1 Introduction

In recent years, ocean decadal variability has attracted ever-increasing attention for its importance in modulating global warming (England et al. 2014; Bordbar et al. 2017). In its sixth assessment report (AR6), the Intergovernmental Panel on Climate Change (IPCC) clearly affirmed the significant contribution of human activity to the warming of the atmosphere, oceans, and land by increasing carbon dioxide (CO2) emissions since the Industrial Revolution (Li 2022; Thapliyal et al. 2023). However, the increase in global mean surface temperature (GMST) is not linear but instead has two alternating phases, which include accelerated warming and a global warming hiatus (IPCC, 2013). GMST increased rapidly during 1920–1945 and 1977–2000 but stalled during 1946–1976 and 2001–2013 (England et al. 2014, 2015; Bordbar et al. 2019). The common view is that greenhouse gases and anthropogenic aerosols dominate long-term warming trends, while natural internal variability determines the climate system phase shift (Farneti 2017). By conducting the pacemaker experiments, it was suggested that the global warming hiatus may be caused by the negative phase of the Pacific Decadal Oscillation (PDO) and Atlantic Multidecadal Variability (AMV) (Kosaka and Xie 2013; McGregor et al. 2014; Deser et al. 2017). This indicates that decadal climate variability should be taken into account for near-term climate predictions (Hawkins and Sutton 2009; Liu 2012).

Ocean decadal variability is not only significant for global low-frequency variability but also plays a key role in extreme weather and climate events along ocean coasts (Alexander 2010; Deser et al. 2010; Di Lorenzo et al. 2023). Ocean decadal variability has been identified as a leading driver of changes in some marine extreme events (Roemmich and McGowan 1995; Mantua et al. 1997; Hare et al. 1999), such as marine heatwaves (Di Lorenzo and Mantua 2016; Holbrook et al. 2019) and tropical storms (Chu and Clark 1999; Li et al. 2015). Based on observational data, many indices have been defined to evaluate the Pacific decadal variability, such as PDO (Mantua et al. 1997), the North Pacific Gyre Oscillation (NPGO; Di Lorenzo et al. 2008), the Interdecadal Pacific Oscillation (IPO; Power et al. 1999), South Pacific Decadal Oscillation (SPDO; Hsu and Chen 2011), and Tropical Pacific Decadal Variability (TPDV; Liu and Di Lorenzo 2018). The AMV index is derived as the latitude-weighted average of the North Atlantic low-passed filtered sea surface temperature (SST) anomaly field. Previous studies have shown that decadal variability has a shortening period and weakening amplitude in the northern high-latitude regions under global warming (Fang et al. 2014; Cheng et al. 2016; Wu and Liu 2020). They speculate that the response of decadal variability is associated with the acceleration of the ocean Rossby wave (Wu et al. 2018; Li et al. 2020). Other works imply that atmospheric stochastic forcing may be the dominant forcing for decadal variability (Clement et al. 2015; Wu and Liu 2020). However, the responses and mechanisms of decadal variability in the tropical and southern hemispheres remain unclear. Different global warming scenarios predicted in the AR6, which are based on different anthropogenic emission pathways, might indicate various ocean decadal variabilities with different impacts on the ocean system. In this research, we attempt to show the responses of decadal variability in different ocean basins to different warming scenarios.

The outline of the paper is managed as follows. Section 2 describes the dataset and methods used in this study. Section 3 includes the ocean decadal variability derived from observations, provided as a reference in Section 3.1, and presents the modeled responses of ocean decadal variability to global warming in Section 3.2. Section 4 presents the conclusion and discusses the mechanisms.

2 Data and methods

2.1 Observational data

This study employs observational data as benchmarks to outline the current ocean decadal variability. The data used here are monthly mean sea surface temperature SST (unit, °C) values extracted from the Extended Reconstructed Sea Surface Temperature Dataset (ERSST) provided by the National Oceanic and Atmospheric Administration (NOAA) (Huang et al. 2017). The dataset is organized in a 2 × 2 spatial grid, covering the period from 1854 onward. Due to the sparse data in the early years, high biases persisted until the 1870s. After the 1920s, the SST bias dropped to very low levels due to ship-based observations (Huang et al. 2015). The dataset used in this study is ERSSTv4, which extends from 1900 to 2016 and is further interpolated at a resolution of 3.75 × 3.75. ERSSTv4 has significant improvements compared with the previous versions (Smith et al. 2008), in representation of global warming. It has a stronger globally averaged warming trend and could better reflect El Niño/La Niña (Huang et al. 2015; Liu et al. 2015) and the PDO (Huang et al. 2017).

2.2 CMIP6 output

The results of nine model simulations are chosen from the World Climate Research Programme’s (WCRP) Coupled Model Intercomparison Project 6 (CMIP6) dataset. These models, including BCC-CSM2-MR, CESM2-WACCM, CMCC-ESM2, EC-Earth3-Veg-LR, FGOAL-f3-L, INM-CM5-0, MIROC6, MPI-ESM1-2-LR, and NorESM2-MM are from different institutions and countries (Table. 1). This study uses the preindustrial (PI) run as the control run; the historical (HIS) and four shared socioeconomic pathways (SSP1-2.6, SSP2-4.5, SSP3-7.0, SSP5-8.5) are taken as the different global warming experiments. The radiative forcing will increase by 2.6, 4.5, 7.0, and 8.5 W/m2 relative to the present-day conditions under SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5, respectively (O’Neill et al. 2016). All PI simulations in the CMIP6 model selected here are longer than 500 years. HIS simulations cover the period from 1850 to 2014, and SSP runs contain the period from the year 2015 to 2100, as shown in Table 1.

Table 1 CMIP6 models used in this study
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2.3 Statistical methods

We first interpolate observation data onto a grid of 3.75 × 3.75 as a benchmark, derive the annual averaged SST from the simulated monthly model results, and calculate the SST anomaly (SSTA) pattern by subtracting the climatological mean from the annual averaged values at each grid point. We then calculate the low-pass filtered data twice using a 3-year running mean for the global region (Zhang et al. 1997). To remove the trend caused by anthropogenic emissions, we remove the linear tendency within the ERSSTv4 and HIS runs and then use the empirical mode decomposition (EMD) method to remove trends in the SSP runs (Cheng et al. 2016; Wu et al. 2022). EMD uses the characteristic time scale to identify intrinsic oscillatory modes contained in the signal. It can continuously extract the components of each scale that make up the original signal from high frequency to low frequency; thus, the last component can represent the global warming trend (Flandrin et al. 2004; Wu and Liu 2020).

We separate the Pacific and Atlantic into four regions, i.e., the North Pacific (NP, 110° E–100° W, 20° N–60° N), the Tropical Pacific (TP, 110° E–100° W, 10° S–10° N), the South Pacific (SP, 110° E–100° W, 60° S–20° S), and the North Atlantic (NA, 80° W–0°, 0–70° N). The PDO, TPDV, and SPDO indices are derived as the principal components of the leading empirical orthogonal function (EOF) mode of the low-passed SSTA data over the NP, TP, and SP, respectively. Meanwhile, the AMV index is calculated by the area-averaged low-passed SSTA over the NA (Enfield et al. 2001). Then the above indices are normalized by the corresponding standard deviations (Wu et al. 2018), and global SSTA fields are regressed on the normalized indices to obtain the decadal variability patterns.

After obtaining decadal variability patterns and time series, we calculate the power spectra and standard deviation (STD) to analyze the change in decadal variabilities’ periods and amplitudes. The multimodel mean value is obtained based on the results of spectral analyses applied to each model. The regional average STD was also calculated for all four ocean regions described above.

3 Results

3.1 Ocean decadal variability

The regression coefficients of the PDO, TPDV, and SPDO show an El Niño Southern Oscillation (ENSO)-like pattern, and the AMV is characterized by a basin-scale pattern (Fig. 1a–d). For instance, the PDO can be modeled to a simple integration of the Aleutian Low variability (1st EOF mode of the sea level pressure anomaly). Moreover, the dynamic adjustment of heat content anomalies in the tropics and the teleconnection between tropical and extratropical regions are important to the PDO (Newman et al. 2016; Ding et al. 2013). Furthermore, the SP also exhibits obvious decadal fluctuations with weaker intensity than that in the NP (Fig. 1a–c). Similar to the PDO, the SPDO integrates the atmospheric forcing from the local and tropical teleconnections (Shakun and Shaman 2009). The tropics seem to play a role in synchronizing the NP and SP (Liu and Di Lorenzo 2018); therefore, the low-passed SSTA is used to discuss the tropical decadal variability below. The maximum regression amplitude of the TPDV is located in the tropics, which shows a clear link between the ENSO and the TPDV (Fig. 1b). However, it is still unclear whether the TPDV arose from ENSO events or teleconnection from extra-tropical or local atmospheric forcing. The typical AMV basin-scale pattern (Deser and Blackmon 1993; Kushnir 1994) (Fig. 1d) can be shaped by only the atmospheric forcing (Clement et al. 2015), while Zhang et al. (2016) argue for the potential opposite effect of the atmospheric signal according to fully coupled model simulations. Some previous works show clear evidence for the linkage between AMV and Atlantic Meridional Overturning Circulation (AMOC). For instance, a stronger AMOC would lead to a warmer subpolar gyre and a colder recirculation gyre (Joyce and Zhang 2010; Zhang et al. 2019).

Fig. 1
figure 1

Observed (top) spatial regression pattern, (middle) time series, and (bottom) power spectrum for a, e, and i PDO; b, f, and j TPDV; c, g, and k SPDO; and d, h, and l AMV indices (1900–2016). A 3-year running mean twice was applied to the local SST (each grid point) over the North Pacific (110° E–100° W, 20° N–60° N), Tropical Pacific (110° E–100° W, 10° S–10° N), South Pacific (110° E–100° W, 60° S–20° S) and North Atlantic (80° W–0°, 0°–70° N). And the PDO, TPDV, SPDO, and AMV indices were calculated prior to computing the regression. The dashed line and dash-dotted line in the bottom row represent 90 and 50% confidence intervals, respectively, calculated by the Monte Carlo method

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The indices of ocean decadal variability are shown in Fig. 1e–h with the power spectrum of the PDO, TPDV, SPDO, and AMV indices (Fig. 1i–l). The three peaks in the PDO power spectrum over the 90% confidence interval are calculated by the Monte Carlo method over the same length with ERSSTv4. The peaks in the power spectrum indicate the periods of 25 and 50 years, respectively (Fig. 1i). Two peaks have also been identified in the power spectrum of SPDO analysis (Fig. 1k). However, the 45-year peak only passes 50% confidence interval, as the shorter period (15–25 years) crosses the 90% confidence threshold. The power of the TPDV at 90% confidence has an obvious peak at approximately 15 years, which corresponds to a bi-decadal periodicity but lacks a multidecadal signal. In contrast, the AMV shows a stronger power at approximately 70 years and no significant signal at less than 50 years (Fig. 1l). This multidecadal variability can easily be seen from the AMV index (Fig. 1h). It is worth mentioning that there is low confidence for multidecadal variability cause the data length.

3.2 Responses to global warming

We then compare the CMIP6 coupled climate model simulations (Table 1) with the observational data. The average of HIS of the nine models reasonably reproduces the spatial patterns of the PDO, TPDV, SPDO, and AMV (b panels in Figs. S1–S4). However, subtle differences still exist between the models and observations, as explained below. The regression coefficients are smaller in the models, especially for the PDO and SPDO patterns in the tropics and the TPDV pattern in the NP and SP. In the NP, the maximum regressing coefficient is located in the Kuroshio–Oyashio Extension region (Fig. S1b) while that is seated in the central North Pacific in observation (Fig. 1d). In the TP, the observed maximum is located in the Niño 3.4 region (Fig. 1b), but it presents in the model simulations as a narrow region along the equator (Fig. S2b). Under different global warming scenarios (SSP runs), the ocean decadal variability shares a similar pattern, but all become weaker, implying the weakening of amplitude (Figs. S1–S4). Figure 2 shows this comparison in the form of a Taylor diagram (Taylor 2001), which indicates that the root mean square (RMS) differences between ERSSTv4, and the nine model members are small (green dashed line). Each circle point in Fig. 2 represents a member of the CMIP6 model, and the pink star indicates the ERSSTv4 values. Although climate models can reproduce similar patterns of ocean decadal variability, the correlation coefficients are quite low. In PDO, TPDV, and SPDO, only 37, 52, and 20% of members have correlation coefficients higher than 0.8. No member is higher than 0.7 for the AMV, which is comparable to the results obtained by using the leading EOF mode as the AMV index Fig. S5). This implies that the models do not actually appear to reproduce the observed ocean decadal variability, especially in NA. With stronger global warming scenarios (comparison between blue and red circles), the STD decreases in all decadal variabilities, which is consistent with the change in the pattern.

Fig. 2
figure 2

Taylor diagrams of a PDO, b TPDV, c SPDO, and d AMV. Pink pentagram represents ERSSTv4. Black, pink, blue, green, yellow, and red dots represent PI, HIS, SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 of nine CMIP6 models, respectively. In this diagram, the distance of a point from the origin is its standard deviation (°C) and the distance from the reference point (pink pentagram, ERSSTv4) is the root-mean-square error (RMSE) between the pattern and the reference pattern. The increment in the pattern correlation coefficient is not linear (0–0.9–0.95–0.99)

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To quantify the weakening of ocean decadal variability, we calculate the STD of the SSTA field over the global ocean (Fig. S6) and the amplitude of the response in four regions (NP, TP, SP, and NA) (Fig. 3). According to the multimodel average (black line in Fig. 3), the decadal variability of the four modes has a significant downward trend. In the mid and high latitudes (NP, SP, and NA), an obvious drop from HIS to SSP126 has been identified compared to the relatively small deviations observed from PI to HIS (Fig. 3a, c, and d). Nevertheless, the weakening trend of the TPDV in the tropic region is mild between different climate background scenarios (Fig. 3b), which means that the sensitivity of the SST variability might be weaker in lower latitude regions. A previous study found that the tropical decadal variations appear largely random under global warming (Ding et al. 2019). However, some models, such as NorESM2-MM and MIROC6, show more distinct variations in the TP, which might be relevant to the higher weight in the temperature calculation (Song et al. 2022). On the other hand, the ranges of the NP, SP, and NA are small in each scenario, but the range is larger in the TP, which shows that the model difference is much greater in the tropics. In the NP and NA (Fig. 3a and d), the strength of the decadal variability is reduced from 0.39/0.36 in the PI to 0.25/0.23 in the SSP5-8.5 run, which is almost a 40% reduction. The SP has the largest decrease (46%), and the TP has the smallest decrease (30%). Overall, the weakening of ocean decadal variability is substantial in the four different regions and is much higher at high latitudes.

Fig. 3
figure 3

The change of SST standard deviation in the a NP, b TP, and c SP, and d) NA. After removing the long-term trend and using a 3-year running mean twice, the standard deviation of yearly data was calculated at each point, and then the regional average was calculated. Nine dots in different colors represent nine CMIP6 models, and black represents multi-model mean. Combining black dots from PI to different global warming scenarios shows the trends of amplitude in the four regions

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Under global warming, ocean decadal variability shows a tendency for shorter periods. The multimodel means of the PDO, TPDV, SPDO, and AMV power spectra for the PI, HIS, SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 are shown in Fig. 4, and the main periods are shown in Table 2. To diminish the impact of the specific model, we use nine model members, which is double the size compared to the relevant previous studies (Cheng et al. 2016; Wu and Liu 2020). The shortening of the period for all four indices is also featured in most models used here (Figs. S7–S10). For the PDO period (Fig. 4a), the peaks of the PI are approximately 40 years, and this peak in the HIS becomes weaker, and the 30-year peak becomes more dominant. Under different global warming scenarios, the peaks tend to shift to shorter periods. Similarly, reductions in the period can also be seen in the SPDO and AMV. These results are still valid when using more models in CMIP6 (13 models, not shown). Two points need to be mentioned based on the power spectra of the four indices. First, the low-frequency power is weak for the TPDV PI and HIS simulations compared to the global warming scenarios (Fig. 4b), and the power shifts to high frequency when the temperature rises. Second is that the AMV only has a period of less than 50 years in future scenarios because of the data length (Table 1). This creates a discrepancy with the observation which has a 70-year period and has no signal in 35-year (Fig. 1l). It is worth mentioning that statistical confidence for decadal variability under the warming scenarios would be lower than during the PI, which is longer than the HIS and SSPs, especially then considering multi-decadal variability. Longer time series simulation data are desired to verify the multidecadal response in the future.

Fig. 4
figure 4

Multi-model mean power spectra of a PDO, b TPDV, c SPDO, and d AMV from the simulations of the PI, HIS, and four projected global warming scenarios (SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5) by nine CMIP6 models. The linear warming trend has been removed before calculating decadal variability and the power spectrum of each model has been normalized at first. The vertical lines over each power spectrum indicate cross-model standard deviation

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Table 2 The main periods of PDO, TPDV, SPDO, and AMV from the simulations of the PI, HIS, and four global warming scenarios (SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5) by nine CMIP6 multi-model mean
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In summary, the analysis above on the ensemble of the nine CMIP6 models suggests that all decadal variabilities become weaker due to shorter periods under different strengths of global warming, although the patterns are still similar to the PI condition. Specifically, the response of the TPDV is relatively modest compared to the other indices, which might represent the weaker temperature response in the tropical regions as compared to the response at higher latitudes.

4 Conclusions and discussion

A systematic study on the response of ocean decadal variability to global warming is performed for the North Pacific, Tropical Pacific, South Pacific, and North Atlantic using nine CMIP6 models under four global warming scenarios. The observed decadal variability shows that the PDO has bi-decadal and multidecadal signals, and the TPDV and SPDO only have periods of approximately 20 to 30 years while the AMV has a strong 70-year period. These four decadal variabilities have periods of approximately 30–40 years in CMIP6 models and have a robust spectral power shift from low frequency toward high frequency, which is clear in wavelet analysis (Fig. S17). The CMIP6 models can reproduce reasonable PDO, TPDV, SPDO, and AMV in the PI and HIS simulations, with the patterns changing little under the global warming scenarios. It is notable that the amplitudes become weaker with warmer background temperatures, which is robust within all decadal variabilities and is consistent with previous findings (Wang and Li 2017; Li et al. 2020). The weakening of the NP and NA is approximately 40% from the PI to SSP5-8.5 simulations in the CMIP6 modes, which is close to that seen in the CMIP5 models (37%) (Wu and Liu 2020). It is worth noting that the multimodel mean of the TP has a 30% decrease under global warming, although some models (e.g., NorESM2-MM) show a different trend from the perspective of the model average. Previous studies imply that this weakening in the decadal variabilities is caused partly by the weakened atmospheric stochastic forcing and the increased SST damping rate (Wu and Liu 2020). This result is established in the mid-high latitudes, and the tropical atmosphere forcing seems to change little under global warming (Fig. S15e–h). The shortened period is caused by the acceleration of ocean Rossby waves (Fang et al. 2014) which is also different in the equatorial regions.

Overall, under global warming, the shortening and weakening of the decadal variabilities are both robust across the global regions in CMIP6 models. And the shortening of periods is also established in the CESM large ensemble with longer data length (180 years) (Fig. S16). However, the TPDV has a weaker response which might be related to the tropical atmospheric forcing. And the pattern of the decadal variabilities will not change in the future, which suggests the dynamical process may not change under global warming. However, the expression outside the chosen regions of each decadal variability is weakened in the future scenarios (Figs. S1–4), which could be related to the change of teleconnection between different regions or the industrial aerosols or greenhouse gases forcing signal in decadal variabilities indices (Baek et al. 2022). In this study, we provide an overview of the responses of global ocean decadal variability in the future. Further studies are needed to verify these results by using longer data and understanding the mechanism in different regions.