1 Supplementary material 2 The Kiel Climate Model (KCM, Park et al. 2009) consists of the ECHAM5 atmosphere 3 general circulation model on a T31 horizontal grid (3.75° x 3.75°) with 19 vertical levels, 4 which is coupled through the OASIS coupler to the NEMO ocean-sea ice model on a 2˚ 5 Mercator mesh amounting on average to 1.3°. Enhanced meridional resolution of 0.5° is 6 employed in the equatorial region and the ocean model is run with 31 levels. A list of 7 references can be obtained from http://www.geomar.de/en/research/fb1/fb1-me/research- 8 topics/climate-modelling/kcms/. Annual-mean SST biases (Fig. S1), although significant, are 9 typical for state-of-the-art climate models. The spectrum of monthly-mean SST anomalies in 10 the Niño3 region (150°W-90°W, 5°S-5°N) compares well to that calculated from observations 11 (Fig. S2). In comparison to the models participating in Coupled Model Intercomparison 12 Project Phase 5 (CMIP5, Taylor et al. 2012), the KCM is well within the multi-model 13 distributions concerning gross indices: SST in the Niño4 region (160°E-150°W, 5°S-5°N), 14 equatorial Pacific zonal SST contrast (Niño4-Niño3), and standard deviation of SST 15 anomalies in the Niño3 region (Figs. S3A, B). The variability is somewhat overestimated and 16 it also extends too far westward (Fig. S4), biases also seen in many other models. Consistent 17 with previous studies (e.g., Wittenberg et al. 2009), a strong decadal to centennial modulation 18 of ENSO amplitude is simulated in the control integration of the KCM (Fig. 1), in which 19 atmospheric CO2 is constant at 348 ppm. 20 1 21 Supplementary figures 22 23 Figure S1: Sea surface temperature (°C) bias in the Kiel Climate Model (KCM) using all 24 years from the 1,000-yr long control run relative to observations (HadISST 1870-2010). 25 2 26 27 Figure S2: Spectra of observed monthly-mean Niño3 SST anomalies from observations 28 (HadISST, 1870-2010) and the control integration of the KCM (blue) using all 1,000 years. 29 3 A B 30 31 Figure S3: Change in SST variability in the Niño3 region as measured by the standard 32 deviation (K) as a function of (A) the absolute Niño4 SST (K) and (B) zonal SST contrast (K) 33 defined as the difference between the Niño3 and Niño4 SSTs. The circles denote the initial 34 states and lines the tendencies. The KCM results (average over the first 30 years) are given by 35 the bold red circles. The black crosses denote observations (HadISST1, 1870-2010). The 36 different CMIP5 models forced by the RCP8.5 scenario are in given by thin circles and lines. 4 37 38 Figure S4: Standard deviations (°C) of observed monthly-mean SST anomalies from (A) 39 observations (HadISST, 1870-2010) and (B) the control integration of the KCM using all 40 1,000 years. 5 41 42 43 Figure S5: Annual-mean SST anomalies in the Niño3 region from the CMIP5 models for two 44 scenarios: (upper) RCP4.5, (lower) RCP8.5. High-variability models are indicated by legends. 45 6 46 47 Figure S6: (A) Precipitation and (B) SAT in Western India (15°N-25°N, 73°E-78°E) for 48 “normal” (yellow) and Super El Niños (red). Climatology is given by the black lines. 49 7 B A 50 51 Figure S7: (A) The ensemble-mean zonal near-surface (5m) currents (ms-1) along the equator 52 during the first 30 years of the global warming integrations. (B) The ensemble-mean 53 centennial trend of the near-surface zonal surface currents (ms-1/century) as a function of the 54 calendar month and longitude along the equator. 55 8 56 57 Figure S8: Ensemble-mean centennial trend of (A) net surface heat flux (Wm-2/century) and 58 (B) upper-ocean (0-300 m) heat transport convergence (Wm-2/century). 9 59 60 Figure S9: (Left) Sensitivity (ms-1/°C) of near-surface (10m) zonal wind to eastern equatorial 61 Pacific SST anomalies in the Niño3 region during the global warming integrations; (middle) 62 regression [m/(ms-1)] of thermocline depth anomalies upon the Niño4 near-surface (10m) 63 zonal wind anomalies; (right) local regressions (°C/100m) between SST and thermocline 64 depth (depth of the 20°C-isotherm) anomalies. The upper panels depict the conditions during 65 the first 30 years, the lower panels during the last 30 years. 10 66 67 68 Figure S10: Annual-mean Niño3 SST anomalies (°C) in two global warming ensembles with 69 the KCM. Top: reproduced from Fig. 2 (entitled “KCM new cloud scheme”). Bottom: when 70 the stratiform cloud scheme is replaced by another parameterization (entitled “KCM old cloud 71 scheme”, see text for details). A third-order polynomial was removed to account for the 72 warming trend. The individual ensemble members are shown by different colors. The dotted 73 red lines depict the evolution of the ensemble-mean Niño3 SST (°C, right scale). 74 11 75 76 Figure S11: Ensemble-mean centennial trend in sea level pressure (SLP, hPa/century) as 77 projected by the standard version of the KCM. 12