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Boxed regions.

For the BJ index analysis (Supplementary Methods), the western and eastern boxed regions were determined considering the model’s own ENSO. They extend from 82° W westward and from 121° E eastward, respectively, to a longitude (H_c; Supplementary Table 3) where the zero contour line passes the Equator in the regressed pattern of oceanic heat content anomalies with the first principal component of the empirical orthogonal function for SST anomalies in the tropical Pacific (120° E–80° W, 20° S–20° N) from individual coupled models and reanalysis data²⁹. The latitudinal range of the boxed region is 5° S–5° N. The H_c was also applied to calculations in Fig. 3. The zonal thermocline slope (Fig. 3a, b) is defined as the difference of thermocline depth (the depth of maximum temperature gradient within 0–400 m) between the western equatorial Pacific (121° E–H_c, 5° S–5° N) and the eastern Pacific (H_c − 82° W, 5° S–5° N). The central-to-western tropical Pacific climatological mean wind stresses (Fig. 3b, c) are averaged over H_c−30°-H_c+30° in longitude and 5° S–5° N in latitude. The climatological zonal SST gradient (Fig. 3c) is the difference between the eastern Indian–western tropical Pacific (60° E–120° E, 10° S–10° N) SST and the eastern Pacific (H_c − H_c + 60°, 10° S–10° N) SST. This boxed region is also applied to Fig. 4b.

CMIP5 models.

We analysed the historical runs over the period 1861–2005 and RCP8.5 experiments over the period 2006–2100 from 22 CMIP5 models to represent the present-day climate and future warmer climate, respectively; the former runs are forced by observed atmospheric compositions over the twentieth century and the latter runs by a high greenhouse gas emission scenario with a radiative forcing that increases to a level of 8.5 W m⁻² at the end of the twenty-first century. The models include ACCESS1-0, ACCESS1-3, CCSM4, CNRM-CM5, CSIRO-MK3-6-0, FGOALS-g2, GFDL-CM3, GFDL-ESM2G, GFDL-ESM2M, GISS-E2-R, HadGEM2-CC, HadGEM2-ES, IPSL-CM5A-LR, IPSL-CM5A-MR, IPSL-CM5B-LR, MIROC5, MIROC-ESM, MPI-ESM-LR, MPI-ESM-MR, MRI-CGCM3, NorESM1-M and NorESM1-ME. More detailed information on CMIP5 coupled models can be obtained from http://cmip-pcmdi.llnl.gov/cmip5/availability.html.

MME analysis.

For the MME analysis, we selected CMIP5 models that have realistic, relative contributions of the three positive and the two negative feedback terms to ENSO stability, as estimated by the BJ index, in comparison with those from the reanalysis data sets. We compared the BJ index and its contributing feedback terms from each of the 22 CMIP5 models over the period 1950–1999 with those from the reanalysis data sets over the period 1958–1999. The reanalysis data sets include ocean potential temperatures, ocean currents, and wind stresses from the Simple Ocean Data Assimilation Reanalysis version 2.0.2 (ref. 29) available over the 1958–2007 period and net heat fluxes from the 40-year European Centre for Medium-Range Weather Forecasts Reanalysis³⁰ over the 1958–2001 period. The correlation coefficients and root mean square error (r.m.s.e.) between each model and the reanalysis were calculated in terms of the relative importance of the five BJ index contributing terms and the BJ index, following the sequence shown in Supplementary Fig. 1. Each model and the reanalysis have six samples (five BJ terms and one BJ index), all in an identical sequence, which permits calculation of the correlation coefficients and r.m.s.e. The selected nine models (GFDL-CM3, GFDL-ESM2M, MIROC5, GISS-E2-R, FGOALS-g2, NorESM1-M, NorESM1-ME, CCSM4, ACCESS1-0) have a significant correlation at the 99% confidence level and also a relatively small r.m.s.e. (that is, red-coloured models in Supplementary Fig. 1) among the 22 CMIP5 models. The MME, which is obtained by simply averaging all models of each group without applying a weight to each model, is calculated separately for the BEST9 and the REM13. The utilization of the BJ index for selecting models is addressed in the Supplementary Information.

Statistical analysis.

To examine how various quantities (including ENSO amplitude, BJ index, climatology, and linear trends) vary over time, in each model we combined the two experiments to form a 240-year-long data set as the RCP8.5 experiments start from 1 January 2006 of the historical runs, and performed analyses over running periods from 1861 to 2100.

Anomalous quantities are departures from a running climatology. In other words, they are obtained by removing the long-term mean seasonal cycle of each running period. A linear trend is computed by a least-squares fit of the monthly anomalous quantities. Before the BJ index analysis, the linear trend is removed from the anomalies and a seven-year running mean was also applied to remove decadal and longer variation (for example, Supplementary Figs 9–11).

For the observed SST, we use two reanalysis data sets, that is, Hadley Centre sea ice and SST version 1 (HadISST; ref. 11) and extended reconstructed SST (ERSST) version 3b (ref. 12) over the period 1871–2012. To examine the observed central-to-western tropical Pacific mean zonal winds, we use the WASWind¹⁸ (1950–2009) and CORE version 2 (ref. 19) (1950–2006) data sets.