly affect the reanalysis results, but aids in the removal of the El Nino-Southern Oscillation (ENSO) signal in some of the models with an excessively strong ENSO signal. When comparing the results from model simulations and reanalysis products, we adjusted the temporal range of the model data to fit that of the corresponding reanalysis dataset.
Estimation of forced signal and internal variability
To estimate the forced signal contained within the CMIP simulated data, single-model ensemble-mean time series were calculated with the annual-mean SAT and wintertime-mean SLP smoothed annually sampled data [15], resulting in 17 estimates for CMIP5 and 21 estimates for CMIP6, as per the number of models we considered in each data stream. There are more complex (and slightly more accurate) ways to isolate the forced signal, such as Multi-channel Singular Spectrum Analysis (see Multichannel Singular Spectrum Analysis (M-SSA) filtering section) based Wiener filtering [36] and signal-to-noise maximizing pattern [18,63], which Kravtsov et al. (2025) used to obtain, essentially, the same global signal isolated here [e.g., 27,36,65].
To find the internal variability, the forced signals so estimated were subtracted from each of the SAT/SLP historical simulations of the corresponding model. For reanalysis data, the internal variability at each grid point was estimated as the residual of the linear regression of the SAT/SLP reanalysis data onto the above CMIP-based estimates of the forced signal. Note that the number of the estimates of internal variability in the CMIP sub-ensemble considered here is equal to the number of individual simulations in this sub-ensemble (see Table 1). For reanalysis data sets, however, the number of estimates of internal variability is the product of the number of models considered (17 + 21 = 38) and the number of ensemble members in the reanalyses (80 for 20CRv3 and 1 for ERA-20C); the spread between these estimates represents a combination of the forced-signal estimation and reanalysis uncertainty.
To increase the signal-to-noise ratio, we ran the statistical pattern-based identification of the dominant internal multidecadal variability (see Multichannel Singular Spectrum Analysis (M-SSA) filtering section) in the subset of five regional climate indices in the Northern Hemisphere [cf. 27], thus reducing the effective dimension from about ten thousand grid points to these five indices to achieve a higher statistical significance. The internal variability in these widely used indices (emphasizing centers of action of multidecadal variability in the Northern Hemisphere) was estimated through the application of the same methods used when analyzing the data on a spatial grid covering the globe, but to the collection of five indices (and, thus, to the spatiotemporal data with a much reduced “spatial” dimension): the AMO, PMO, NMO, the NAO, and the ALPI (see Introduction section). The selection of the regions these indices characterize avoids many of the historically data-sparse regions of the globe, primarily located in the Southern Hemisphere (see [39], their Fig 1), thereby avoiding any potential spurious biases in our further pattern-recognition based analysis.
The AMO, PMO, and NMO indices are defined as the area-averaged SAT anomalies over their respective regions, more specifically, from 0°N–60°N, 80°W–0° and 0°N–60°N, 120°E–100°W regions for the AMO and PMO, respectively, excluding land. The NMO was defined by 0°N–60°N at all longitudes, including land data. The NAO and ALPI SLP-based indices are defined as the leading principal components (PCs) of the monthly cold season (DJFM) SLP time series over the 15°N–75°N, 90°W–10°W (North Atlantic) and 15°N–75°N, 130°E–120°W (North Pacific) regions, respectively. These monthly PCs were normalized to unit standard deviation and then time-averaged to obtain one value per year to form the annual versions of these indices. The signs of these PCs were chosen to correspond to the NAO+ and ALPI+ loading patterns. The NAO+ pattern has positive SLP anomalies over the midlatitude North Atlantic region and negative anomalies further north; the ALPI+ pattern is a monopolar pattern with negative SLP anomalies over the North Pacific region.
Fig 1 shows the 17 forced-signal estimates of the five climate indices derived from the individual CMIP5 single-model ensembles and rescaled using linear regression [7] to best match the (ensemble-mean 20CRv3-reanalysis-based) version of each index (thick red curves). These rescaled model-based forced signals are the ones that are subtracted from the reanalysis indices to define the observed internal variability in these indices. Thus, using multiple forced signal estimates not only provides a range of internal variability estimates in observed indices, but also allows one to gauge the associated model (forced-signal estimation) uncertainty.
In further analysis, we will first obtain the objectively filtered versions of the observed and model-simulated 5-index time series of the estimated internal variability that represent the dominant multidecadal variability in each data set (Multichannel Singular Spectrum Analysis (M-SSA) section) and then run an additional analysis to further reduce it to just one time series and one pattern (the latter pattern obtained by regression of the index-based or gridded internal variability on this time series), in either the ‘space’ of five climate indices or that of full gridded two-dimensional SAT and SLP fields (EOF analysis of M-SSA-filtered low-frequency signals section). We will then compare the typical time scales, magnitudes, and patterns of the observed and model simulated variability characterized in this way.
Multichannel Singular Spectrum Analysis (M-SSA) filtering
The key element of our methodology is objective filtering of the multi-variate five-index time series of the reanalysis based and CMIP simulated internal variability, as defined in the Estimation of forced signal and internal variability section, via the Multi-channel Singular Spectrum Analysis [M-SSA: 66]. M-SSA is a version of the standard PCA; this procedure is also known as the Empirical Orthogonal Function, or EOF analysis, applied to an extended data set comprised of the original data matrix and lagged copies thereof, up to a maximum lag M, referred to as the embedding dimension. Due to the inclusion of the time-lagged information, M-SSA isolates the dominant low-frequency behavior more efficiently than the EOF analysis, which maximizes the zero-lag variances irrespective of the time scales associated with each EOF pattern and tends to identify mixtures of low-frequency modes with higher-frequency noise. Further, the M-SSA filter is more appropriate for global, multidecadal signals than, for example, a single-channel bandpass filter, since it is designed to automatically account for lead–lag relationships between the members of the multivariate time series being filtered, whereas the bandpass filter is much less efficient in removing the types of noise that do not follow such relationships. Essentially, M-SSA serves as a filter to isolate the low-frequency signal, i.e., the global multidecadal signal. However, the M-SSA reconstruction does not reduce the data dimension — it is simply an optimally filtered version of the original multivariate time series that already accounts for lagged correlations between the different indices.
For this study, prior to M-SSA analysis, both reanalysis-based and CMIP5 simulated input 5-index sets are normalized by the ensemble-mean standard deviations of their reanalysis versions; this provides means to analyze a combination of SAT and SLP indices together and to directly compare the magnitudes of the observed and model simulated low-frequency variability identified by the M-SSA analysis. The results we report on below were obtained using the M-SSA embedding dimension M = 40. Kravtsov (2017) found that an embedding dimension less than 40 did not isolate the lowest frequency mode as efficiently as 40 (and greater). The physical argument for using M>=40 is a better focus on the low-frequency (multidecadal) variability. Kravtsov et al. (2018) and Kravtsov et al. (2024), for example, used M = 65, but found that results are robust for M ≥ 40. Therefore, the embedding dimension of 40 used here can be considered the lower bound for robust results for the detection of the dominant multidecadal signal.
To reconstruct the dominant low-frequency signal, we focus here on either one or two leading M-SSA modes (as ranked by their “space-time” variance, similar to EOF modes’ ranking by the fraction of total variance they “explain”) and, in particular, their reconstructed components (RCs) —which are, in effect, the data-adaptively filtered versions of the original multi-variate time series associated with (the sum of) these M-SSA modes. We decide on how many leading M-SSA modes to retain in the low-frequency signal reconstruction (either one or two) by requiring the modes in the leading pair to have similar frequency, with frequencies given here by the estimated location of the peak in a high-order Yule-Walker spectrum [67] of the leading PC of the corresponding RCs. In particular, if these frequencies differ by more than 30%, only the first mode containing the lower-frequency signal is retained. On rare occasion, in some of the internal variability estimates based on ERA-20C data, we replace the higher-frequency mode from the leading M-SSA pair by the next lower-ranked mode of the frequency that is a better match to the frequency of the leading M-SSA mode.
Upon completing the above procedures, we thus end up with M-SSA filtered sets of five climate indices for each estimate of the observed or model simulated internal variability (Estimation of forced signal and internal variability section). These filtered time series quantify the salient multidecadal (internal) variability in reanalysis-based and CMIP simulated data; our main goal is to provide a detailed comparison of the spatiotemporal content within and between these two streams of estimated multidecadal variability.
EOF analysis of M-SSA-filtered low-frequency signals
The M-SSA analysis used to isolate the dominant multidecadal signal in models and observations already supplies requisite estimates of the magnitudes and dominant time scales associated with this variability for further comparison. To compare the effective structures, we computed the leading PC for each of these M-SSA filtered low-frequency signals and obtained the associated patterns of internal variability in both our 5-dimensional space of normalized climate indices and for the gridded, spatially extended SAT and SLP time series of the estimated internal variability (in this case, we will still call these patterns the EOFs for brevity, despite that they are in fact spatial signatures associated with the leading PC of our five-index data set). These EOF patterns were computed in a standard way by regressing each of these vector time series onto the above leading PC. The sign of the EOF pattern was fixed so that the leading PC was positively correlated with the AMO index in each case. All of the patterns of internal multidecadal variability obtained in this way were then compared using Taylor diagrams [68]; see the Taylor diagrams in the ‘space’ of climate indices and leading multidecadal patterns of SAT and SLP in physical space sections for further details.
Results
M-SSA spectra
The M-SSA variance spectra in Fig 2 (which, however, exclude the outlier runs from the CMIP6 ensemble: see Data section) show that the internal variability estimated in reanalysis datasets is stronger than the simulated internal variability, as reflected in the “observed” variances being larger than the ones inferred from the CMIP models. Furthermore, the observed spectra have a clear leading pair of modes that account for a major fraction of the total (space–time) variance and is well separated from the rest of the trailing M-SSA modes, whereas the M-SSA spectra associated with CMIP model simulations do not have a pronounced leading pair but, instead, a near-continuous spectrum of modes with comparable, gradually decreasing variances. Finally, projections of the simulated M-SSA modes onto the observed (reanalysis) space-time EOFs (the green error bars in Fig 2) result in very weak variances, thereby indicating that the space-time structures that dominate the observed (estimated) internal variability are not at all pronounced, essentially nonexistent, in all CMIP historical simulations [27,36]. These findings corroborate all the earlier results by Kravtsov and collaborators [15,27,36,41,44,69,70] obtained using variations of the input data (different subsets of SAT/SLP based climate indices and reanalysis products) and forced-signal removal strategies.
These results are generally consistent between the comparisons based on the two reanalysis products and either of the two CMIP datasets (CMIP5 and CMIP6). The spectra associated with CMIP6 exhibit slightly larger variances but also a larger spread in the mode variances than the CMIP5 spectra. This indicates a tendency of CMIP6 models to simulate a higher level of multidecadal variability in the Northern Hemisphere. However, there is also a greater amount of uncertainty contained within the CMIP6 simulations. Likewise, the ERA-20C variances, while still generally larger than those based on the CMIP historical simulations, also exhibit a greater amount of uncertainty relative to the 20CRv3 spectra. This leads to a less distinct leading pair, with more of the variance being spread across the first four modes of the “observed” spectra. Nevertheless, the space-time structures contained within ERA20c are 1) similar to those in 20CRv3 (see below) and 2) are not pronounced in all CMIP simulations.
Certain runs of the CMIP6 outlier models — CNRM-CM6–1, EC-Earth3, and EC-Earth3-Veg — are characterized by a very pronounced multidecadal variability at the levels matching and, in some simulations, well exceeding those of the observed multidecadal variability. The CMIP6 outlier spectra substantially differ from the nonoutlier runs and from those based on CMIP5, as can be seen from Fig 3, which compares the CMIP6 outlier spectra with those of the 20CRv3 data (these comparisons are similar for the ERA-20C reanalysis dataset). Not only are the simulated variances significantly higher, but the spread between the spectra associated with different runs is much larger. The larger uncertainty contained within the outlier models indicates that not all runs of these models (but roughly half of these runs; see sections 3.3 and 3.5) possess abnormally large variances. The abnormal outlier-run variances are so high, however, that the projection of their underlying patterns (which are generally very different from the observed patterns, see the Taylor diagrams in the ‘space’ of climate indices and Taylor diagram comparisons in physical space sections) onto the observed patterns results in the variances being similar in magnitude to the variances of the observed multidecadal modes (compare blue and green bars in Fig 3). Hence, we argue that the outlier runs do not really provide a better match to the observed multidecadal variability than the rest of the CMIP models.
Observed multidecadal signal in the NH climate indices
The reconstruction of internal multidecadal signal associated with the leading pair of M-SSA modes for the five input climate indices considered here (Fig 4) produces results analogous to those reported in Kravtsov (2017) [Fig 2 there] and Kravtsov et al. (2018) [S6 Fig of Supplementary Information there] despite differences in input data sets and pre-processing methodologies, thereby reconfirming the robustness of this multidecadal signal with respect to CMIP-based forced-signal estimation and reanalysis uncertainties (a condensed version to compare all ensemble means together can be found in S2 Fig). Each of these M-SSA filtered indices exhibits pronounced multidecadal undulations with the amplitude exceeding the forced-signal uncertainties (error bars in Fig 4) and a large degree of spatial coherence across the entire set of five indices. This behavior is most robust for the four indices that reflect climate variability over the North Atlantic and North Pacific regions (AMO, NAO and PMO/ALPI, respectively); in particular, the timing of the maxima and minima of their multidecadal M-SSA filtered signals are all consistent between their versions based on different reanalyses (20CRv3 vs ERA-20C: left vs right column of Fig 4) and different forced-signal estimates used to isolate the internal variability (CMIP5 vs. CMIP6: top vs bottom row of Fig 4). This is further verified in S2 Fig, which overlays just the ensemble mean of all four estimates of each index. The consistency (including the robust identified shape of the multidecadal signals in the first decades of the twentieth century) is particularly encouraging given a shorter period covered by the ERA-20C reanalysis, as it suggests that end effects do not substantially affect the identification of the predominant multidecadal signal by M-SSA, at least in the chosen subset of climate indicators analyzed here. On the other hand, the least robust multidecadal behavior is detected in the NMO index, which describes the average SAT variability over ocean and land. This sensitivity is largely reflecting a somewhat smaller magnitude of the NMO’s multidecadal variability combined with inconsistencies in the estimates of low-frequency internal SAT variability over land due to both reanalysis and forced-signal estimation uncertainties [cf. 36].
Taylor diagrams in the ‘space’ of climate indices
To visualize similarities and differences between and within the observed and model simulated low-frequency internal signals, we used Taylor diagrams [68]. We first computed these diagrams for the 5-valued “patterns” associated with the leading EOF of each M-SSA filtered set of our five climate indices; see the EOF analysis of M-SSA-filtered low-frequency signals section. Here, the 5-valued internal variability patterns being analyzed were normalized by the standard deviation of the reference ensemble-mean reanalysis pattern (20CRv3 or ERA-20C, whichever is the case). The Taylor diagrams (Fig 5) are plotted in polar coordinates in which the distance from the origin indicates the pattern’s standard deviation and the cosine of the angle between the diagrams’ horizontal axis and a ray emanating from the origin and passing through the point associated with this pattern gives the value of the spatial correlation between this pattern and the reference pattern; the reference pattern itself (large, solid dot) thus takes the location (0, 1) on this diagram (corresponding to the unit standard deviation and zero angle, indicating the perfect spatial correlation of the pattern with itself). The distance between each cross (reanalysis estimate) or circle (model run) and the reference location (0, 1) is a measure of dissimilarity between a given pattern and the reference pattern. In addition to the above standard characteristics of the Taylor diagram, we also used colors to indicate the dominant timescale associated with each pattern shown (These timescales are also plotted in S1 Fig, where their periods can be compared directly to the average period of each reanalysis ensemble). These diagrams are supplemented with S1 Table, which lists the mean and the standard deviation of the magnitude, correlation and time scales associated with each model and reanalysis product.
As shown by the high correlations between and similar magnitudes of the observed individual patterns and (their ensemble-mean) reference pattern, these patterns are relatively consistent and are characterized by a relatively close proximity to the ensemble-mean reference pattern and small spread between the individual observed estimates of the internal variability. The latter spread reflects the forced signal uncertainty, thus showing that the spread in the model-based rescaled estimates of the observed forced signal is also small regardless of the CMIP model suite used to isolate this forced signal. One notable difference between CMIP5- and CMIP6-based observed estimates is the bimodality of the CMIP6-based estimates of internal-variability patterns — namely, the existence of two distinct clusters, one of them being clearly associated with smaller periods, thus indicating that the subtraction of the forced signals that tend to cancel the observed dominant multidecadal undulation result in higher-frequency residual spatial patterns with weaker magnitudes. Further inspection of these clusters reveals they are indeed dominated by two distinct subsets of CMIP6 models (S3 Fig and S5 Fig). The “shorter-time scale” Cluster 1 is associated with 6 model-based forced signal estimates and the “normal” cluster 2 is made up of the internal variability estimates using the other 15 model-based forced signals. The ensemble-mean observed multidecadal signal composited over cluster-1 and cluster-2 members (S6 Fig, otherwise analogous to Fig 4) shows smaller-magnitude and shorter time scale undulations in the second half of the century, consistent with its properties in the Taylor diagram. We believe that this dichotomy is an artifact of the particular choice of climate indices chosen to represent the reduced climate state, since it does not generalize when more advanced objective methods of signal detection are used to isolate the forced signal [64].
Note that we discuss here the forced-signal uncertainty within the ensemble of the observed estimated internal patterns, and not yet the comparisons with model simulations, which are discussed below. These comparisons show, first of all, that a majority of the CMIP simulations are characterized by smaller magnitude and perhaps somewhat shorter yet statistically consistent timescales of their dominant variability than observations, in line with the M-SSA spectra in Fig 2. Further, while some 5-valued model patterns have relatively high effective correlations with the observed reference pattern, albeit still lower than the observed individual patterns, Taylor diagrams containing runs from a single model show that this is not uniform from run to run within a given model (not shown). Thus, no model is able to consistently produce effective patterns similar to the reference pattern or even a consistent spatial pattern among different runs within the same model.
With the climate-index dimension being as low as five, one would expect to observe relatively high effective correlations between random 5-valued patterns (fixed to have a positive value along the first dimension, to model the positive AMO phase) by chance. A quick numerical estimation using 5-valued pseudo-random-number patterns shows that the 95th percentile of such random correlations is approximately equal to 0.88, deeming the majority of model-based correlations not statistically significant, even in the a priori sense. Thus, once again, CMIP5 and non-outlier CMIP6 models are unable to replicate the pattern of the observed multidecadal variability and exhibit, instead, random patterns reflecting, most probably, integrated climatic noise.
The CMIP6 outlier runs’ patterns, as compared to the 20CRv3 (left) and ERA-20C (right) patterns via Taylor diagrams in Fig 6 and S1 Table, are more similar to the reference pattern and, importantly, consistent between different simulations. A majority have pattern correlations higher than 0.8 and about half have magnitudes (much) greater than that of the reference pattern. Also, the time scales of the multidecadal signal in many of the model runs are comparable (or, in some cases, even longer) to the observed time scales. A “nonoutlier” model, IPSL-CM6A-LR, has a similar correlation and period to the outlier models, albeit with a smaller magnitude. However, it does stand out among the nonoutlier models and so it could in principle be counted as an outlier as well.
The relatively high correlations, magnitudes, and periods contained within the outlier runs all suggest that these models tend to replicate the observed multidecadal signal. We conclude, given the significant overlap between the outlier models and those with centennial-scale AMOC variability, that the high correlations, magnitudes, and periods contained within these runs are likely driven by the AMOC on multidecadal timescales. However, as we will see in the Leading multidecadal patterns of SAT and SLP in physical space section, these relatively high values do not extend to the multidecadal 2-D gridded SAT and SLP patterns of the outlier runs, which are very different from the observed patterns. Hence, once again, the apparent similarity between the observed and simulated multidecadal 5-valued patterns is an artifact of the low dimensionality of the climate-index space, while the observed and simulated 2-D patterns in the space of gridded SAT and SLP fields do not significantly overlap.
We also computed and plotted in Fig 7 and Fig 8 analogous Taylor diagrams for the observed and simulated patterns using the multi-model ensemble mean as the reference pattern (instead of the reanalysis ensemble mean reference pattern used in Fig 5 and Fig 6). Fig 7 shows the results for non-outlier runs. The observed patterns, somewhat surprisingly, not only exhibit mutual agreement as visualized through their proximity to one another but are also well correlated with the model-based ensemble-mean reference pattern (yet have a much larger magnitude). By contrast, the individual patterns from CMIP models typically have much larger magnitudes than and low correlation with their ensemble-mean pattern. The large spread, coupled with large magnitudes, demonstrates the noisy character of the multidecadal variability patterns detected in individual CMIP simulation and large run-to-run disagreement, with the ensemble average being but a weak-magnitude residual after the averaging of relatively strong heterogeneous extended spatial patterns contained in the individual runs.
The CMIP6 outlier-model-based reference-pattern plots (Fig 8) show that approximately half of the outlier runs have magnitudes larger than the reference pattern, while almost all runs have patterns with correlations exceeding 0.8. Similar high correlations are seen between the observed patterns and the outlier-run ensemble-mean pattern, thus corroborating the same details as the discussion around Fig 6; namely, the consistency between the leading multidecadal variability between different runs of the outlier models and their significant spatial similarity to the observed patterns in the space of the five climate indices. We will see, in the next section, that this similarity between models and observations does not extend to the 2D, spatially extended gridded SAT and SLP patterns of these modes.
Leading multidecadal patterns of SAT and SLP in the physical space
To visualize the leading EOF of the M-SSA filtered multidecadal signal in the physical space, we regressed the estimates of the reanalysis- and CMIP-based internal variability onto the leading (normalized) PC of the corresponding (M-SSA filtered) set of (our five) climate indices (recall that the sign of this PC was chosen to be positively correlated with the M-SSA filtered AMO index in each case; we still refer to these patterns as the leading EOF in figure titles for brevity).
The ensemble-mean SAT patterns for the two versions of the reanalysis, are reasonably consistent over most of the world ocean (Fig 9A, Fig 9B), including the Pacific and Atlantic regions featuring the familiar AMO and PDO/IPO patterns [71–73], as well as over large portions of the Southern Hemisphere oceans despite the lack of early observations and large reliance on interpolation and error reduction schemes in the compilation of the reanalysis data [e.g., 74–76 and references therein]. The spatial correlation of 0.54 between these patterns is statistically significant (S4 Fig). These patterns are also completely consistent with the AMO-like patterns identified in Kravtsov et al. (2024) who used a conceptually related pattern-recognition analysis to characterize global-scale multidecadal variability. They are also a reliable representation of the dominant patterns of multidecadal variability in the (majority) of individual estimates of the internal variability for each reanalysis data set, as indicated by the pre-dominance of stippling (over the locations of substantial SAT anomalies over the World Ocean) in Fig 9A, Fig 9B. Therefore, the leading multidecadal signal over the ocean overwhelms both the forced signal estimation and reanalysis uncertainties.
However, the consistency between the two reanalysis datasets is not entirely uniform, particularly over land and in the polar regions, where the ensemble-mean patterns differ considerably, a finding consistent with previous work [36,46]. Such discrepancies between reanalyses on long time scales are most probably due to different responses (teleconnections) of the underlying dynamical atmospheric models to the multidecadal SST anomalies. Several other studies have shown discrepancies between these reanalyses in variables other than SAT, such as mid-latitudinal flow [54] and atmospheric rivers [77].
The ensemble-mean pattern of multidecadal variability from the CMIP5/6 (non-outlier) ensemble (Fig 9C, Fig 9D) shows ubiquitous low magnitudes resulting from inconsistencies between and substantial cancelations among (much) larger-magnitude patterns derived from individual model runs (note the small area of stippled regions) — consistent with Fig 7. In almost all regions with no stippling, runs with different signs average to near zero and exhibit an inconsistent sign from simulation to simulation. In regions with stippling and near-zero magnitudes, there is agreement in sign between the CMIP simulations but there is virtually no multidecadal signal present in those regions regardless of this agreement.
Similar to SAT patterns, the ensemble-mean multidecadal SLP patterns for the two reanalyses exhibit consistency over the Northern Hemisphere (Fig 10A, Fig 10B), including the NAO and ALPI-like anomalies in the North Atlantic and Pacific regions, respectively. Their SLP patterns over the Southern Hemisphere are, however, very different, consistent with previous work showing that reanalysis datasets disagree on trends in several variables in the Southern Hemisphere, including SLP [78 and citations therein]. Simulated SLP spatial plots exhibit little to no signal (as compared to the magnitude of the observed signal) in the ensemble average across all model datasets (Fig 10C, Fig 10D). A notable and most interesting feature of this simulated ensemble-mean SLP signal — which, by construction, is associated with the AMO-like SAT variability — is its apparent negative spatial correlation with the reanalysis patterns in the Northern Hemisphere, which will be further quantified in the Taylor diagrams of the Taylor diagram comparisons in physical space section. This might point to the different dynamics behind the multidecadal SAT/SLP anomalies in the models vs observations (see further discussion in the Summary and conclusion section).
The SAT and SLP ensemble-mean patterns for the CMIP6 outlier models analogous to those in Fig 9 and Fig 10 (bottom rows) are shown in Fig 11. The outlier runs’ dominant multidecadal variability exhibits large positive, statistically significant SAT anomalies over much of the Northern Hemisphere, with maximum magnitude over the North Atlantic and Arctic regions (Fig 11A), as well as substantial areas of statistically significant (consistent among the multiple simulations) SLP anomalies in the mid-latitude Northern Hemisphere and tropical belt (Fig 11B). These patterns are very different from the observed patterns (Fig 9 and Fig 10, top rows), thus indicating that the multidecadal variability of the outlier models, while having time scales, spatial scales and magnitude consistent with observations, falls short of replicating teleconnections of the observed variability.
Taylor diagram comparisons in physical space
Taylor diagrams for the dominant multidecadal signal’s SAT patterns over the Northern-Hemisphere region for non-outlier models and observations vs. the observed ensemble-mean reference pattern (Fig 12) paint the same picture as the analogous analysis in the space of the climate indices (Fig 5), namely that of the models tending to have a similar time scale (see S1 Fig for a comparison between individual model runs and the observed ensemble-period), weaker-magnitude multidecadal variability with the simulated patterns uncorrelated with the observed patterns and with one another (model-specific values are included in S2 Table and S3 Table). The latter property is further verified using the Taylor diagrams in which the multi-model ensemble-mean pattern is used as the reference pattern (instead of the reanalysis ensemble mean): the latter reference pattern is of a much smaller magnitude than individual patterns and is only weakly if at all correlated with individual patterns (figure not shown).
There is also a seemingly larger diversity (hence, larger forced-signal uncertainty) in the observed multidecadal Northern Hemisphere’s SAT patterns in Fig 12 for 20CRv3/CMIP6 based estimates of observed internal variability, as compared to the corresponding Northern-Hemisphere climate-index based analysis in Fig 5.
The same Taylor-diagram analysis as above applied to the SAT patterns from the CMIP6 outlier runs only (Fig 13) produces essentially the same results as that for the non-outlier runs in Fig 12, which is in stark contrast to the climate-index space analysis (Fig 6) that suggested that outlier runs produce multidecadal variability similar to the observed variability. Furthermore, the analysis of the outlier-runs SLP patterns (figure not shown) demonstrates that the magnitude of the multidecadal SLP variability in these simulations is much weaker than that of the observed multidecadal variability (despite enormously large SAT anomalies), essentially indicating the lack of the atmospheric dynamical response to the, apparently, ocean induced multidecadal SAT variability. These results are summarized, on a model-by-model basis, in S2 Table.
The Taylor-diagram analysis of the observed and non-outlier models’ SLP patterns (Fig 14, with the underlying numerical data listed in S3 Table) sends the same message as the SAT-based Fig 12: the modeled SLP patterns — largely uncorrelated with one another within the model ensemble, thus suggesting their random origin — are mostly of weaker magnitude and different extended spatial structure than the observed patterns. The random character of simulated SLP patterns was further verified by fitting a stochastic linear inverse model [LIM: 79] to mimic the CMIP-simulated internal SLP variability over the Northern Hemisphere (see S1 Text). The ensemble of synthetic SLP time series generated by the LIM were 20-yr boxcar averaged and regressed onto the normalized ensemble-mean reconstructed component of the reanalysis-based multidecadal signal, thus producing an ensemble of synthetic SLP patterns under the assumption that they are not statistically connected to the SST variability and are just due to sampling. The associated spread of synthetic pattern correlations is statistically indistinguishable from that of the CMIP based pattern correlations in Fig 14 (not shown).
The Taylor-diagram analysis of the observed and non-outlier models’ SLP patterns (Fig 14, with the underlying numerical data listed in S3 Table) sends the same message that the SAT-based Fig 12: the modeled SLP patterns — largely uncorrelated with one another within the model ensemble, thus suggesting their random origin — are mostly of weaker magnitude and different extended spatial structure than the observed patterns. This large spread was further verified via significance testing with synthetic timeseries (not shown), where virtually all model runs fell within the spread of correlations.
An interesting property of the model simulated multidecadal SLP behavior that contrasts the observed behavior can be seen in the Taylor diagrams based on the Northern-Hemisphere SLP pattern analysis with respect to the multi-model ensemble-mean (MMM) reference pattern (Fig 15). As previously alluded to in the previous section, the reanalysis pattern tends to be negatively correlated with the MMM SLP pattern. The statistical significance of this anticorrelation was shown by confirming that the 97.5th percentile of the 1000 correlations between the MMM of bootstrapped model patterns (sampled from our collection of SLP patterns within CMIP5 or CMIP6 models) and the ensemble-mean (20CRv3 or ERA-20C) reanalysis pattern is below zero for each of the four model–reanalysis pairs in Fig 15A–Fig 15D, which allows us to reject the null hypothesis of zero correlation at the 5% level with respect to the two-sided alterative (see Table 3). This property may point to key differences in the mechanisms behind the observed and simulated multidecadal climate variability. In particular, the observed variability may originate from the oceanic internal sources [e.g., internal variability of the AMOC: 80] then leading to the atmospheric response to SST (and the associated SLP anomalies). By contrast, the model simulated multidecadal SAT variability (at least that in the non-outlier models) appears to be forced by the ultra-low-frequency variability of atmospheric circulation and the associated SLP (and wind) anomalies and is, thus, random in nature. If this conjecture holds true, it would mean that the actual climate predictability at decadal and longer time scales may be larger than that implied by the climate models [80].
Same as Fig 9 and Fig 10, but for SAT and SLP from the outlier models. Coastline data were obtained and plotted using The MathWorks, Inc.’s Mapping Toolbox.
Taylor diagrams for the Northern Hemisphere multidecadal SAT patterns’ comparisons to the (ensemble-mean) reanalysis reference pattern (analogous to climate-index pattern analysis of Fig 5).
Same as Fig 12, but for the CMIP6 outlier models and with the AMO patterns that display higher multidecadal variability.
Same as Fig 12, but for the Northern Hemisphere SLP internal variability patterns.
Same as Fig 14, but with the multi-model ensemble-mean SLP pattern as the reference pattern.
Summary and conclusion
We analyzed decadal and longer time scale climate variability (DCV) in the twentieth century (1880–2005) annual surface air temperature (SAT) and sea level pressure (SLP) gridded global time series in the 20CRv3 and ERA-20C reanalysis datasets, as well as the CMIP5 and CMIP6 model suites (see Table 1 and Table 2). All input time series were smoothed using 11-year boxcar running mean prior to the analysis, to focus on long (multidecadal) time scales. The simulated forced signals were isolated through forming the single-model ensemble means, rescaled them using linear regression to best fit the reanalysis data, and then subtracted from the original time series of each field to obtain multiple estimates of internal climate variability in models and observations. Finally, the single dominant DCV mode, comprised of one pattern and one time series for each estimate of the observed or simulated internal variability was computed as the leading EOF and PC of an objective filtered (hence, smoothed) version of five widely used Northern-Hemispheric SAT and SLP based Atlantic, Pacific and (northern) hemispheric climate indices: namely, the AMO, PMO, NMO, ALPI, and NAO indices. Global patterns associated with this mode were also computed by regressing the time series of estimated internal variability onto this PC in each case. We then compared the time scales, magnitudes, and spatial patterns of the observed and simulated DCV using a version of harmonic analysis for the former and Taylor diagrams for the latter two.
We found that multidecadal SAT/SLP variability simulated by the majority of the CMIP5 and 6 models tend to have similar time scales, yet weaker magnitudes and completely different spatial patterns compared to the observed DCV, with no obvious improvement in the multidecadal variability replication from one generation of simulations to another. A small subset of models (three of the 38 models analyzed here) — we called them the outlier models — behaves differently. In particular, their ultra-low-frequency (multidecadal) DCV has time scales similar or even exceeding the observed time scales of 70–80 years and vastly exceeds in magnitude the observed variability in the Northern Hemisphere’s SAT, especially in the North Atlantic and Arctic regions. However, this simulated variability has a negligible SLP expression compared to the observed variability and a very different from the observed global SAT pattern. Therefore, the apparent similarity of this simulated variability to the observed in the ‘space’ of the five climate indices considered can be deemed accidental, and the physics behind the observed multidecadal climate variability is likely to be different from that in the outlier models.
An important clue to possible dynamics underlying the differences between the observed and simulated climate variability lies in the fact that the models, on average, tend to exhibit an SLP pattern associated with the AMO-like SAT anomalies (persistent decadal temperature anomalies over the North Atlantic region) that is not only weak but also negatively correlated with its observed counterpart. One interpretation of this discrepancy could be that the modeled multidecadal SAT patterns are in fact driven by quasi-random atmospheric circulation (SLP) anomalies; this is also consistent with the lack of consistency between or, perhaps, even the apparent randomness of the simulated multidecadal patterns from individual model simulations. By contrast, the observed multidecadal SAT/SLP anomalies may instead be associated with the internal oceanic multidecadal signal [e.g., with the variability in the AMOC, 80] in some ways efficiently communicated throughout the globe via pronounced atmospheric (e.g., SLP) teleconnections [cf. 36]. Indeed, it has been suggested before, through estimating the parameters of data-driven models able to replicate observed or CMIP simulated climate variability [44] that the CMIP models’ efficiency in communicating the deep-ocean signals to the surface oceanic and variability is strongly suppressed compared to the one inferred from the observed data [cf. 81,82]. Our present results provide some additional support for this notion. Another potential, possibly related mechanism that may be behind the differences between the model simulated and observed multidecadal variability is through the effects associated with stratospheric conditioning of the coupled ocean–atmosphere dynamics across a range of time scales [81,83–88]. For example, Studholme et al. (2025) demonstrated how a warm bias in mid-latitude stratosphere is responsible for overly weak linkage between AMOC and multidecadal climate variability over the North Atlantic in many CMIP models through modulation of the tropospheric midlatitude jet and the ensuing shifts in the AMOC subduction sites [see also 84]. Such dynamical connections or lack thereof are conceptually consistent with our diagnosed differences between the observed and model simulated SAT and SLP multidecadal co-variability.
Previous multi-model analyses of the decadal and longer time scale climate variability often focused on a regional variability in the Pacific [72] and Atlantic sectors [80,89–91]. This is different from our present approach that considers dominant hemispheric-scale multidecadal modes in a combination of climate indices in the Northern Hemisphere. It is thus more challenging for the climate models to replicate the spatiotemporal structure of such variability compared to regional studies; for example, the climate models tend to capture the observed PDO patterns [Fig 2 of 72] better than the leading patterns identified by our multivariate analysis (Fig 5 here). Our results are not directly comparable to those on the Pacific or Atlantic Multidecadal Variability (AMV) but rather pertain to the hemispheric-to-global scale variability with its inter-basin teleconnections. Yet, some of our main conclusions are consistent with those previous studies. For example, [85] finds the lack of oceanic internal AMV in CMIP5 model control simulation, with the NAO driving the AMV without much feedback from the ocean; a similar statement is also implicit in [80] review, which argues that the role of the Atlantic Meridional Overturning Circulation has been largely underestimated by climate models. This, alongside a possible underestimation of the sea-surface temperature effects on the atmospheric decadal anomalies [44,81,82], may be behind an apparently random character of the model simulated multidecadal climate variability identified here.
While the present study is rooted in our previous work [15,27,36,44], its extension to new reanalysis datasets (in particular, 20CRv3), the inclusion of the CMIP6 ensemble (as opposed to CMIP5-only in the previous studies), the use of the common SAT/SLP analysis [92], as well as the focus on comparing the leading EOF patterns through Taylor diagrams, are all new. Our approach provides a compact yet comprehensive description and analysis of the dominant hemispheric-scale multidecadal variability in state-of-the-art climate models and reanalysis products and offers new clues as to physical causes of the differences between them. Note that the apparent inability of climate models to replicate a global multidecadal internal signal present in the observed climate time series increases the uncertainty in historical, such as the mid-twentieth century and early twenty-first century “hiatus” periods, and future trends at the decadal and longer timescales [e.g., 93].
From here, we aim to expand upon our findings by utilizing several other datasets to create a 3-dimensional version of this multidecadal signal. Not only will these additional datasets include SAT and SLP, but upper-atmospheric and oceanic subsurface data, thus creating the 3-dimensional signal. The addition of these variables will hopefully shed light on the physical properties and dynamics responsible for the absence of the simulated variability on decadal timescales.
Supporting information
S1 Table. Climate index space model and reanalysis magnitudes, correlations, and periods.
Denotes the individual model standard deviations (magnitudes), correlations, and periods for the 5-index based climate index space data, as well as the values for reanalysis data (with the model suite used to estimate the observed forced signals in parentheses, with CMIP6 only containing nonoutlier members). The secondary numbers in each cell denote ± 1 standard deviation. Statistically significant correlations are in bold.
https://doi.org/10.1371/journal.pclm.0000519.s001
(DOCX)
S2 Table. Physical space SAT model and reanalysis magnitudes, correlations, and periods.
Same as S1 Table, but for the SAT grid point data in physical space. These values are based on Northern Hemisphere points only, corresponding to the physical space Taylor Diagrams.
https://doi.org/10.1371/journal.pclm.0000519.s002
(DOCX)
S3 Table. Physical-space SLP model and reanalysis magnitudes, correlations, and periods.
Same as S2 Table, but for the SLP grid point data in physical space.
https://doi.org/10.1371/journal.pclm.0000519.s003
(DOCX)
S1 Fig. Simulated periods.
Periods of model runs (circles) from CMIP5 (left column) and CMIP6 (right column), with shading differentiating from the different models contained within each model suite. Solid lines denote the observed ensemble-average period for 20CRv3 (top row) and ERA-20C (bottom row) and ± 1 standard deviation (dashed line).
https://doi.org/10.1371/journal.pclm.0000519.s004
(TIF)
S2 Fig. Observed multidecadal signal ensemble.
Same as Fig 4 but condensed to compare all ensemble means together. Each reanalysis (20CRv3 and ERA20C, both whose forced signal estimates are from CMIP5 and CMIP6, resulting in four averages in total) is depicted for each climate index, revealing that no matter the CMIP suite or reanalysis dataset, what is essentially the same multidecadal signal is isolated.
https://doi.org/10.1371/journal.pclm.0000519.s005
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S3 Fig. Climate index taylor diagram clusters.
The same as the bottom left panel in Fig 5, but with the model data and observations outside of these two clusters removed. Observations that make up each cluster were isolated by 1) limiting Cluster 1 to only include estimates with periods less than 65 years and 2) magnitudes less than 1. Cluster two only contains estimates with periods greater than 65 years and magnitudes greater than 1. These thresholds were visually determined, as there is a clear separation between each of these clusters around these thresholds.
https://doi.org/10.1371/journal.pclm.0000519.s006
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S4 Fig. Synthetic SAT patterns.
Taylor diagrams showing synthetic SAT patterns relative to the (left) 20CRv3 and (right) ERA20-C ensemble average. The 97.5th percentile of the correlation between the synthetic data and reference pattern are 0.30 and 0.41 for the 20CRv3 and ERA20-C reference patterns, respectively. The red dots show the ensemble average of the reanalysis dataset not used as the reference pattern. The correlation between these patterns is 0.54, demonstrating the statistically significant similarity between them.
https://doi.org/10.1371/journal.pclm.0000519.s007
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S5 Fig. Cluster forced signal fractions.
The fraction of each forced signal estimate contained within each cluster was computed, e.g., the forced signal estimate originating from model 1 makes up roughly 6% of Cluster 1 and 0% of Cluster 2. From this, we can clearly see that the clusters originate by differences in the forced signal estimate. It is important to note that the forced signal estimate from model 13 does not contain runs in either of these clusters, or, happen to fall near the clusters on the Taylor diagrams but outside of the thresholds established.
https://doi.org/10.1371/journal.pclm.0000519.s008
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S6 Fig. Cluster multidecadal signals.
Same as Fig 4, but where the multidecadal signal is isolated with only the observed estimates of the internal variability contained within each cluster. The difference in period is visualized here, with Cluster 1 having a slightly different period, particularly over land. However, each cluster produces similar estimates of the signal.
https://doi.org/10.1371/journal.pclm.0000519.s009
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Acknowledgments
We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP and thank the climate modelling groups for making their model output available. Support for the Twentieth Century Reanalysis Project data set is provided by the U.S. Department of Energy, Office of Science Innovative and Novel Computational Impact on Theory and Experiment (DOE INCITE) programme, and Office of Biological and Environmental Research (BER), and by the National Oceanic and Atmospheric Administration Climate Program Office. Finally, we greatly appreciate the time invested in reading and commenting on our paper by the anonymous reviewers, as well as their constructive suggestions towards improving the paper’s readability and potential impact.
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