Supplementary Figure S1: Uncertainty of runoff changes Assessments of. R [mm/yr/k] for each model and the ensemble mean.

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1 Supplementary Figure S1: Uncertainty of runoff changes Assessments of R [mm/yr/k] for each model and the ensemble mean. 1

2 Supplementary Figure S2: Schematic diagrams of methods The top panels show uncertainty propagation. The bottom panels indicate our analysis methods. 2

3 Supplementary Figure S3: Expansion coefficients of SVD (a) Fraction of the squared Frobenius norm of the covariance matrix explained by the l-th pair of the R mode and the ( T, P ) mode. (b) The scatter plot of the expansion coefficients of the first R mode and the first ( T, P ) mode (normalised by the inter-model standard deviation). (c) The scatter plot of the expansion coefficients of the second R mode and the second ( T, P ) mode (normalised by the inter-model standard deviation). (d) Correlation coefficients between the expansion coefficients of the R mode and the ( T, P ) mode. 3

Supplementary Figure S4: Changes in horizontal and vertical winds Vectors represent the regressions between the expansion coefficient of the second R mode and changes in horizontal wind at the 85-hPa

4 Supplementary Figure S4: Changes in horizontal and vertical winds Vectors represent the regressions between the expansion coefficient of the second R mode and changes in horizontal wind at the 85-hPa level [m/s/k]. The shading shows the regression map between the expansion coefficient of the second mode and changes in vertical pressure velocity at the 7-hPa level [1 3 Pa/s/K] (negative values indicate upward motions). R 4

5 Supplementary Figure S5: Biases of surface air temperature Biases of surface air temperature [K] in the present climate for each model and the ensemble mean relative to the climatology of supplementary reference 39. 5

6 Supplementary Figure S6: Biases of precipitation Biases of precipitation [mm/day] in the present climate for each model and the ensemble mean relative to the climatology of supplementary reference 4. 6

7 Supplementary Figure S7: Schematic diagram of our method for obtaining metrics This figure indicates the procedure of calculating metrics. 7

Pa/s/K]. The second modes of (e) R [mm/yr/k], (f) T [K/K] and (g) P [%/K].

8 Supplementary Figure S8: First and second modes without the HadCM3 model The first modes of (a) R [mm/yr/k], (b) T [K/K] and (c) P [%/K]. (d) The regression map between the expansion coefficient of the first R mode and changes in vertical pressure velocity, averaged between 85 and 25 hpa [1 3 Pa/s/K]. The second modes of (e) R [mm/yr/k], (f) T [K/K] and (g) P [%/K]. (h) The regression map between the expansion coefficient of the second R mode and changes in vertical pressure velocity, averaged between 85 and 25 hpa [1 3 Pa/s/K]. Contours in the all panel indicate statistically significant correlations at ±1% t-test levels. 8

Supplementary Figure S9: Present climate patterns without the HadCM3 model Left panels show regression maps between the expansion coefficient of the

Right panels are regression maps between the expansion coefficient of the second R R mode and (d) T [K], (e) P [mm/yr] and (f) vertical pressure

9 Supplementary Figure S9: Present climate patterns without the HadCM3 model Left panels show regression maps between the expansion coefficient of the first mode and (a) T [K], (b) P [mm/yr] and (c) vertical pressure velocity, averaged between 85 and 25 hpa [1 3 Pa/s], in the present climate. Right panels are regression maps between the expansion coefficient of the second R R mode and (d) T [K], (e) P [mm/yr] and (f) vertical pressure velocity, averaged between 85 and 25 hpa [1 3 Pa/s], in the present climate. Contours in the all panels indicate statistically significant correlations at ±1% t-test levels. 9

10 Supplementary Figure S1: Metrics without the HadCM3 model (a) Scatter plot of the expansion coefficient of the first R mode (normalised by the inter-model standard deviation) and the T biases [K]. (b) Scatter plot of the expansion coefficient of the first R mode and the P biases [mm/day]. (c) Scatter plot of the expansion coefficient of the second R mode and the T biases [K]. (d) Scatter plot of the expansion coefficient of the second R mode and the P biases [mm/day]. The bold and thin lines indicate linear regressions and their corresponding 1% and 9% t-test-based confidence intervals, respectively. 1

11 Supplementary Figure S11: The runoff change assessments without HadCM3 (a) Changes in runoff [mm/yr/k] for the ensemble mean. (b) Changes in runoff [mm/yr/k] for the observationally constrained best estimate. 11

12 Supplementary Figure S12: Influence of the natural variability on the results The 1st and 2nd R mode coefficients and the corresponding T and P biases for the models whose sizes of different initial condition ensemble (DICE) are larger than 2 only. (a) Scatter plot of the expansion coefficient of the first R mode (normalised by the inter-model standard deviation) and the T biases [K]. (b) Scatter plot of the expansion coefficient of the first R mode and the P biases [mm/day]. (c) Scatter plot of the expansion coefficient of the second R mode and the T biases [K]. (d) Scatter plot of the expansion coefficient of the second R mode and the P biases [mm/day]. Crosses and squares indicate the members of DICE and their averages for each model, respectively. 12

13 Supplementary Table S1: AOGCMs analysed in this study NO. Model name abbreviation Modeling centers, Country T, P Wind Ensemble size 1 BCCR-BCM2. 2 CCSM3 3 CGCM3.1(T47) 4 CNRM-CM3 5 CSIRO-MK3. 6 ECHAM/MPI-OM Bjerknes Centre for Climate Research, Norway National Center for Atmospheric Research, USA Canadian Centre for Climate Modelling and Analysis, Canada Météo-France/Centre National de Recherches Météorologiques, France Commonwealth Scientific and Industrial Research Organisation (CSIRO) Atmospheric Research, Australia Max Planck Institute for Meteorology, Germany Y 1 Y Y 5 Y Y 5 Y Y 1 Y 1 Y Y 3 7 ECHO-G Meteorological Institute of the University of Bonn, Meteorological Research Institute of the Korea Meteorological Administration (KMA), and Model and Data Group, Germany/Korea Y 3 8 GFDL-CM2. U.S. Department of Commerce/National Y Y 1 9 GFDL-CM2.1 1 INM-CM3. Oceanic and Atmospheric Administration (NOAA)/Geophysical Fluid Dynamics Laboratory (GFDL), USA Y Y 1 Institute for Numerical Mathematics, Russia Y Y 1 11 IPSL-CM4 Institut Pierre Simon Laplace, France Y Y 1 12 MIROC3.2(M) Center for Climate System Research (University of Tokyo), National Institute for Environmental Studies, and Frontier Research Center for Global Change (JAMSTEC), Japan Y Y 3 13 MRI-CGCM2.3.2 Meteorological Research Institute, Japan Y Y 5 14 UKMO-HadCM3 Hadley Centre for Climate Prediction and Research/Met Office, UK Y Y 1 Y indicates that the corresponding output is included. 13

14 Supplementary References 39. Uppala, S. M., et al. The ERA-4 re-analysis. Q. J. R. Meteorol. Soc. 131, (25). 4. Xie, P. and Arkin, P. A. Global Precipitation: A 17-year monthly analysis based on gauge observations, satellite estimates, and numerical model outputs. B. Am. Meteorol. Soc. 78, (1997). 14

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION DOI: 10.1038/NGEO1189 Different magnitudes of projected subsurface ocean warming around Greenland and Antarctica Jianjun Yin 1*, Jonathan T. Overpeck 1, Stephen M. Griffies 2,