Introduction

Global warming has been attributed to persistent increase in atmospheric greenhouse gasses (GHGs), especially in CO2, since the beginning of the Industrial Revolution1,2. Nevertheless, the upward trend in the global mean surface temperature (GMST) slowed or even paused during the first decade of the twenty-first century3, even though CO2 levels continued to rise and reached nearly 400 ppm in 2013 (https://www.climate.gov/news-features/understanding-climate/2013-state-climate-carbon-dioxide-tops-400-ppm). This episode has typically been termed the global warming hiatus (GWH)4. The GWH is often attributed to internal climate variability, external forcing, or both. Recent cooling in the middle and eastern regions of the tropical Pacific has seemingly involved a phase change of the Interdecadal Pacific Oscillation (IPO)5,6 accompanying intensified trade winds7,8. The GWH may also be associated with an increase in aerosols in the stratosphere during the period 2000–2010 because aerosols can increase optical depth, which generates countervailing forces against global warming9,10. The GWH may also be explained in part by extensive heat uptake by the deep ocean11,12 or an extremely low number of sunspots during the latest solar activity cycle13,14.

Results

The hiatus or slowdown can be identified by comparing the statistical characteristics of the GMST/GMAT series during the early 2000s with those for the decades during the late twentieth century (e.g., decadal trends and standard deviations). Figure 1a shows that a decadal platform appears in all of the 3-yr (year) smoothed GMST series of the HadCRUT4, Cowtan & Way, NOAA-old, NOAA-new, GISTEMP, ERA-Interim and NCEP-R2 datasets since the 21st century after the rapid warming period in the two or three decades of the late twentieth century. Differences among these series can be found throughout these platforms, in which the GISTEMP contains the maximum values and the ERA-Interim contains the minimum values. The NOAA-new dataset has values greater than the NOAA-old dataset, while the Cowtan & Way dataset has values greater than the HadCRUT4 dataset, which indicates that infilling and bias correction in the datasets increase the temperature, especially during the early 2000s, probably due to rapid warming in the Arctic region32,33. In addition, the decadal platform corresponds to a minimum standard deviation (STDEV) from 2001–2013, where the datasets of NOAA-new and Cowtan & Way are greater than those of the NOAA-old and HadCRUT4 (Fig. 1b), which reflects the effects of infilling or bias correction on the STDEV. In addition, the NCEP-R2 shows the largest STDEV of all the datasets, especially circa 2004. Further calculations show that the STDEVs from 2002–2012 and 2000–2014 are all larger than those from 2001–2013. Thus, the platform represents a unique period in which the interannual variabilities of the GMSTs become the weakest throughout all the seven series since the 1980s.

However, whether the early 2000s temperature platform can be regarded as the early 2000s hiatus or slowdown requires further assessment of the temperature trends surrounding this period at different scales. Linear trends in the seven series are estimated by using moving windows with widths of 11, 12, 13, 14, and 15 years using linear regressions based on the ordinary least squares (OLS) method (see data and method) to determine the location and duration of the hiatus. Figure 2a shows that the 11-yr trends in the series all reached their minimums during the period 2002–2012, and the minimum trends in the ERA-Interim are near zero, while those of NOAA-new, Cowtan & Way and GISTEMP are slightly greater than zero, corresponding to the maximum P-values obtained via an F-test and representing the most nonsignificant trends over the period. Those from the HadCRUT4, NOAA-old and NCEP-R2 are negative (below bottom axis; Fig. 2a), which correspond to a valley between two P-value peaks (Fig. 2c), implying that the period (2002–2012) for the minimum trends is shorter than the period that should be expected in the three series, except in the ERA-Interim series, in which it has the smallest trend (−0.0011 °C/decade) and the largest P-value (0.9885) among the series (Fig. 2c). For the 13-yr window, the trends of HadCRUT4, NOAA-old and NCEP-R2 become 0.0076 °C/decade, 0.0010 °C/decade and 0.0047/decade, with P-values of 0.8393, 0.9758 and 0.9271, respectively, indicating that the trends are all most nonsignificant (Fig. 2b,d). Hence, the minimum trends of ERA-Interim, HadCRUT4, NOAA-old and NCEP-R2 may become the potential candidates for the early 2000s hiatus, while those of NOAA-new, Cowtan & Way and GISTEMP can to some extent be regarded as a slowdown. However, further tests at different scales under moving windows are needed to identify whether the minimum trends in the windows of 11 years and 13 years are the smallest relative to longer or shorter windows.

Figure 3a shows that the minimum trends within a window increase with the width of the window, which corresponds to a decreasing in the P-value for the NOAA-new, GISTEMP, Cowtan & Way and ERA-Interim datasets; however, the P-values for the HadCRUT4, NOAA-old and NCEP-R2 first increase to their maximums in the 13-yr window (2001–2013; 2002–2014 for NCEP-R2) and then decrease (Fig. 3b). The weakest trend (of near zero) for the period 2002–2012 comes from the ERA-Interim, with a P-value much greater than those of the other datasets, while HadCRUT4 and NOAA-old have the weakest trends for the period 2001–2013, and the NCEP-R2 dataset from 2002–2014 had the largest P-value over the window. Hence, the four smallest trends, circled in yellow, from 2002–2012/2001–2013/2002–2014 should be regarded as the hiatus, while the others, circled in pink, from 2002–2012 (Fig. 3a) may be regarded as slowdowns, with maximum P-values less than those of the hiatus (Fig. 3b). Figure 3c depicts the minimum trends in yellow and pink circles in Fig. 3a along with uncertainties.

The smallest trends and durations and their uncertainties are listed in Table 1. By comparing the trends with their uncertainties, one can see that the trends with the P-values can be separated into two groups: 1) those for HadCRUT4, NOAA-old, ERA-Interim and NCEP-R2, with trend norms below 0.01 °C/decade and P-values above 0.8, and 2) those for NOAA-new, GISTEMP and Cowtan & Way, with trend norms above 0.01 °C/decade and P-values below 0.8. Hence, a group’s trends over the period 2002–2012 or 2001–2013 or 2002–2014 (circled in yellow in Fig. 3a) should be regarded as the early 2000s hiatuses, and the rest (circled in pink in Fig. 3a) over the period 2002–2012 may be referred to as slowdowns. The hiatus periods we found differ from those estimated by Easterling and Wehner due to the limitations of the temperature series length they used34.

In addition, a similar hiatus can also be found in the GMAT from the ERA-Interim and NCEP-R2 reanalyses, which are dynamically consistent and have full data coverage of the surface. Figure 4a shows that there is also a decadal platform similar to that observed for the GMST (Fig. 1a) during the first decade of the 21st century, and a corresponding minimum STDEV appears for the period 2001–2013 for the ERA-Interim and for the period 2002–2014 for the NCEP-R2 in comparison with the trends over the larger or smaller window widths surrounding these periods (Fig. 4b). These results indicate that the interannual variability of the GMAT also became much weaker during the platform period than during previous decades when the interannual variability of the GMAT greatly intensified in approximately 2000. Hence, 2001–2014 can be regarded as a potential hiatus period to be tested further.

Figure 5 shows that the 11- and 13-yr running trends in the GMAT series are similar to those of the GMSTs (Fig. 2a,b). The trends increased following the 1990s, reached their maximums in approximately 2000, and transitioned to decreasing to minimums over the period 2002–2012, and the corresponding P-values obtained via an F-test reached their maximums during the same period (2002–2012), which also contained their minimum STDEVs. The minimum trends for the two reanalysis datasets are also the smallest relative to those over wider windows, for example 12- or 13-yr windows. The minimum trend (with uncertainty) of the ERA-Interim dataset over the period 2002–2012 is approximately −0.0001 ± 0.0361 °C/decade, with a maximum P-value of 0.9885 (Table 1; Fig. 5a), while that of the NCEP-R2 dataset is 0.0082 ± 0.0337 °C/decade, with a maximum P-value of 0.9057 (Fig. 5b), which indicates that the minimum trends were the most nonsignificant. Over the period 2001–2013, the minimum trend is approximately 0.0216 ± 0.0259 °C/decade, with a maximum P-value of 0.6848 for the ERA-Interim dataset (Table 1; Fig. 5a), while the trend for the NCEP-R2 is 0.0377 ± 0.0245 °C/decade from 2002–2014 dataset, with a maximum P-value of 0.4581 (Fig. 5b). These trends are all greater than those from the period 2002–2012, and their corresponding P-values are also less than those from the period 2002–2012. Hence, the trends over the period 2002–2012 should be regarded as the early 2000s hiatuses based on the two reanalysis datasets because their minimum trends are all below 0.01 °C/decade.

Multiscale decomposition

The hiatus is associated with contributions from temperature components at various scales, which can easily be associated with either external forces or the internal variability of the climate system. To include the reanalysis datasets, two new time series of the GMST from the period 1889/1901–2016 are established in addition to the five time series from the gridded HadCRUT4, Cowtan & Way, NOAA-old, NOAA-new and GISTEMP datasets. The first is a combination of the 20th-century Coupled European Centre for Medium-Range Weather (ECMWF) Reanalysis (CERA-20C) dataset and the ERA-Interim (hereafter CERA-Interim), and the second is created by merging the NCEP-R2 and NOAA-CIRES Twentieth Century Reanalysis (V2c) (NOAA20C-NCEP-R2, hereafter) after bias corrections between them (see data and methods and Supplementary materials), where the ERA-Interim or NCEP-R2 is regarded as the standard reference in the correction. The seven series are decomposed into a series of orthogonal wavelet components at the cascade scales of 2a, 4a, 8a, 16a, 32a, 64a (a refers to year in wavelet analysis) and beyond (i.e., nonlinear trends at the century scale) based on the Daubechies-4 (Daub4) wavelet basis30 (see data and methods). The components are sorted into three parts: the interannual composite, with the scale of 2–8a; the multidecadal composite, with the scale of 16–64a; and the nonlinear trend at the century scale. Here, the nonlinear trend may be defined as a component of global warming because it represents the evolution of temperature at the century scale since 1889. This is after 1870, which is regarded as the beginning of the global Industrial Revolution epoch.

Global warming

Figure 8a shows that the evolutions of the interannual composites coincide well with the Niño3.4 SST anomalies for the period 1950–2016. Their correlation coefficients all exceed the critical value (0.317) at a significance level of α = 0.01 for an effective number of degrees of freedom (63; see data and methods). The coefficients are 0.480, 0.408, 0.404, 0.466, 0.381, 0.403 and 0.328 for the HadCRUT4, Cowtan & Way, NOAA-old, NOAA-new, GISTEMP, CERA-Interim and NOAA20C-NCEP-R2 datasets, respectively. The interannual variability of the GMST essentially results from an ENSO cycle that is typically described by Niño3.4 SSTA or the Niño 3 SST anomaly (see data and methods). There is also an extremely low STDEV for the period 2000–2013 for every temperature series and Niño3.4 SSTA during the second half of the twentieth century, except for CERA-Interim, in which extremely low STDEVs appeared approximately in the early 2000s and 1960s (Fig. 8b). This result reveals that the interannual variability of the GMST became extremely weak during the hiatus period (2001–2013), which was coupled with an extremely weak ENSO cycle in the east equatorial Pacific. Furthermore, the 13-yr running trends of the composites of the time series also coincide with the trends of the Niño3.4 SSTA38,39, especially those in the period 2001–2013. Hence, the cooling trend of the interannual composite most likely results from the ENSO cycle, because this result is consistent with the numerical experiment forced only by SSTAs in the east equatorial Pacific5. Calculation confirmed that the extreme cooling during the hiatus period results from warmer SST in the first half of the hiatus period (2001–2013) and cooler SST in the second half, which is associated with asymmetrical ENSO events around the middle of the period.

Discussion

The early-2000s hiatus ended as soon as a sharply warming appeared in 2015–2016 with a new extreme El Niño event developing in the east equatorial Pacific. Under such circumstances, we quantitatively examined the existence of the hiatus and its duration in various data sources, including gridded and reanalysis datasets. The results demonstrate that the hiatus has a decadal duration with minimum STDEV on average and a near-zero trend over 2002–2012/2001–2013/2002–2014 at the most nonsignificant level that corresponds to the maximum P-value obtained via an F-test. The hiatus identified here differs from that shown in published literature3,4,5,6, in which the hiatus or slowdown began with the great 1997/1998 El Niño event40, as is well known. The hiatus of 2002–2012/2002–2014 is found in the GMST/GMAT of ERA-interim and NCEP-R2 datasets, while that in the period 2001–2013 is in the GMSTs of HadCRUT4, NOAA-old. The minimum trends for the period 2002–2012 in the NOAA-new, GISTEMP and Cowtan & Way datasets are slightly higher than their counterparts in the NOAA-old and HadCRUT4 datasets, as a result of the infilling of data coverage and the bias correction of the SSTs, and their trends over the period 2002–2012 are thus regarded as slowdowns, following prior arguments on the definition of the hiatus17,21. A slowdown may be also regarded as a hiatus if the trends (0.0255, 0.02 and 0.0482 °C/decade) are considered smaller or near zero. As the 2002–2012 hiatus is included in the 2001–2013 or 2002–2014 or 2002–2012 periods, the last can be suggested as the common hiatus duration in the all GMSTs/GMATs of the nine time series included in this study. Additionally, statistical analysis reveals that the hiatus or slowdown was accompanied by a minimum STDEV, which is an additional characteristic of the hiatus that indicates that the near-zero trend over the hiatus period resulted from a platform-like segment of the time series rather than a decadal valley or ridge of a GMST/GMAT wave.

Multiscale decomposition reveals that the hiatus essentially results from a decadal balance between cooling from the interannual composite and global warming, in addition to weak warming from the interdecadal and multidecadal composite because their maximum magnitudes appeared in the positive phase after 2000. This is somewhat different from the argument that proposes the negative phase of the Interdecadal Pacific Oscillation (IPO) as the major mechanism for hiatus formation on PCA analysis6. Further decomposition shows that only the interdecadal component (scale: 16 a) makes a small contribution (through cooling) to the hiatus, while the multidecadal composite contributes weak warming. The most important finding is that the variability of the interannual composite well coincides with the Niño3.4 SST anomaly, which is of almost the same statistical characteristics as the composites, such as the running STDEV and trend, especially over the period 2001–2013 (Fig. 8b,c). This indicates that the interannual variability of the GMST is coupled with the ENSO cycle38,39, and thus, the hiatus results mainly from the east equatorial Pacific SST anomalies41, as the numerical experiment that reproduced the early 2000s hiatus was performed by using a climate model forced only by the SST anomalies in the east equatorial Pacific5.

Data and methods

The linear trend in temperature within a moving window is estimated using a linear regression (Excel function: slope) based on the OLS method48,49,50, which is used to search for the location of the hiatus or slowdown. The null hypothesis is that no trend exists, and the significance of the trend is measured by P-values obtained via an F-test using an effective degree of freedom Ne. Ne is estimated as follows

$${N}_{e}=N(\frac{1-\rho }{1+\rho }),$$
(1)

where N represents the length of the series, and ρ is the first-order autocorrelation coefficient. The uncertainty of the trend estimate can be approximated by the following formula21

$${S}_{tr}={[\frac{{S}_{e}^{2}}{{\sum }_{t=1}^{N}{(t-\bar{t})}^{2}}]}^{1/2},$$
(2)

where $$\bar{t}$$ represents the arithmetic mean of t, and $${S}_{e}^{2}$$ represents the error variance, which is defined as

$${S}_{e}^{2}=\frac{1}{N-2}{\sum }_{t=1}^{N}{e}^{2}(t),$$
(3)

where e2(t) represents the residual of the linear regression equation, and N represents the sample size rather than the corresponding effective degree of freedom, Ne21, due to the small sample size in the moving window in which the trend is estimated. The decadal STDEV is calculated with the Excel function STDEV.

In addition, the seven long-term GMST time series involved are also decomposed into series of orthogonal wavelet components at cascading scales of 2a, 4a, 8a, 16a, 32a, 64a and beyond (i.e., the century scale) for 128 sampling points (1889–2016/1887–2014) based on the orthogonal wavelet decomposition with a regional basis of Daub430.

The signal S(t) can be reconstructed as

$${\rm{S}}({\rm{t}})={A}_{5}+{\sum }_{k=1}^{5}{D}_{k},$$
(4)

where Dk represents the k-th detail of the signal at decomposition level k, and A5 represents the approximate signal at the highest level (5) for 128 samples, which is usually regarded as the nonlinear trend in the signal. The wavelet time scales of (2–8a), (16–64a) and beyond 64a represent the interannual scales, multidecadal scales and the scales beyond 64a, respectively. Here, the last one (A5) represents the global warming component of the GMST for 128 samples (1889–2016 or 1887–2014 for the NOAA-old dataset). The scale is usually proportional to the period of a periodic signal. The wavelet decomposition is conducted using Python45 (https://www.python.org/).