The 500 m upper Ocean Heat Content (OHC500) in reanalysis and models is computed as follows: 1OHC500=ρ0Cp∫0500Tzdz where Cp = 4186 J kg⁻¹ K⁻¹ is the specific heat capacity of the sea water and ρ0 = 1026 kg m⁻³ is the reference sea water density, T(z) is the vertical profile of regridded potential temperature.

Variables from piControl simulations, that are not subject to transient forcing, should be stationary over time. However, a common issue in climate models is the drift. Drift is a spurious trend in different state variables that are unrelated to changes in external forcing (Sen Gupta et al., 2013). Drift may occur for various reasons such as insufficient spin up and errors in the model's energy budget (Hobbs et al., 2016). This shortcoming in the models when integrated over century scales can result large changes in ocean temperature, and ocean heat content etc. (Sen Gupta et al., 2013; Hobbs et al., 2016). To remove model drift, a linear trend was fitted and removed at each grid cell over the full duration of the piControl simulations for regridded SST, OHC500, SLP, and 500 hPa geopotential height (ZG500).

We have calculated eight widely used climate modes (IPO, EP and CP El Niño, AMO, NAO, IOD, SDM, and SAM), using standard definitions of these modes in the literature (Table 2). First, monthly anomalies are calculated by subtracting the long-term (duration of piControl) monthly mean climatology from the SST, SLP, ZG500, and OHC500, after the data had already been regridded and linearly detrended as described above.

A Lanczos filter was applied to the above processed datasets prior to computing the AMO, ENSO and IPO indices. For the AMO and IPO, a 10-year low-pass filter with a 10-year cut-off and a filter length of 121 months was used, which removes approximately five years of data from the beginning and end of the record. For ENSO, a band-pass filter with lower and upper cut-offs at 24 months and 108 months respectively, and a filter length of 109 months, was applied. The Lanczos filters (low-pass and band-pass) were chosen to retain only the desired frequency ranges required for defining climate mode (AMO, ENSO and IPO). To maintain consistency, we removed five years from the start and end of the record used for computing each of the climate mode index (Table 2). While the AMO is defined as the average of 10 year low pass filtered SST anomaly over the North Atlantic as preferred in most literature, the other seven climate modes are defined based on Empirical Orthogonal Function (EOF) and applied separately to different regions/variables (as mentioned in Table 2).

EOF analysis decomposes spatiotemporal data into orthogonal spatial patterns and corresponding temporal coefficients, known as principal components (PCs), ranked by the variance they explain (Hannachi et al., 2007). In the present study, we have implemented EOF based indices to examine the spatial and temporal structure and representation of modes across CMIP6 piControl simulations. The reason for using EOF definitions in our study is because models represent climate modes differently to the real world. As such fixed area definitions may not be appropriate for those models, particularly in applications where we are trying to understand how a mode impacts other parts of the climate system in a model. These indices are employed as a complementary, pattern-based diagnostic to the area averaged indices (such as Niño 3.4 for ENSO, DMI: Dipole Mode Index for IOD) adopted in Climate Variability Diagnostics Package (CVDP; Phillips et al., 2014; Maher et al., 2025) data repository and facilitate a direct comparison between pattern based and regionally averaged representations of modes of variability.

Overall, the datasets generated and the analysis undertaken here has similarities to the CVDP data repository in certain climate modes, they also exhibit important differences. These differences reflect variations in the definitions, filtering methods, and latitude ranges used in the simulations. We have introduced the SDM for the first time and produced EOF based 500 hPa geopotential height definition for both the NAO and SAM, complementing the existing SLP based definitions. Our datasets provide an alternative view of common climate modes, enabling the community to assess uncertainties arising from different scientifically valid approaches, including those of the CVDP repository. Evaluating such uncertainties is a key component of robust climate science and IPCC assessments. This additional collection now allows ensemble approaches as well.

To compare the spatial patterns of climate modes extracted from CMIP6 models with those from observations, we have employed Taylor diagrams. Taylor diagrams provide a concise visual representation of the spatial correlation coefficient (r) and the standard deviation (SD) between a model field and an observed field, while also incorporating their combined measure, the root-mean-square difference (RMSD) (Izzaddin et al., 2024; Taylor, 2001). The RMSD is calculated as: 2RMSD2=σm2+σr2-2σmσrr Where σm and σr are the standard deviations of the model and observed patterns, respectively, and r is their spatial correlation coefficient.

In our analysis, the model results were standardised relative to observation. This allows the distance from each model point to the reference (observed) point on the diagram to directly indicate the overall agreement between the simulated and observed spatial patterns.

We would like to note that a direct comparison between piControl simulations and the historical/observational record is not appropriate for a rigorous assessment of model skill, as human emissions can modulate the characteristics of modes of variability (Klavans et al., 2025). Our primary objective of this comparison is not to rank or evaluate model skill, but rather to provide a qualitative assessment of the large-scale spatial structures of the derived modes. In this context, observational datasets are used only as a reference for general pattern realism, and not as a benchmark for quantitative agreement. We also note that, prior to the EOF analysis, long term trends were removed from the observational datasets to minimize the influence of externally forced climate change and to better isolate internal variability. However, we acknowledge that such preprocessing does not fully reconcile the differences between pre-industrial and present-day climates.

We analysed the periodicity of the climate mode indices using the Fast Fourier Transform (FFT) and tested the statistical significance of spectral peaks via Monte Carlo simulation. For each time series, the mean was removed, and the series was normalised to unit variance before spectral estimation. The power spectrum was computed using the variance-normalised periodogram with a Hanning window and normalised such that. 3∑k=1KPfk=1 Where Pfk is the power at frequency fk, and K is the number of positive frequency bins.

To construct the null distribution, we fitted a first-order autoregressive (AR(1)) model to each series by estimating its lag-1 autocorrelation coefficient α (Wilks, 2011). A total of 1000 Monte Carlo time series were generated with the same length as the original data following the approach of Schulz and Mudelsee (2002): 4xt=αxt-1+εt,εt∼N0,1 The FFT is applied to each surrogate, and the resulting simulated spectra are used to estimate the mean P‾f, standard deviation σPf, and the Effective degrees of freedom (EDF) at each frequency (Bretherton et al., 1999): 5EDFf=P‾fσPf2 The significance threshold at each frequency was then calculated as 6Tf=P‾f+σPfEDFf And peaks in the observed spectrum exceeding this threshold (mean + standard error) are considered statistically significant. This procedure is repeated for all CMIP6 models, observational and reanalysis datasets to assess the robustness of periodic signals in the extracted climate mode indices. For the heat maps, we plot the fraction of significant spectral power in each period bin for every dataset. Within each dataset, these fractions are normalized to sum to 1 (i.e., we condition on the significant part of the spectrum), so the heat map reflects the relative distribution of significant power across periods rather than absolute magnitude. Bins with no significant power are left blank.

The tropical Pacific Ocean exhibits a dominant interannual climate mode known as El Niño Southern Oscillation, comprising of two types of EP and CP El Niño. These two types of modes are defined as the first two leading modes of SST anomaly in the tropical Pacific within 30° S–30° N (Xu et al., 2017). The EP El Niño represents the primary leading mode and is characterized by warming in the eastern tropical Pacific and explains 63.4 % of the variance of tropical Pacific SST anomaly in observation (Fig. 1a). Spatial expression, obtained by regressing SST anomaly against the normalised time series of mode indices (EOFPC1) show that most models capture the broad scale features, particularly warming in the eastern and central tropical Pacific Ocean during its positive phase (Fig. 1a). All the models reproduce the observed wedge-shaped warming in the central and eastern Pacific, with a weaker cooling signal in the surrounding regions. In order to have a qualitative assessment of pattern realism with observation, we have plotted the Taylor's diagram. Pattern correlations indicate a generally strong spatial correspondence (with correlations above 0.7), with relatively small errors across models (Fig. 4a). Models (particularly CanESM5, BCC-CSM2-MR, IPSL-CM6A-LR, ACCESS-ESM1.5, and SAM0-UNICON) present warming signal that extends too far to the west along the equator and show maximum anomalies too far to the west. Despite these limitations, all the models broadly replicate the observed spatial pattern, with lower RMSE values.

Unlike the EP El Niño, models demonstrate a large inter-model spread in representing the observed warming in the central Pacific expanding to lower latitudes towards the east and with cooling in the eastern and western tropical Pacific Ocean which are the characteristics of the positive phase of CP El Niño (Figs. 2, 4b). This mode explains only 8.1 % of the variance in the observation, which is much less than the EP El Niño. Similarly low variances are seen across the models varying between 5 %–15 % (Fig. 2). With respect to observation, majority of 23 models have correlations that exceed 0.5, while a smaller subset exhibits weaker or even negative correlations (Fig. 4b). Models such as CanESM5, CMCC-CM2-SR5, BCC-CSM2-MR, ACCESS-ESM1-5 and MIROC6 show the central Pacific warming extending into the western Pacific, whereas EC-Earth3-CC, E3SM1-0, CESM2, and CIESM display warming in the central and eastern Pacific, indicating deviations in the spatial expression of this mode. These differences are also reflected in relatively larger RMSE values. These deviations are likely due to the smaller variance associated with this mode. Despite these issues, the MMM effectively captures the observed climate mode by reducing non-systematic biases coming from individual models (Fig. 4b).

The IPO is a multidecadal climate mode and captured as the first leading mode of variability in low frequency SST anomaly in the Pacific Ocean (Dong and McPhaden, 2017; Han et al., 2014; Power et al., 1999), accounting for 32.3 % of variance in observation (Fig. 3a). However, for EC-Earth3 and HadGEM3-GC31-LL, IPO appears as the second and third leading modes of SST, respectively (Fig. 3c, i), as indicated by the corresponding EOFs that show strong correlations with the observed IPO spatial pattern. In most CMIP6 models, the IPO explains 25 %–35 % of the variance, consistent with observations, though models such as CNRM-CM6-1, GISS-E2-1-G, FGOALS-g3, and CNRM-ESM2-1 show lower values (<20 %), while CESM2 shows higher variance (44 %). The observed IPO pattern exhibits a characteristic tripolar structure with warming in the central to eastern tropical Pacific and cooling in the western-central North and South Pacific, corresponding to the positive phase of the IPO (Fig. 3a).

To examine the robustness of spatial pattern, we have calculated the spatial correlation between the observed and modelled IPO pattern (Fig. 4c), revealing that most CMIP6 models exhibit strong correlations above 0.7, with low RMSE around 0.5 °C. However, most models simulate the characteristic warming in the equatorial eastern Pacific extending westward, though with varying amplitudes compared to observation. For example, GISS-E2-1-G simulates positive anomalies over the western North Central Pacific (Fig. 3g), in contrast to the observed negative anomalies. Similarly, BCC-CSM2-MR shows basin-wide warming across the South Pacific (Fig. 3n). Overall, the MMM reproduces the IPO spatial pattern and variance reasonably well, demonstrating robust representation of the observed low-frequency Pacific variability.

The IOD, an internal mode of variability in tropical Indian Ocean SST, is characterised by warming (cooling) in the WEIO (EEIO) during its positive phase (Krishnamurthy and Kirtman, 2003; Saji et al., 1999). Most models represent the IOD as the second leading mode of variability in SST anomaly, while 7 models (CMCC-CM2-SR5, BCC-CSM2-MR, ACCESS-ESM1-5, CESM2, CIESM, FGOALS-g3, SAM0-UNICON) exhibit the IOD as 1st leading mode (Fig. 5). Observed IOD accounts for 12.7 % of the total SST anomaly variance in the tropical Indian Ocean (Fig. 5a). The explained variance in CMIP6 models varies widely, from 9.5 % (CanESM5) to 31.5 % (CIESM), while 8 models explain within the observed range of 10 %–15 %. A strong agreement exists between the simulated and observed spatial patterns of the IOD, with pattern correlations ranging from 0.4 to 0.9 across all the models (as shown in Taylor diagram in Fig. 7a), though notable regional differences remain in reproducing the magnitude of warming and cooling over the western and eastern IO. The MMM mitigates individual model biases (particularly those arising from models that exhibit exaggerated warming and cooling in the western and eastern regions, respectively) and achieves a closer representation of the observed IOD spatial pattern.

The SDM is an internal mode of variability in the upper 500 m OHC of the tropical Indian Ocean, characterised by a distinct dipolar pattern with warming in the south-western Indian Ocean (SWIO) and cooling in the EEIO during its positive phase (Mohapatra and Gnanaseelan, 2021). All 23 models, along with reanalysis data (ORAS5), represent the SDM as the dominant EOF in OHC500 anomaly (Fig. 6). Reanalysis data accounts for 21 % of the total variance. The explained variance in CMIP6 models varies widely from 14.4 % in HadGEM3-GC31-MM to over 40 % in CIESM and FGOALS-g3. The SDM pattern in reanalysis shows warming (cooling) in the SWIO (EEIO) (Fig. 6a). Most models reproduce the observed SWIO and EEIO dipole structure of SDM, though a few models underestimate the observed warming over the Arabian Sea (Fig. 6).

All the models exhibit a strong correlation with reanalysis, ranging from 0.6 to 0.9 (Fig. 7b), with relatively low RMSE values. However, a few models (e.g., CMCC-ESM2) exhibit noticeably larger deviations, primarily associated with an overestimation of amplitude in the southwestern Indian Ocean (Fig. 6b). Overall, the CMIP6 models demonstrate good skill in capturing the SDM's spatial characteristics, underscoring their ability to represent key OHC variability in the tropical Indian Ocean.

The AMO is an important multidecadal oceanic climate mode in the North Atlantic Ocean, characterised by basin-wide warming in the North Atlantic Ocean (Fig. 8a). All the models display the large-scale features of the observed AMO pattern (Fig. 8), through several show regional deviations. 10 out of the 23 models (EC-Earth3-CC, GISS-E2-1-G, EC-Earth3, E3SM1-0, MIROC6, MRI-ESM2-0, GFDL-CM4, FGOALS-g3, SAM0-UNICON, CNRM-ESM2-1) exhibit a cooling pattern in the western-central North Atlantic Ocean. The North Atlantic cooling pattern, an issue that persisted from CMIP5 into CMIP6, arises from a combination of factors: misplacement and weakening of the Gulf Stream due to insufficient ocean resolution and excessive mixing, weak AMOC transport, surface heat flux errors, and freshwater-induced stratification. These combined processes reduce the northward and vertical ocean heat transport, inducing the cold bias in the north Atlantic (Huo et al., 2024; Moreno-Chamarro et al., 2022; Weijer et al., 2020). Several models also show amplitude deviations from observation, particularly north of 40° N, where the warming is either stronger or weaker than observed. These differences are reflected in the broader correlation range (0.2 to 0.7) between the models and observation (Fig. 11a). For example, eight models (EC-Earth3, CMCC-CM2-SR5, CMCC-ESM2, CNRM-ESM1-0, FGOALS-g3, CNRM-CM6-1, and IPSL-CM6A-LR) show excessive warming north of 40° N, while FGOALS-g3 exhibits strong cooling in the western-central North Atlantic. The MMM effectively mitigates these discrepancies, providing a more consistent representation of the canonical AMO pattern, with a correlation of 0.6 and RMSE below 2 °C, demonstrating improved overall skill relative to individual models.

The NAO, an atmospheric mode of variability in SLP over the North Atlantic Ocean, is defined as a distinct north-south dipolar SLP pattern, with high (low) SLP anomaly in the north (south) of the North Atlantic Ocean during its positive phase (Hurrell et al., 2003; Hurrell and Deser, 2009). Reanalysis (ERA5) and all 23 models represent the NAO as the leading mode of variability in SLP anomaly (Fig. 9). Reanalysis data explains 33.1 % of the total variance, while models account 28 %–35 % in SLP anomaly, indicating a strong imprint of the NAO in atmospheric circulation over this region. Models successfully reproduce this canonical NAO spatial pattern with varying amplitude across the basin. All the models exhibit very strong spatial correlation (>0.95) with reanalysis and maintain very low RMSE values (<5 Pa), underscoring the overall robustness and consistency of CMIP6 models in representing the observed NAO structure (Fig. 11b).

The southern hemisphere extra-subtropics are dominated by an atmospheric mode known as the SAM, which is characterised by a north-south shift in westerly wind belts. Reanalysis (ERA5) and all CMIP6 simulations capture SAM as the primary climate mode in SLP anomaly. Reanalysis explains 26 % of total variance, while models capture 26 %–35 %. The regression based spatial pattern of the SAM shows negative SLP anomalies over the polar region and positive anomalies over the extra-subtropical latitudes, a feature reproduced by the models (Fig. 10). All models show very strong correlation (>0.97) and low RMSE (<5 Pa) with reanalysis (Fig. 11c), confirming the robustness of SAM representation and the reliability of the CMIP6 derived SAM index for studying southern hemisphere climate variability.

In addition to the SLP based definition, we derive NAO and SAM from ZG500. The NAO and SAM are defined as the 1st leading mode in ZG500 anomalies over the North Atlantic and extratropical SH respectively based on 22 CMIP6 models (EC-Earth3-CC has been excluded due to insufficient data) (Figs. S1 and S2 in the Supplement). All the models capture the canonical spatial structure of both NAO and SAM in ZG500 as EOF1, demonstrating strong inter-model robustness. These indices represent the mid-tropospheric expression of these modes and are more closely associated with large scale atmospheric dynamics, such as jet variability and eddy activity. In contrast, definitions based on SLP primarily reflect near surface variability and are directly linked to air–sea interaction and surface forcing and serve a complementary purpose. The indices defined based on SLP and ZG500 are highly correlated (figure not shown), however the variance explained by modes differs between fields. NAO explains 23 %–27 % of variance in ZG500 and 28 %–35 % of variance in SLP while SAM accounts 20 %–25 % of variance in ZG500 and 26 %–35 % of variance in SLP. These different definitions follow standard published approaches. Their combined use provides complementary perspectives on the vertical structure of these modes and the associated physical processes.