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The Pacific Decadal Oscillation (PDO; refs 11, 12), or more generally the IPO (refs 13, 14), switched from a warm phase to a cold phase around 1999¹⁵. This switch has been associated with a cooling trend since the early 1990s over the Equatorial Central and Eastern Pacific (ECEP; 15° S–15° N, 180°–80° W) that has contributed to the recent hiatus in global-mean T (refs 4, 5). Modelling studies^{1, 16, 17} have also shown that the IPO can modulate the rate of global warming through changes in ocean heat uptake. Given the well-documented extra-tropical response to tropical forcings^{18, 19}, it is not surprising that IPO-associated sea surface temperature (SST) variations in the ECEP have had a large impact on global-mean T (ref. 1). The recent cooling of the ECEP has been accompanied by strengthening trade winds⁵ and increasing ocean heat uptake^{4, 16, 17, 20}, typical of a La Niña event²¹ but over decadal timescales. Although these studies all point to a major contribution of the ECEP to the recent global warming slowdown, it is unclear how much of the observed SST change in the ECEP is associated with ICV, particularly the IPO, and how much is due to external forcing change, such as stratospheric aerosols^{7, 8, 9, 10}. Previous analyses^{22, 23} suggest that changes in the Atlantic Multidecadal Oscillation (AMO; ref. 24) may have been associated with the rapid global warming since the late 1970s, but these and other²⁵ studies did not address how the AMO, IPO and other decadal modes of ICV modulated global-mean T before the 1970s and during the early twenty-first century. The rate of global warming from 2000 to 2013 also remains to be fully reconciled between observations and climate models. Furthermore, the T change patterns (Supplementary Fig. 1) suggest that the recent warming hiatus resulted from a cancellation of warming over most land areas and the Atlantic and Indian Oceans by cooling concentrated over the eastern Pacific Ocean, and that recent natural or anthropogenic aerosol forcing or GHG increases cannot explain the observed T change patterns.

Here we quantify the contribution of ICV to the historical evolution of global-mean T, including over the warming hiatus period since about 2000. We average over a large number of Coupled Model Intercomparison Project Phase 5 (CMIP5) simulations to derive an estimate of the forced response in global-mean T to GHG and other external forcing changes (see Methods). Changes associated with this estimate of the forced response in global-mean T are then removed via linear regression from the time series of observed T (refs 26, 27) at each gridpoint (see Supplementary Information). The goal of the CMIP5-based detrending is to remove forced T changes, so that the residual is mostly due to ICV. We choose this over other detrending methods for this purpose as the CMIP5 ensemble mean represents our best estimate of the forced change. Having removed the externally forced component in observed T, we then perform an empirical orthogonal function (EOF) analysis (see Supplementary Information) to examine the contributions of the leading modes of ICV to decadal changes in global-mean T. We focus on the 1920–2013 period, as observations are sparse in the tropical Pacific and many other regions before 1920. We note that the CMIP5 models on average overestimate the observed warming from 1920 to 2013 by about 14% (see Supplementary Information). As this model bias is not the focus of our study, it is removed through re-scaling without affecting our overall conclusions (see Supplementary Section 4).

We find that the first and fourth leading EOFs of the ICV can account for the large decadal swings in observed global-mean T, for example, by up to ±0.1 °C around 1925, 1940, 1950, and after 2005 (Fig. 1). These fluctuations in observed global-mean T are absent in the corresponding model-mean time series (Fig. 1a), which approximates the mean forced response to historical GHG and other external forcing changes. By construction, the EOF method maximizes the spatially integrated variance explained by the leading EOFs, but it does not require them to explain any variations in the global-mean T. In fact, EOFs 2 and 3 contribute little to the global-mean T, as their spatial patterns approximately cancel each other. Thus, it is surprising that it takes only two EOF modes to explain most (88%) of the observed global-mean T deviations from the forced response. The re-scaling of the model T in Fig. 1 improves the visual agreement with the observations, but even without this re-scaling the two EOFs still account for most (67%) of the observed decadal T variations (Supplementary Fig. 2).

a, Annual T′ from the GISTEMP observational data set²⁶ compared with the ensemble mean surface air temperature from 66 historical all-forcing runs from 33 CMIP5 models multiplied by a scaling factor of 0.863, and the scaled model T′ plus the T′ represented by the two leading EOFs given in Fig. 2. The contribution of the two leading EOFs is shown as the blue line in b. b, Three-year moving averaging was applied to the local T time series before regional averaging or EOF analyses in this study and also to the lines in b. The correlation coefficient (r) is for the black versus red and black versus blue lines, respectively. The scaling removes the overall warming bias in the models and improves visual agreement between the observations and models, but does not affect the decadal change patterns (Supplementary Section 4 and Supplementary Fig. 2). The orange shading in a represents the 95% confidence interval of the model ensemble mean (red curve) and the blue vertical bar indicates the 10th to 90th percentile range of the internal variability of T′ estimated using the CESM1 30-member ensemble simulations²⁹.

We used the GISTEMP (ref. 26) and HadCRUT4 (ref. 27) gridded monthly surface T data sets, which incorporate SST observations over oceans and surface air T observations over land. Small data gaps in the HadCRUT4 data set were filled using spatial bilinear interpolation. Model data of monthly surface air T were obtained from 66 historical (1919 to 2005) and RCP4.5 (2006 to 2013) simulations from 33 CMIP5 models³⁰ (http://cmip-pcmdi.llnl.gov/cmip5/index.html). Model-mean averages were obtained by averaging equally over the 66 available realizations. All observed and simulated fields were interpolated onto a common 2.5° (longitude) by 2.5 ° (latitude) grid. Area-weighted EOF analyses were performed. To focus on decadal- and longer-timescale variations, three-year moving averages were applied to the T anomaly data. All anomalies are relative to the 1961–1990 mean.

To derive an estimate of internally generated variability in observations, we first computed the global-mean T time series from the CMIP5 ensemble mean, and then removed the changes and variations associated with this model T series using linear regression from the observed T time series at each gridpoint. As the model-mean T series contains a primarily forced response, this procedure removes as much as possible the externally forced component from the observations. Similar procedures have been widely used in climate detection and attribution studies^{6, 31}. After removing the forced component, the observational T fields were subjected to an EOF analysis. Further technical details and validations of this procedure are provided in the Supplementary Information. Ten-year running linear trends were estimated using the pair-wise slope method³², which was found to outperform conventional least squares fitting for small samples (N < 40) inour tests.

The results are similar when the HadCRU4 data set is used as the observations (Supplementary Figs 5–8), although some quantitative differences exist between the GISTEMP and HadCRU4 cases. However, these differences do not change our main conclusions.

To verify our method and examine whether similar conclusions can be made in a coupled climate model, we repeated our analysis using the 30-member ensemble of historical all-forcing runs from the NCAR CESM (ref. 28; http://www.cesm.ucar.edu/experiments/cesm1.1/LE/). We used run no. 11 as the target realization (‘observations’), as it had little warming during 2000–2013, and the 30-member ensemble mean as the forced signal (without re-scaling).

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