Identifying the early 2000s hiatus associated with internal climate variability

This study focuses on re-examining the early 2000s hiatus and the associated key components of the global mean surface temperature (GMST) using multiscale statistics for five well-known gridded surface temperature and two reanalysis datasets. The hiatus is characterized as a near-zero trend on the decadal scale corresponding to the maximum P-value via an F-test in statistics. The results reveal that the hiatus exists in both the GMST and global mean air temperature (GMAT) time series, rather than in global warming component, which has maintained an approximately constant rate of change of approximately 0.08 °C/decade over the past three decades. The hiatus’s duration is different from that of time series such as 2002–2012/2001–2013/2002–2014 in HadCRUT4, NOAA-old, ERA-Interim and NCEP-R2. The newly gridded datasets with data infilling or bias correction for interpreting the sea surface temperature (SST) measurement from the old versions show a slightly higher trend from 2002–2012 than the hiatus, which is thus regarded as a slowdown. Comparison suggests that the hiatus should be during the period 2002–2012. Orthogonal wavelet decomposition of the temperature time series shows that the hiatus was merely a decadal balance between cooling from interannual variability and global warming, in addition to weak warming from interdecadal and multidecadal climate oscillations. In addition, the evolutions of the GMST’s interannual composites are well coincided with Niño3.4 SST anomalies, which is consistent with the numerical simulation performed by Kosaka and Xie in 2013. Hence, it is the anomalous El Niño Southern Oscillation (ENSO) events in the early 2000s that caused the hiatus despite a constant rate of global warming and the maximum magnitude of the multidecadal composite that led to the limited contribution to the trend during this period. The multidecadal composite follows a downward path, which implies that future climate conditions will likely rely on competition between multidecadal cooling and global warming if the multidecadal climate cycle repeats, as was experienced during the second half of the twentieth century.

observation that could influence the GMST. Two noticeably updated datasets were released near the end of the hiatus. The first dataset (hereafter Cowtan & Way) 17 was updated via infilling over the Arctic region and the African continent from the Hadley Centre-Climatic Research Unit Version 4 (HadCRUT4) [17][18][19][20] , and the second, which was a new bias-corrected dataset (hereafter NOAA-new) 21 , was updated from an older with infilling and bias-correction from the National Oceanic and Atmospheric Administration (NOAA) global surface temperature dataset (hereafter NOAA-old) 22,23 . The presence of the hiatus in HadCRUT4 was regarded as the result of sparse data over the Arctic region and African continent, which suppressed the GMST trend 17 , while the hiatus was considered to even possibly be an artifact created by data biases in the NOAA-old dataset or its earlier version 21 . These problems affect observation and the definition and identification of the hiatus 24,25 . Thus far, two approaches have been used to identify the hiatus or slowdown 26 : (i) when the trend in GMST is observed to be approximately zero or nonsignificant at the 0.05 significance level and (ii) when the decadal trend is observed to be less than the long-term trend, in addition to the identification of the change point (CP) in the trend 27 . The first approach is a well-known general measure for trend in scientific literature. The second approach seems to be unsuitable for assessing the hiatus or slowdown at a decadal scale because the decadal trend during the hiatus period is compared with the long-term trend from 1951 to 2012 1 , which can be influenced by interdecadal and multidecadal climate oscillations. The additional approach involves identifying the CP in the trend and may be difficult to use in identifying the early 2000s hiatus because the formation of the hiatus (in terms of trend) occurred gradually from the previous maximum warming trend to the following minimum trend. Hence, arguments seem to result not only from the biases in the SST measurements 16,21 or sparse data in the datasets 17,20 but also from the absence of properly quantitative assessments of the contributions of multiscale components to GMST, which are easily tied to the mechanisms responsible for the hiatus (e.g., internal factors or external forcing). This study first quantitatively re-examines the existence of the hiatus in the HadCRUT4, Cowtan & Way, NOAA-old, NOAA-new, NASA GISS Surface Temperature (GISTEMP) 23 , ERA-Interim 28 and NCEP-DOE Reanalysis 2 (hereafter NCEP-R2) 29 series and the reanalysis global mean air temperature (GMAT) series. Furthermore, it compares the potential hiatus in the gridded instrumental data and reanalysis datasets to obtain an overarching statement, where the former series are based on some kind of three dimensional interpolation methods, and the latter are produced by a four-dimensional data assimilation system with many more four-dimensional observations (regular and irregular) than the former, leading to datasets that are dynamically consistent. Second, the contributions from the multiscale components are analyzed using orthogonal wavelet decomposition 30 to distinguish the key components in terms of their contributions to the hiatus and their potential links with the El Niño/Southern Oscillation (ENSO) cycle in the equatorial eastern Pacific 31 .

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 21 st 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 region 32,33 . 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.   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.  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 used 34 .
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 21 st 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.  , 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;   Global warming. Figure 6a shows that nonlinear trends increased monotonically from the 1900s to the 2000s, which implies that the global climate at the century scale warmed gradually over the past hundred years. Fig. 6d shows that global warming started in the 1900s rather than in 1870, which was the first year of the Industrial Revolution epoch, as is well known, and that the warming gradually accelerated towards its maximum value just after World War II (1950s). And the warming turned to declining until the 1980s and then exhibited almost constant trends for approximately three decades (excluding the trends in NOAA-old). Almost all of the maximum trends appeared over the period [1945][1946][1947][1948][1949][1950][1951][1952][1953][1954][1955][1956][1957]    on average, from the 1980s to the 2000s, while the NOAA-old trend kept decreasing during the last three decades at a rate similar to that during previous decades after World War II. There was no GWH in the early 2000s in the century-scale component of the GMSTs of the seven series. In addition, data infilling or bias correction in the SST measurements caused the NOAA-new trend to be higher than that of the NOAA-old in the component, while no significant difference was found among those from the 1940s-1990s for HadCRUT4 and Cowtan & Way, except for in the 2000s, when the latter's trend became higher than the former's, which may reflect accelerated warming in the Arctic region in recent decades. Furthermore, the trend of NOAA20C-NCEP-R2 is above that of CERA-Interim and coincides with the NOAA-new after World War II. The difference may result from the data assimilation systems of the two reanalysis datasets. As the relative strength of the warming differs before and after World War II, this may reflect the influences of the different interpolation approaches on the properties of the datasets, as there was extremely sparse data coverage in the early part of the time series.
Interannual and multidecadal oscillations. Figure 6b shows that there is an apparent oscillation with a large magnitude at the scale of approximately 16-64 a for all the GMST series, in which the negative phases in the 1960s-1970s correspond to a relatively cool period in the global climate during the twentieth century, as is well known, and then the composites increased to a new maximums in 2016. As shown in Fig. 6a and b, the hot global climate experienced since the 1980s resulted from an overlap in global warming and a positive phase in the multidecadal composite, while the cool decades (1960s-1970s) appeared only with the negative phase of the multidecadal composite (Fig. 6b). However, Fig. 6b (Fig. 6e). This result indicates that the multidecadal composite makes a minimal contribution to the GMST trend during the hiatus period, except for that of the HadCRUT4, which exhibits a small cooling trend during the period that works against a trend of global warming. Hence, the global warming trend cannot be balanced by the trend in the multidecadal composite during this period. However, the variability of the interannual composite (2-8 a) becomes weak over the period 2001-2013, with an apparent cooling trend (Fig. 6c,f). By comparing Fig. 6d,e, and f, one can see that the early 2000s hiatus results from an overlap of the three trends (i.e., a nonlinear trend and those of the multidecadal and Additionally, there is a significant difference between the multidecadal composites of the two reanalysis datasets and between their trends, which may reflect the different data assimilation systems and SSTs because the composite may be correlated with the interdecadal and multidecadal modes of climate, such as the Atlantic Multidecadal Oscillation (AMO) 35 , Pacific Decadal Oscillation (PDO) 36 or Interdecadal Pacific Oscillation (IPO) 37 . Similarly, the differences between NOAA-new and NOAA-old are larger than those between HadCRUT4 and Cowtan & Way, reflecting the importance of bias correction in the SST measurement. Figure 7a and b clearly show the differences in the three composite trends for the seven time series, which seemingly result from different interpolation approaches/data assimilation systems, bias corrections or numbers of observation records used. For example, the infilling and bias correction both increased warming and reduced cooling of the composite at the interannual scale from 2002-2012, but for 2001-2013. The increase in the trend in NOAA-new relative to NOAA-old is larger than that in Cowtan & Way relative to HadCRUT4, which reflects the effect of bias correction on the reported warming (Fig. 7). In addition, the infilling or bias correction has more influence on the trends in the multidecadal composites than in other composites over the same periods, implying that temperature changes in the oceans, Arctic region and African continent are important contributors to global mean climate change, which leads to the slowdown observed over the period 2002-2012 in the NOAA-new and Cowtan & Way (Fig. 7c) datasets rather than the hiatus observed over 2001-2013 in the HadCRUT4 and NOAA-old datasets (Fig. 7d). In addition, the hiatus can also be found in the CERA-Interim dataset over the period 2002-2012, which implies that infilling and bias correction may lead to overestimated warming trends in the interdecadal and multidecadal composites and underestimated cooling trends in the interannual composite during the early 2000s (Fig. 7a) if the reanalysis is taken as a reference, because the reanalysis is dynamically consistent and incorporates many more four-dimensional observation records (regular or irregular) using the state-of-the art four-dimensional data assimilation system 28    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 SSTA 38,39 , 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 Pacific 5 . 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. 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 analysis 6 . 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 cycle 38,39 , and thus, the hiatus results mainly from the east equatorial Pacific SST anomalies 41 , 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 Pacific 5 . Figure 8b and c also shows that there were several cooling events at decadal or even multidecadal scales during the period 1950-2016, while there were three minimum trends in the interdecadal and multidecadal composite (Fig. 6e), in which only the last one encountered strong cooling from the interannual composite during the 2000s, which implies that the early-2000s hiatus was a transient event, in comparison with the long-term cooling event observed during 1960s-1970s, which was caused by the negative phase of the interdecadal and multidecadal composite ( Fig. 6b) with extreme cooling that was much stronger than global warming at a two-decade scale during this period (Fig. 6b,e). Figure 6b also shows that the multidecadal composites reached their maximums in magnitude in 2016 and then will probably turn onto a downward path, i.e., a cooling phase will soon be observed. This suggests the beginning of a new multidecadal cycle of global climate similar to that experienced in the second half of the twentieth century following the hiatus. Hence, future multidecadal climate changes should depend on the competition between global warming and cooling at the multidecadal scale if global climate repeats the last cycle observed at multidecadal scales in the coming decades.
Data and methods. Seven GMST series and two GMAT anomalies were used in this investigation, including the 1889-2016 HadCRUT4 dataset 18,19 , which was downloaded on 10/10/2017 from the Climate Research Unit (CRU) at the University of East Anglia (UEA, https://crudata.uea.ac.uk/~timo/diag/tempdiag.htm), along with its updated dataset (version 2) that includes infilling over the Arctic region and African continent (hereafter, Cowtan & Way 17 ), which was downloaded on 18/11/2017 from the Department of Chemistry at the University of York (http://www-users.york.ac.uk/~kdc3/papers/coverage2013/had4_krig_annual_v2_0_0. txt); the old version 21 of the bias-corrected GMST series from 1887 to 2014 (hereafter NOAA-old), or NOAA's merged land-ocean surface temperature dataset, which was downloaded on 16/07/2015 at ftp://ftp.ncdc.noaa. gov/pub/data/scpub201506/OldAnalysis/, and its new version, which is the bias-corrected GMST series (hereafter, NOAA-new 23 ) that was downloaded on 17/11/2017 from the NOAA National Centers for Environmental  where t represents the arithmetic mean of t, and S e 2 represents the error variance, which is defined as where e 2 (t) represents the residual of the linear regression equation, and N represents the sample size rather than the corresponding effective degree of freedom, N e 21 , 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 Daub4 30 .
The signal S(t) can be reconstructed as where D k represents the k-th detail of the signal at decomposition level k, and A 5 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 (A 5 ) 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 Python 45 (https://www.python. org/).