1 Introduction

The global warming rate keeps fluctuating despite the monotonically rising greenhouse gas emission, posing puzzles about the global temperature change mechanisms. The alarming global warming over the last quarter of the twentieth century raises widespread concerns about the climate change. However, since a then-record extreme warmth in 1998 driven by the strongest 1997/1998 El Niño event, the global temperature unexpectedly started a slow warming period which is dubbed “global warming hiatus” (Meehl et al. 2011) and lasted until 2013 (Trenberth 2015; Yan et al. 2016; Xie and Kosaka 2017; Cheng et al. 2018; Folland et al. 2018). This warming slowdown observed during 1998–2013 challenges the global warming mechanisms, as it does not match the steadily rising greenhouse gas concentration which is thought to be responsible for the global warming (Stocker et al. 2013). Since this phenomenon was observed (Easterling and Wehner 2009; Knight et al. 2009), a variety of mechanisms have been proposed to explain it, which can be roughly classified into two schools: external forcing and energy redistribution. Earlier work tends to attribute the weak warming to the incoming energy reduction due to negative external forcing. Potential causes include declining solar insolation (Lean and Rind 2009; Stauning 2014), decreased stratospheric water vapor concentrations (Solomon et al. 2010), and increased stratospheric and tropospheric aerosols (Solomon et al. 2011; Santer et al. 2014). However, further research shows that all aforementioned negative forcing is too small to offset the radiative imbalance at the top-of-atmosphere (TOA) up to 1 W/m2 (Loeb et al. 2012; Smith et al. 2015). Therefore, the climate system should continue to accumulate energy. As the surface fails to warm as fast as it did in previous decades, the excess heat must be held by other parts within the climate system. The oceans, with great depth and huge heat capacity, are generally recognized as the most likely culprits. At present, there is a growing consensus that the recent global warming hiatus during 1998–2013 primarily results from energy redistribution within the oceans (Meehl et al. 2011; Loeb et al. 2012; Guemas et al. 2013; Cheng et al. 2018; Wang et al. 2018).

Recent studies reveal that the processes rearranging heat within the oceans are closely related to large-scale climate internal variabilities ranging from interannual to multidecadal timescales (Zhang 2016; Cheng et al. 2018; Liu and Xie 2018; Chen and Tung 2018a). At interannual timescale, El Niño-Southern oscillation (ENSO) associated changes of cloud, temperature and humidity, along with variations in atmospheric and oceanic circulations, affect the radiative imbalance at the TOA and thus the global temperature (Loeb et al. 2012). And some studies point out that the recent global warming hiatus during 1998–2013 is associated with La Niña-dominated conditions in the Pacific between two super El Niño events in 1997/1998 and 2014–2016, which restricts the global temperature growth (Kosaka and Xie 2013; Banholzer and Donner 2014). However, the interannual timescale of ENSO is soon thought too short to explain a decades-long hiatus period, and more attention is turned to low-frequency Pacific decadal oscillation (PDO) or interdecadal Pacific oscillation (IPO) (Meehl et al. 2013; Trenberth and Fasullo 2013; Meehl et al. 2016). The slow pace of the global surface warming is assumed to be linked with the La Niña-like (negative) phase of the IPO or PDO since the late 1990s during which the unprecedentedly intensified Pacific trade winds cool the surface but enhance the subsurface ocean heat uptake by driving a sequence of ocean-atmosphere circulations (England et al. 2014). However, Chen and Tung (2014) argue that the Pacific has little impact on the vertical heat redistribution since the wind-driven dominant Pacific variations are difficult to penetrate to deep oceans. Chen and Tung (2018a) further illustrate that the PDO contribute little to the global temperature change because of its self-cancelling spatial patterns. Instead, the Atlantic multi-decadal oscillation (AMO) is regarded to play a more important role (Wu et al. 2011; Tung and Zhou 2013; Chen and Tung 2018a). This is because the AMO is the surface manifestation of the multidecadal variation of the Atlantic Meridional Overturning Circulation (AMOC) which directly determines the heat transport and distribution in the climate system (Chen and Tung 2014, 2018b; Kostov et al. 2014). Besides, some studies suggest that the AMO could act as a remote driver, and indirectly contribute to the warming hiatus through driving anomalous variations in tropical Pacific by a tropic-wide teleconnection (McGregor et al. 2014; Li et al. 2016; Sun et al. 2017). Overall, the interannual-, interdecadal-, and multidecadal-scale climate natural variabilities, represented by ENSO, PDO and AMO, respectively, are highlighted and individually recognized as potential causes to recent warming slowdown in previous studies, but disagreements still exist on their relative importance (Wang et al. 2018).

Moreover, the recent warming hiatus during 1998–2013 is not an isolated case. In fact, the warming and cooling episodes periodically alternate in historical records, and the hiatus during 1998–2013 is just a common case among them. The changing global warming rates are the apparent manifestation of various natural climate variabilities, especially ones ranging from interannual to multidecadal timescales (Dai et al. 2015; Guan et al. 2015; Trenberth 2015; Zhang 2016; Liu and Xie 2018). However, it is unclear during which period and to what extent these variabilities influence the global warming rate, especially which ones primarily contribute to the recent warming slowdown.

In this study, we aim to identify the key-scale natural variabilities and quantify their contribution in regulating the global warming rate. First, we decompose the global mean temperature timeseries into several quasi-periodic fluctuations and a monotonical nonlinear warming trend, and then quantify the importance of interannual-, interdecadal-, and multidecadal-scale fluctuations in modulating the global warming rate during 1850–2017, including the recent slowdown during 1998–2013. Finally, we further demonstrate that these three key-scale fluctuations mainly arise from ENSO, PDO and AMO, respectively. Our work partly reconciles the controversy over the importance of different scale natural variabilities, such as ENSO, PDO and AMO, by quantifying their contribution in the modulation of the global warming rate.

2 Data and method

To avoid the potential impact of the dataset choice and to guarantee robust, comparable and general results, in this work, we used six global combined land/marine surface temperature datasets and six sea surface temperature (SST) datasets to analyze the global warming rate change. These datasets include almost all the accessible routinely updated surface temperature observation datasets with enough temporal coverage for our research (1975–2013). Six combined land/marine surface temperature datasets are: BEST from Berkeley Earth (Rohde et al. 2013), GISS from NASA/GISS (Hansen et al. 2010), HadCRUT4 from Met Office Hadley Centre (Morice et al. 2012), HadCRUT4krig produced by Cowtan and Way (2014), JMA from JMA, and MLOST from NOAA/NCEI (Vose et al. 2012). Six SST datasets are: COBE-SST (Ishii et al. 2005) and COBE-SST2 (Hirahara et al. 2014) from JMA, ERSST5 from NOAA/NCEI (Huang et al. 2017), HadISST (Rayner et al. 2003) and HadSST3 (Kennedy et al. 2011a, b) from Met Office Hadley Centre, and ICOADS3 from NOAA/NCEI (Freeman et al. 2017). The detailed information of these 12 datasets is listed in Table 1.

Table 1 Information of surface temperature datasets used in this study
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We collected the monthly data from all the aforementioned 12 datasets and calculated their monthly global mean anomalies referenced to the monthly climatology during 1981–2010. Then the monthly global mean anomalies were decomposed into different scales using ensemble empirical mode decomposition (EEMD) (Huang et al. 1998; Wu and Huang 2009). The EEMD is a reliable and effective scales decomposition tool which can effectively divide any complicated sequences into a few intrinsic mode functions (IMFs) and a nonlinear secular trend (ST). Without linear and stationary assumptions on data (Huang et al. 1998), the EEMD is outstandingly suitable for analyzing data in the complex and coupled climate system, and particularly powerful in extracting low-frequency oscillations and the intrinsic secular trend from complex climate data (Wu et al. 2007). By employing this method, Ji et al. (2014) reveal the non-uniform features of the spatial-temporal evolution of the global land surface air warming which have not been found by linear trend. Moreover, benefiting from robust adaptivity and locality, EEMD method is insensitive to the data length, allowing us to compare components derived from datasets with different length (Wu et al. 2011).

Further, to explore the sources of three key-scale IMFs which are identified as main contributors to the global mean warming rate change, we compared their timeseries and spatial patterns with some climate indices of large-scale climate oscillations which are closely related to the ocean and notably influence the global temperature change, such as Niño 3.4, PDO, AMO and so on (Chen and Tung 2018a). Niño 3.4, PDO and AMO indices were calculated using ERSST5 based on the methods referenced to Trenberth (1997), Mantua et al.(1997) and Enfield et al. (2001), respectively. To enable these multi-scale climate indices to be comparable with the narrow-band IMFs, the typical scales of these climate indices were extracted by EEMD method. Each climate index was decomposed into eight IMFs and a ST. For Niño 3.4 index, we added up the IMF4, IMF5 and IMF6 at interannual timescale as the typical-scale variability of ENSO. In the same way, the interdecadal variability (IMF6 and IMF7) of PDO and the multidecadal variability (IMF8) of AMO were extracted to represent the typical-scale variabilities of PDO and AMO, respectively. The spatial patterns of three key-scale IMFs and three climate indices were obtained by regressing the gridded surface temperature onto each IMF and index. Taking the uncertainty from datasets into consideration, we applied the regressions to all the datasets in Table 1 except for the ICOADS3 and got similar patterns. For brevity, only the results from GISS and ERSST5 were presented for examples in this paper.

3 Results

3.1 Modulation of interannual, interdecadal and multidecadal variabilities on the global warming rate

Figure 1 shows that both global mean surface temperature (GMST) and global mean SST show a similar change, and the results from the 12 datasets are in good agreement. Six GMST and six global mean SST anomalies series consistently exhibit multi-scale fluctuations, accompanied by periodically alternating warming and cooling episodes (Fig. 1). Since 1850 there have been two obvious cooling events lasting several decades during 1880s–1910s and 1950s–1970s, and the latter one is called “big hiatus”. The short-term hiatuses like the recent one during 1998–2013, which last one or two decades with small warming or cooling trend, occur more frequently (Fyfe et al. 2013, 2016). This quasi-periodic warming slowdown or slight cooling is believed to be involved in various natural variabilities of climate system (Dai et al. 2015; Guan et al. 2015; Trenberth 2015; Zhang 2016; Liu and Xie 2018).

Fig. 1
figure 1

a Global mean surface temperature (GMST) and b global mean sea surface temperature (SST) anomalies (°C, relative to 1981–2010) derived from observed datasets. The relevant datasets are described in Table 1

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To extract the global temperature natural variability signals at different timescales from intricate temperature data, we apply the EEMD method to all GMST and SST monthly anomalies series derived from observational datasets. The decompositions of GMST timeseries from HadCRUT4 and SST timeseries from ERSST5 are shown as examples in Fig. S1. Every temperature series is decomposed into eight IMFs and a remainder. The IMFs are a set of fluctuations at different timescales and the remainder is the intrinsic nonlinear ST. The IMF4, IMF5 and IMF6 are at interannual timescale and the sum of them is named as the interannual variability (IAV). The IMF7 at interdecadal timescale and IMF8 at multidecadal timescale are called interdecadal variability (IDV) and multidecadal variability (MDV), respectively. The three key-scale IMFs (IAVs, IDVs and MDVs) and the STs derived from six GMST and five SST datasets are shown in Figs. 2 and S2, respectively. Note that the data length of the ICOADS3 (1960–2017) is too short to clearly distinguish the ST and the MDV, which deprives its comparability with other records and therefore it is excluded from Fig. S2. Figures 2 and S2 show that the IMFs decomposed from different datasets are in good accordance. The IMFs at the same timescale from different datasets share similar periods, amplitudes, and consistent phases. Periods for three key-scale IMFs (IAV, IDV and MDV) of GMST are 4.06 ± 0.39 (4.06 is mean value, and 0.39 is two standard deviations), 21.39 ± 1.34 and 67.03 ± 8.40 years, and the corresponding amplitudes are 0.11 ± 0.01, 0.04 ± 0.00, 0.10 ± 0.03 °C, respectively. The periods and amplitudes of three key-scale IMFs of SST are 4.48 ± 0.70, 22.66 ± 3.53, and 68.70 ± 16.32 years, and 0.09 ± 0.02, 0.03 ± 0.01, and 0.08 ± 0.05 °C, respectively. The STs from different datasets also evolve in the same way (Figs. 2d and 2Sd), they nearly increase linearly after the first quarter of the nineteenth century. The warming rates during the last four decades (1978–2017) are 1.46 ± 0.41 °C/decade for GMST and 1.06 ± 0.34 °C/decade for SST. The larger amplitudes of three IMFs and higher warming rate of ST derived from GMST than those from SST are associated with the amplification of the temperature change signals by the land that has small heat capacity.

Fig. 2
figure 2

a–d Three key-scale IMFs and STs extracted by EEMD method from six observational derived GMST monthly anomalies in Fig. 1a. e The reconstructed temperature series by linear additivity of left four terms superimposed on the original GMST records. f The detrended reconstructed temperature series by superposition of three key-scale IMFs superimposed on the detrended GMST records. The colors represent different datasets

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The three key-scale IMFs and the ST explain nearly all the global temperature change. This can be seen in Figs. 2, S1, and S2. The Figs. S1c and S1f from the bottom up successively show the superposition of the ST and one more IMF ranging from multidecadal to interannual scales. As more IMFs join, the superposition series get closer to the original series. After the IAV is added, the superposition is already able to accurately reproduce the original temperature timeseries. Therefore, we take the superposition of four terms (IAV, IDV MDV and ST) as the reconstruction of the original temperature timeseries (Figs. S1c and S1f). As shown in Figs. 2e and S2e, the reconstruction series capture the main temperature change signals in all datasets. During the study period (1850–2017), the variance ratios of the reconstructed series to the original series are 89 ± 4% for GMST and 94 ± 3% for SST. Among four terms, the ST represents the pure anthropogenic warming (Wu et al. 2011) and is responsible for the monotonous growth of the global temperature. It presents almost a linear increase with near constant rates since 1920s and hence has not much influence on the warming rate change after 1920s (Figs. 2d and S2d).

In contrast, the three key-scale IMFs are primarily responsible for the variable rates of global warming. After the ST is removed from the GMST and SST timeseries, the unforced natural fluctuations underlying the global temperature evolution come to light. In Figs. 2f and S2f, the detrended temperature series clearly present quasi-periodically alternating warming and cooling episodes which are primarily regulated by IAV, IDV and MDV. Over the whole instrumental period (1850–2017), the three key-scale IMFs together amount to 64 ± 7% of GMST and 84 ± 8% of SST unforced fluctuation variance. The IAV, IDV and MDV account for 39 ± 9%, 5 ± 1% and 20 ± 6% of the GMST fluctuation variance, and 51 ± 18%, 5 ± 3% and 27 ± 22% of the SST fluctuation variance, respectively. Among the three IMFs, the IAV provides the greatest contribution to the unforced global temperature variability during 1850–2017, followed by the MDV. The contribution of IDV is obviously smaller than IAV and MDV. These results agree well with Chen and Tung (2018a) who examine the interannual, interdecadal and multidecadal climate variability modes and estimate their contribution to global mean temperature variability by employing a pairwise rotated EOF method.

However, here it is more important to illustrate how different-scale variabilities modulate the warming rate and to estimate the roles of three key-scale variabilities in regulating the global warming rate. For a certain period, the warming rate is generally defined as the linear trend of the temperature timeseries during this period. Then the warming rate change from one period to another is indicated as the linear trends difference between these two periods. As the IMFs are quasi-periodic cycles, their linear trends are sensitive to the start and end points (Wei et al. 2015). Considering a special case, linear trends for two interceptions located on opposite sides of the peak or trough have opposite signs. Generally, the MDV, with six- to seven-decades period and large amplitude, dominates the long-term global warming rate change while the IAV and IDV, with higher frequencies than MDV, have more influence on relative short-term trends such as the interannual and interdecadal timescales.

As an example, the recent slow warming during 1998–2013 can be primarily attributed to the IAV and IDV. Essentially, the recent hiatus period is noticed because the warming rate during 1998–2013 is remarkably smaller than previous rapid warming (Fyfe et al. 2016). As the 1998–2013 is defined as the hiatus period, the well-known rapidly warming period 1975–1997 is chosen as the reference period here. The linear trends of IAV, IDV, MDV and ST during two periods are calculated to investigate their contributions to recent global warming rate change. The linear trends change between the hiatus period (1998/01–2013/12) and previous rapid warming period (1975/01–1997/12) can be fully explained by these four terms. As Fig. 3 shown, the linear trends for those two periods derived from the reconstructed series are almost the same as those from original series. During the rapid warming period (1975/01–1997/12), the GMST warms at the rate of 0.16 ± 0.02 °C/decade which is virtually all from the warming ST and the warming phase of MDV. The ST explains 67 ± 12% (0.11 ± 0.02 °C/decade) and the MDV explains 33 ± 8% (0.05 ± 0.01 °C/decade) of the warming rate of this period. Whereas the IAV and IDV with near-zero trends contribute little to the strong warming during this period. During the hiatus period (1998/01–2013/12), both the ST and the MDV continue to warm with a slightly higher rates than rapid warming period and together result in a 0.19 ± 0.05 °C/decade warming rate. However, 59 ± 22% of this rate is canceled out by the negative trends from IAV (36 ± 12%, − 0.07 ± 0.01 °C/decade) and IDV (23 ± 14%, − 0.04 ± 0.02 °C/decade). Similar results can be drawn from SST data. During the fast warming period, the warming ST and the warming phase of MDV are respectively responsible for 66 ± 26% (0.08 ± 0.02 °C/decade) and 21 ± 5% (0.03 ± 0.01 °C/decade) of the SST warming at 0.12 ± 0.03 °C/decade. During the following hiatus period during 1998–2013, ST and MDV continue to lead to a warming at 0.12 ± 0.06 °C/decade, however, 65 ± 38% is offset by the cooling trend of IAV (36 ± 16%, − 0.04 ± 0.02 °C/decade) and IDV (29 ± 32%, − 0.03 ± 0.04 °C/decade). In summary, the rapid global warming since 1975 is a result of concurrence of the steadily warming ST and the warming phase of MDV, however, over half is offset by the cooling trend from the IAV and IDV during 1998–2013, which directly leads to the current warming slowdown.

Fig. 3
figure 3

Linear trends of IAV, IDV, MDV and ST for a GMST and b SST during the rapid warming period (1975/01–1997/12) and warming hiatus period (1998/01–2013/12) derived from long observational datasets in Figs. 2 and S2. The word “Reconst.” represents the reconstructed GMST or SST timeseries by superposition of left four terms and the word “Original” represents the original GMST or SST timeseries. The diamonds or triangles at the center of the bar indicate the mean trends of six GMST series in Fig. 2 or five SST series in Fig. S2 while the error bars indicate twice standard deviations apart from the mean trends

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Specifically, during the hiatus period, the cooling trend of IAV results from the decadal variability of its amplitudes while the cooling trend from IDV is along with its descending phase. During the previous rapid warming period (1975/01–1997/12), the IAV presents seven complete cycles with similar amplitudes without significant variations and the IDV displays roughly one complete cycle, so both trends of IAV and IDV calculated by a least-squares fit method are near-zero. However, during the hiatus period (1998/01–2013/12), the IAV keeps small amplitudes after the record in 1998, thus show an evident negative trend. That means the decadal variability of the amplitudes of an interannual-scale variability could lead to a decadal trend. Meanwhile, the IDV passes its peak and converts to a descending phase, presenting a negative linear trend, too. Consequently, two negative trends from IAV and IDV cancelled out over half of the warming from the ST and MDV during the hiatus period. It should be noted that the MDV transformed to the ascending phase since the mid-1970s and showed similar warming rates during the rapid warming period and recent hiatus period, failing to account for the warming slowdown. But if the concerned periods change, the influence of MDV could probably not be ignored. For example, the big hiatus during 1950s–1970s, with distinctly lower warming rate than previous decades, is mainly cooled by the descending phase of MDV following its peak in 1940s.

3.2 The physical sources of global IAV, IDV and MDV

To trace the physical sources of the three key-scale IMFs (IAV, IDV and MDV), we compare them with some well-known modes of climate internal variability with profound influence on global climate system. We find that the IAV, IDV and MDV signals mainly originate from three notable large-scale natural climate oscillations: ENSO, PDO and AMO, respectively. The detailed calculations for the Niño 3.4, PDO and AMO indices can be found in Sect. 2. Figure 4 displays the three key-scale IMFs (IAVs, IDVs and MDVs) derived from six observational GMST timeseries and the typical-scale variabilities of three climate indices (filtered indices) calculated from ERSST5. The IAVs, IDVs and MDVs are consistent with the typical-scale variabilities of ENSO, PDO and AMO indices, respectively. For each dataset, we individually compute the correlation coefficients between each IMF and the corresponding-scale climate index: IAV and Niño 3.4, IDV and PDO, MDV and AMO. As six observational datasets start from different times, to ensure the correlations are during the same time span and to avoid the early data-sparse era, the period 1900–2017 is selected to calculate the correlation coefficients. The correlation coefficients of three-scale pair timeseries from six datasets are 0.55 ± 0.04 (0.55 is mean value, and 0.04 is two standard deviations), 0.41 ± 0.09 and 0.84 ± 0.20, respectively. Even the lower limits of three coefficients pass the t test with 95% significance level, indicating the three GMST IMFs and three climate indices are pair significantly correlated.

Fig. 4
figure 4

Normalized IMFs (IAVs, IDVs and MDVs) and climate indices (Niño 3.4, PDO and AMO). The IMFs (colorful curves) are the normalization of the IAVs, IDVs and MDVs in Fig. 2 which are decomposed from 6 monthly GMST timeseries in Fig. 1a. The colors of IMFs indicate different datasets. The climate indices (gray bars and black curve) are calculated based on ERSST5 and also have been normalized here. The gray bars show the original unfiltered monthly indices and the black curves show the EEMD band-pass filtered indices representing the corresponding typical-scale variability

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To further examine the relationships between three IMFs and three climate indices, we identify their spatial patterns by individually regressing the global gridded surface temperature on each IMF and the typical-scale variability of each climate index during 1900–2107 in Fig. 4. Figure 5 show the spatial structures of three IMFs and three climate indices based on GISS dataset. Actually, we calculated the spatial patterns based on all six observational combined land/marine datasets, considering the uncertainty from datasets. Six datasets display analogous spatial structures and the patterns based on GISS are presented for example. All the datasets consistently show that the spatial patterns of IMFs (left panels) agree well with those of corresponding-scale climate indices (right panels). The spatial structure of IAV are identical to that of ENSO. The spatial correlation coefficient between the IAV and the interannual variability of Niño 3.4 is 0.73 ± 0.14. The IDV pattern matches well with the interdecadal variability pattern of PDO. The spatial correlation coefficient between them is 0.67 ± 0.17. The MDV highly resembles to the multidecadal variability of AMO and the spatial correlation coefficient between them is 0.86 ± 0.34. The minimum values of these spatial correlation coefficients are significant at 95% level, which provides further evidence that three key-scale IMFs mainly arise from the corresponding-scale variability of three climate oscillations.

Fig. 5
figure 5

The spatial patterns of three key-scale IMFs and the typical-scale variabilities of three climate indices based on GISS combined land/marine surface temperature dataset during 1900–2017. The left spatial patterns (a, c and e) are obtained by regressing the global surface temperature onto the normalized IAV, IDV and MDV timeseries during 1900–2017 based on GISS dataset (blue curves in Fig. 4). The right panels (b, d, f) are the global surface temperature regressed onto the normalized typical-variabilities of three climate indices during 1900–2017 (black curves in Fig. 4). The spatial correlation coefficients between three-scale pair temperature anomalies based on GISS are 0.82, 0.72 and 0.88, respectively

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However, it should be noted that the ENSO, PDO and AMO are responsible for most of the IAV, IDV and MDV signals, respectively, but not the globe. We notice the correlations between IDV and PDO are generally lower than those between IAV and ENSO and those between MDV and AMO, whether for time or space, although they also pass the t-test with 95% significance level. This suggests the PDO may be not enough to explain the global IDV and there may be other sources contributing to the IDV. For example, there are noticeable differences between IDV and PDO located in northern and southern Atlantic oceans where are dominated by the AMO. So, the AMO is expected to partly plug these gaps. After blending the interdecadal variability of AMO signals into the PDO, the discrepancy over the southern Atlantic Ocean is compensated (Fig. S3). This indicates the AMO not only accounts for MDV but also partly contributes to IDV, at least over the southern Atlantic Ocean. But the IDV warming over the Central Asia remains lack in Fig. S3d, implying that the PDO and AMO are still insufficient to explain the interdecadal signals here.

In addition, as the low-frequency variability at interannual, interdecadal and multidecadal scales mainly originate from the ocean, we also examined the spatial-temporal structures of three-scale SST variabilities and draw consistent results with those from combined land/ocean datasets. The temporal correlation coefficients of three-scale pair timeseries from five SST datasets are 0.64 ± 0.07, 0.32 ± 0.28 and 0.84 ± 0.27, respectively. The spatial correlation coefficients of three-scale pair SST patterns from five SST datasets are 0.94 ± 0.01, 0.61 ± 0.41 and 0.82 ± 0.31, respectively.

Different mechanisms have been proposed to be responsible for the global surface temperature changes accompanied with different modes of climate variability. Previous studies suggest that the global surface temperature change is controlled by the tropical Pacific SST which is in turn governed by ENSO, the strongest internal variability with global impacts at the interannual timescale (Roemmich and Gilson 2011; Kosaka and Xie 2013, 2016). The ENSO exerts considerable influence on the surface temperature through changing both the global ocean heat distribution (Roemmich and Gilson 2011) and the net radiation imbalance at the TOA (Loeb et al. 2012). Generally, the El Niño (La Niña) years are significantly globally warmer (cooler) than neutral years (Trenberth 2002). Recent studies reveal that the recent warming slowdown can be explained by the frequency variability of El Niño and La Niña events or different El Niño types. Kosaka and Xie (2013) show that the La Niña events dominate the Pacific during 1998–2013, leading to a decadal cooling here and further slowing the global warming rate over this period. Banholzer and Donner (2014) suggest that as atmospheric teleconnections differ between traditional eastern Pacific (EP) and central Pacific (CP) events, the global surface temperatures are anomalously warm only during EP El Niño events but not during CP El Niño events. Therefore, the frequency variability of different El Niño types will cause decadal variability in rates of global surface warming, including the recent slowdown. Similarity, Cheng et al. (2015) imply the global warming rate strongly depends on the frequency variability of El Niño and La Niña events. They find there are more El Niño events at the early stage of the recent hiatus period and more La Niña events appear in the late stage, which converts the anomalous warming to anomalous cooling and results in a cooling trend. Risbey et al. (2014) provide reasonable estimates of the recent 15-year warming rate using models with ENSO largely in phase with the real world. Actually, all abovementioned studies, including this paper, partly attribute the recent slowdown to the phase and amplitude decadal variability of ENSO from different aspects, although the cause of the decadal variability of ENSO remains unclear.

However, as the interannual timescale of ENSO is commonly supposed to be too short to explain the decadal scale hiatus period, more studies focus on the low-frequency variability such as PDO and AMO. PDO is the most popular candidate accounting for the recent slow pace of the global surface warming (Meehl et al. 2013, 2016; Trenberth and Fasullo 2013). England et al. (2014) clarify the physical mechanisms on how the PDO slows the global warming. The PDO transfers to negative (La Niña-like) phase since the late 1990s, characterized by a considerable intensification of the Pacific trade winds which drive a sequence of ocean-atmosphere circulations changes and alter the ocean heat uptake. The anomalously strong Pacific trade winds accelerate the surface currents, the Equatorial Undercurrent and the Pacific shallow overturning cells, which in turn enhance the subsurface ocean heat uptake but cool off the surface over the tropical Pacific, thereby the GMST. Meanwhile, followed the intensified trade winds, the wind-driven Ekman poleward transport increases and strengthens the equatorial upwelling in the central and eastern Pacific, cools the surface there and ultimately the GMST, too.

More recently, however, the roles of Pacific in rearranging the ocean heat and cooling the global surface temperature are questioned. Chen and Tung (2014) point out that the wind-driven dominant Pacific variations are difficult to penetrate to deep ocean. Further, they indicate that with compensating warm-cold spatial pattern, the PDO directly contributes little to the GMST change (Chen and Tung 2018a). In the same year, Cheng et al. (2018) also show PDO fails to fully explain the global OHC changes. Instead, the AMO has been proved to play a key role mainly through two processes. On the one hand, the AMO is the SST imprint of the multidecadal variation of the AMOC which directly determines the heat transport and distribution in the climate system (Knight et al. 2005; Chen and Tung 2018b). Chen and Tung (2014) attribute the recent warming slowdown primarily to heat delivery to the deep Atlantic and Southern oceans which is driven by a recurrent salinity anomaly in the subpolar North Atlantic. In 2018, they further investigate the relation of the AMOC phase and the global surface warming rate and highlight that during an accelerating phase from mid-1990s to the early 2000s, AMOC held about half of the global excess heat, and in turn brought about a global surface warming slowdown (Chen and Tung 2018b). On the other hand, there is a close connection between the Atlantic and Pacific variability on decadal timescales (Cai et al. 2019). Li et al. (2016) find the Atlantic dominates the tropical SST and circulation changes through tropic-wide teleconnection. McGregor et al. (2014) reveal the pronounced acceleration of Pacific trade winds during hiatus period originates from the anomalous warming Atlantic. Since the early 1990s, the AMO turns to the positive phase, the rapid warming Atlantic SST generates an inter-basin sea level pressure see-saw, strengthening the Walker circulation and the Pacific trade winds which further amplify the tropical eastern Pacific cooling. Sun et al. (2017) prove the SST multidecadal variability of the tropical western Pacific can also be attributed to the atmospheric teleconnection forced by the AMO warming phase.

In this work, the relative importance of three-scale variabilities in global temperature variability has been implied by the shaded values in the left panels of Fig. 5 as the IMFs timeseries have been normalized before the regression. The three-scale variabilities show different importance in different regions since they are caused by different climate processes. The ENSO-like IAV dominates the tropical Pacific, while the PDO-like IDV and AMO-like MDV prevail over the pan-Pacific and Atlantic Oceans, respectively. The spatial standard deviations of IAV, IDV and MDV are 0.11 ± 0.02, 0.07 ± 0.02 and 0.14 ± 0.10 °C, respectively. On the whole, during 1900–2017, the MDV has the largest amplitudes, followed by IAV, while the IDV shows smaller amplitudes than MDV and IAV. This ranking is slightly different with the results draw from the variance ratios in Sect. 3.1 owing to different periods and uncertainty from datasets. Specifically, at time scales shorter than decade, the ENSO dominates the global temperature high-frequency variability. At decadal and longer time scales, both the temporal amplitude and spatial variance of AMO-like MDV are larger than those of PDO-like IDV (Figs. 2b, c and 5c, e). Besides, AMO not only accounts for MDV but also partly contributes to IDV. Add all those together, the AMO play the leading role in global temperature low-frequency variability. This conclusion seems to be contrary to the larger amplitudes of PDO than AMO (Fig. 5d, e). The minor contribution of PDO to the global temperature variability has been explained by Chen and Tung (2018a) as that the warming and cooling centers in PDO spatial pattern cancel each other, which diminishes the global average contribution of PDO.

4 Discussion and conclusions

In summary, the global temperature change is dominated by three key-scale IMFs (IAV, IDV and MDV) and a ST. The three key-scale IMFs modulate the global warming rate as the ST, which represents the human-induced global warming, increases with a near constant rate since 1920s. For instance, the recent global warming slowdown during 1998–2013 is primarily attributed to the negative trends of IAV and IDV. The steadily warming from ST is accelerated by the warming phase of MDV since 1975. However, during 1998–2013, 59 ± 22% of GMST and 65 ± 38% of SST warming are offset by the obvious cooling trends from the IAV and IDV, which directly leads to an apparent warming slowdown. Further, our calculation shows that the global mean IAV, IDV and MDV signals in turn mainly come from ENSO, PDO and AMO, respectively.

We partly reconcile the controversy over the importance of different-scale natural variabilities by quantifying their contribution in regulating the global warming rate. Our results show that rather than one-scale variability controls the warming rate change alone, the interannual-, interdecadal- and multidecadal-scale variabilities combine to dominate the global warming rate change. Specifically, the ENSO-like IAV accounts most of the global temperature high-frequency variability. At decadal and longer time scales, the AMO-like MDV dominates the temperature low-frequency variability. Although the PDO-like IDV dramatically affects the Pacific regional climate change, its direct contribution to the global mean temperature variability is obviously smaller than AMO-like MDV. Notably, the ranking of three scales varies with time and region. For example, the warming slowdown during 1998–2013 can be primarily attributed to the decadal variability of ENSO-like IAV and the descending phase of PDO-like IDV. This conclusion does not support the prevailing view that the PDO is the leading contributor to the current hiatus and refutes the argument that the interannual timescale of ENSO is too short to explain the decades-long hiatus period. Instead, we illustrate the interannual-scale ENSO can remarkably impact the decadal-scale trend because its amplitudes present decadal variations. This result provides observational evidence for the conclusion drawn from models (Risbey et al. 2014). Considering the decadal variability of ENSO amplitudes, the super El Niño event in 2014–2016 could be followed by some relatively weak El Niño or La Niña events and may result in a cooling trend as 1997/1998 El Niño did. Moreover, the AMO is the primary contributor to the global temperature low-frequency variability. Based on its period and the tremendous thermal inertia of the ocean, the AMO has reached its peak during the last decade and will probably shift to a descending episode which may persist over several decades. These two cooling effects may bring us to another warming hiatus in the next one or two decades.

Essentially, this work emphasizes the vital role of natural variability in changing the local linear trends which represent the warming rates of corresponding periods. Our results imply that to rightly attribute the climate change and accurately forecast future climate, more attention should be paid to various quasi-periodic natural variabilities, particularly ones at interannual, interdecadal and multidecadal scales. Of upmost importance, the key points to improve the simulation and prediction skills of climate models lie in correctly distinguishing the true anthropogenic warming from natural variability and accurately simulating the phase, period and amplitude of important natural variability, in which the phase is particularly important. Unfortunately, even the state-of-the-art CMIP5 models still confuse the natural climate variability and the anthropogenic warming trend and show low skills for natural variability simulations, which is the primary cause that they fail to simulate the recent global warming hiatus (Wei and Qiao 2017). When one brings the internal variability of the models in phase with the real word, the models will provide quite good estimates of the recent warming rate (Risbey et al. 2014). For example, Kosaka and Xie (2013) perfectly reproduced the global warming hiatus by prescribing the observed SST anomalies in the equatorial eastern Pacific as a pacemaker in their coupled global climate model. The climate in equatorial eastern Pacific, a key region of air-sea interaction, shows strong interannual and interdecadal variabilities and relatively weak multidecadal variability (Fig. 5) with global influence by various coupled dynamics and teleconnections processes. The observed SST anomalies in this region provide accurate natural climate variability for climate model. Essentially, the SST prescription imposes the model SST to be restored to the observed state and forces the model to lock phase with the observed natural variability in this region. The model then propagates the natural variability signals through the complicated dynamic system and consequently gives reasonable simulation of global warming rate. In the same way, England et al. (2014) successfully simulated the recent warming hiatus by prescribing the Pacific trade winds. Therefore, to improve the simulation and prediction skill of climate change and correctly attribute the climate change, the climate models should exactly separate the external forced change from the unforced natural variability and enhance the ability to simulate some key natural variability like the AMO, ENSO and PDO.