CMIP5 models used in this ... - Nature

Supplementary Table 1. AMIP5/CMIP5 models used in this study. The corresponding equilibrium climate sensitivity (ECS) and the hydrological sensitivity based on the temperaturemediated precipitation change per unit surface warming (LvdP/dTs) from the abrupt4×CO2 simulations are listed. The percentage of precipitation change in parentheses is relative to the multi-model-mean global-mean precipitation of 85.78 W m−2. Missing values are marked ‘-’. ECS Hydrological Model Modeling Center in K Sensitivity in W m−2 K−1 (% K−1) a. BCC_csm1.1*#

Beijing Climate Center, China

2.79

2.14 (2.49)

b. BCC_csm1.1m*#

Beijing Climate Center, China

2.83

2.33 (2.72)

c. CCCMA_canam4/esm2*#

Canadian Centre for Climate Modelling and Analysis, Canada Centre National de Recherches Météorologiques, France Commonwealth Scientific and Industrial Research Organization - Bureau of Meteorology, Australia Commonwealth Scientific and Industrial Research Organization - Bureau of Meteorology, Australia Commonwealth Scientific and Industrial Research Organization - Queensland Climate Change Centre of Excellence, Australia Geophysical Fluid Dynamics Laboratory, USA

3.68

2.02 (2.35)

3.22

2.26 (2.63)

3.78

1.81 (2.11)

3.42

2.17 (2.53)

4.04

-

3.78

2.21 (2.58)

2.24

1.87 (2.18)

j. GISS_e2r*#

Geophysical Fluid Dynamics Laboratory, USA (no AMIP simulation results) Goddard Institute for Space Studies, USA

2.07

2.67 (3.11)

k. INM_cm4*#

Institute for Numerical Mathematics, Russia

1.97

2.33 (2.72)

l. IPSL_cm5a-lr*#

Institut Pierre Simon Laplace, France

3.94

2.48 (2.89)

m. IPSL_cm5a-mr*#


4.02

2.52 (2.94)

n. IPSL_cm5b-lr*#


2.56

2.26 (2.63)

o. MIROC_esm*#

Model for Interdisciplinary Research On Climate,

4.60

2.14 (2.49)

2.66

2.33 (2.72)

d. CNRM_cm5*# e. CSIRO_access1.0*# f. CSIRO_access1.3*# g. CSIRO_mk3.6* h. GFDL_cm3*# i. GFDL_esm2g*#

Japan

p. MIROC_miroc5*#

Model for Interdisciplinary Research On Climate, Japan

q. MPI_esm-lr*#

Max Planck Institute, Germany

3.43

2.06 (2.40)

r. MPI_esm-mr*#

Max Planck Institute, Germany

3.29

2.17 (2.53)

s. MRI_cgcm3*#

Meteorological Research Institute, Japan

2.63

2.73 (3.18)

t. NCAR_cam5*

National Center for Atmospheric Research, USA

4.10

-

u. NCAR_ccsm4*#

National Center for Atmospheric Research, USA

2.88

2.34 (2.73)

v. NCC_noresm1-m*#

Norwegian Climate Center (NCC), Norway

2.71

2.26 (2.63)

w. UKMO-hadgem2-a*#

UK Met Office Hadley Climate Center, UK

3.81

1.85 (2.16)

* 23 AMIP5 and coupled historical-RCP4.5 model simulations are analyzed. # 21 models are available for the temperature-mediated precipitation response analysis.

Supplementary Table 2. Observations used in this study and corresponding interannual sensitivities to surface temperature. All cloud fraction and water vapor sensitivities are for tropical-means and precipitation sensitivity is for global-mean. Analysis Interannual Dataset Period Resolution References Sensitivity to Ts HadCRUT 4.4.0.0 surface temperature

1/1995-12/2005

5°×5°

Morice et al. (2012)Error!

N/A

Reference source not found.

3.79±0.41 W m−2 K−1

CERES EBAF 2.8 fluxes all-sky outgoing longwave radiation Terra MODIS high cloud fraction Collection 6 Aqua MODIS high cloud fraction Collection 6 Terra-Aqua combined MODIS high cloud fraction, Collection 6 AIRS effective high cloud fraction Version 6 Joint CloudSat/CALIPSO high cloud fraction

3/2000-10/2015

6/2006-6/2015

2.5kmx1.5km

ISCCP high cloud fraction

1/1995-12/2005

2.5°×2.5°

Aqua AIRS-Aura MLS upper tropospheric water vapor GPCP Precipitation

8/2004-12/2015

3°×1°

1/1995-12/2005

2.5°×2.5°

Huffman et al. (2009)Error! Reference source

CMAP Precipitation

1/1995-12/2005

2.5°×2.5°

Xie and Arkin (1997)Error! Reference −0.55±1.04 W m−2 K−1

1°×1°

Loeb et al. (2012)Error! Reference source not found.

7/2002-6/2010

1°×1°

Baum et al. (2012)Error!

−1.48±0.37 % K−1


7/2002-6/2015

1°×1°


−1.43±0.32 % K−1


7/2002-6/2010

1°×1°


−1.55±0.36 % K−1


9/2002-12/2013

1°×1°

Kahn et al. (2014)Error!

−0.68±0.24 % K−1


Sassen et al. (2008)Error! Reference source not found. Wang et al. (2012)Error! Reference source

−0.88±2.41 % K−1

not found.

Norris and Evan (2015)Error! Reference source

−2.39±0.29 % K−1

not found.

Jiang et al. (2012)Error!

9.58%±1.48 % K−1


2.71±0.90 W m−2 K−1

not found.

source not found.

2

Supplementary Figure 1. Correlations between the inter-model spread in precipitation sensitivity and the inter-model spread in various components of radiative flux sensitivities. The interannual rates are marked in blue and centennial rates are marked in red. All quantities are global-means.

3

(a) Interannual

(b) Centennial 3

s

2.5

b

2.0 1.5

m p oj

1.0

q

0.5

g

lh k u f t w v dn c e r

a

correlation = 0.80

Global dOLR/dTs (W m−2K−1)

Global dOLR/dTs (W m−2K−1)

3.0 t

2

l ho p w vc qg d

1 i

0 j -1

s

k

correlation = 0.94

0.0 0

1 2 3 4 5 6 Tropical dOLR/dTs (W m−2K−1)

-1 0 1 2 3 4 Tropical dOLR/dTs (W m−2K−1)

a BCC_csm1.1 b BCC_csm1.1m c CCCMA_canam4 d CNRM_cm5 e CSIRO_access1.0 f CSIRO_access1.3 g CSIRO_mk3.6 h GFDL_cm3 i GFDL_esm2g j GISS_e2r k INM_cm4 l IPSL_cm5a-lr m IPSL_cm5a-mr n IPSL_cm5b-lr o MIROC_esm p MIROC_miroc5 q MPI_esm-lr r MPI_esm-mr s MRI_cgcm3 t NCAR_cam5 u NCAR_ccsm4 v NCC_noresm1-m w UKMO_hadgem2-a

Supplementary Figure 2. Inter-model spread in global-mean OLR sensitivity to surface temperature versus that in tropical-mean OLR sensitivity to surface temperature. (a) interannual (b) centennial. Each model is represented by a lowercase letter. Multi-model-means are marked in solid colored circles. The least-squares linear regression lines and correlation coefficients between the x-axis and y-axis variables are shown.

4

55

(a) MIROC-miroc5 [-20,20]

°

70

(b) MRI-cgcm3 [-20,20]

°

55

50

50

CF above 440hPa (%)

45

40

ISCCP simulator Max Overlap Random Overlap 3/2 Max + 1/3 Random

35 30

50

40


40

30 25

20

30 20

15 1997

1999

2001

2003

20 1995

2005

1997

1999

Year

Weighted-Average CF anomaly (%)


35

25

3

°

60

45

10 1995

(c) UKMO-hadgem2-a [-20,20]

2001

2003

15 1995

2005

1997

1999

Year

(d) MIROC-miroc5, [-20,20]

°

3

(e) MRI-cgcm3, [-20,20]

°

2

Corr=0.927, slope=0.824

Corr=0.924, slope=1.06

1.5

2

2

2001

2003

2005

Year

(f) UKMO-hadgem2-a, [-20,20]

°

Corr=0.901, slope=0.838

1 1

0.5

1

0 0 -0.5

0 -1

-1 -1.5

-1

-2 -2

-2

-2

-1

0

1

2

ISCCP simulator CF anomaly(%)

3

-3

-4

-2

0

2


4

-2.5

-3

-2

-1

0

1

2


Supplementary Figure 3. Calculating total high cloud fraction using weighted averages under maximum and random overlap assumptions. (a)-(c) The tropical averaged (20°S-20°N) total high cloud fractions based on maximum and random overlap assumptions and the weighted averages of the high cloud fractions under the maximum and random overlap (2/3 maximum and 1/3 random) assumptions, compared to the ISCCP simulator high cloud fractions for three AMIP5 models. (d)-(f) The tropical-averaged de-seasonalized high cloud fraction anomalies based on the weighted averages from the maximum and random overlap assumptions scattered against the ISCCP simulator high cloud anomalies for the period of 1995 to 2005 in the three AMIP5 models.

5

Supplementary Figure 4. Relationship between interannual high cloud fraction anomalies and local surface temperature anomalies. The color shadings are the regression coefficients in % K−1 for high cloud fraction regressed onto local surface temperature from 1995 to 2005 for 14 AMIP5 model simulations and the multi-model-mean.

6

IPSL

6 -15

6

MPI

-15

25

4 86

MMM

-20

25

25

3 3

-1

-1

-1

-1

-1

-1

0.4

-1

-1

-1

dP/dTs (black-contour)

-3

-1

-1

-1

-1 0.4

-1

-4

-1

3

dω/dTs (white-contour)

3

3

-1

-1 -1

-5

-8-5

-13

3

-1

3

0.6 3

MMM

-1

-1

0.4 1.2

-1

3

3

-1

3

-1

-1

-1 3

-1

MPI

dCF/dTs (color-shading)

3

0.6 -5 3 0.4 0.4

3

3

3

3

-1

-1

3

-1 -1 0. 4

-1

-1 00.4 .6

-1

-1

-5 0.6

-1

-1

GISS

-1

--35

0.6

-05.6

0.4

-3

3 0.40.65

3

3

0

NCC

-1

-1

-1

-1

0.4

-1

-1 3 -1

-1

0.4 -3 -3

-1

-1

3

3 -1

-1

-3

0.4

-1

-5

1

0.4

-1

-1 0.4

-1

-1

3

-3

-1

-1

3

0.4

-8

-1

MOHC -1

4

NCAR

0.4

GFDL

3

-1

-1

-1

-1

3

3

-1

0.4

0.4

0.4

0.6

3

-1 -1

0.4

-5

1.2

31

25

-1

-1 -1

0.4 -1

-1

-1

MIROC

-5

3 0.4

3

-1

3

-1

-1

0.4

0.4

CSIRO

0.4 0.6

MRI 3

-1

-1

-30

(a) Interannual Rates

-1

0.4 -1

3

4

IPSL -1

-35

68

25

dP/dTs (black-contour)

CCCMA

0.6

4

-15

-15

dω/dTs (white-contour)

10 86

25

-5 5 -3 5

-

-15

-15

15

-35

8 610 4

-1525

3 3

-10

dCF/dTs (color-shading)

-25

25

4

-145

25

0

-15

GISS

NCC 25

86

-15

-145

25

25

-15

-1

25

-15

-35

-15

10

-15

-35

68 4

55 4 6 8-10 -4 -35

-35

25

-15

MOHC -15

-15

-1

8

46

20

NCAR

-15

-3 5

-15

-15

4

25

25

MIROC

GFDL

-1

--35 15

25

-15

-35

4 -15

CSIRO 68 4

25

46

30

4

68

8

25

810

MRI

-15

-15

25

CCCMA

(b) Centennial Rates

Supplementary Figure 5. Spatial distributions of upper tropospheric vertical velocity at 250 hPa, precipitation and high cloud fraction changes per unit surface warming. (a) interannual rates, represented by the regression slopes of each variable onto tropical-mean (20°S-20°N) surface temperature. (b) centennial rates, represented by the differences between the 21st and 20th centuries for each variable normalized by tropical-mean surface temperature change.

7

(a) Temperature mediated

(b) Temperature mediated

0.4

0.0 -0.2 -0.4

t

w l m ec b r a q j h

3

o

dOLR/dTs (W m−2K−1)

0.2 dCF/dTs (% K−1)

s

n

p

s -0.6 -0.8 -1.0 -1.0

f g

g f

par q

2 j

b

o

e w n l cm

1

correlation = 0.62

-0.5 0.0 0.5 dFω/dTs (% K−1)

th

correlation = −0.71

1.0

0 -1.0

-0.5 0.0 dCF/dTs (% K−1)

0.5


Supplementary Figure 6. Relationships between the inter-model spreads in the tightening of Hadley ascent, the tropical high cloud fraction sensitivity, and the OLR sensitivity for the temperature-mediated rates. (a) Tropical-mean dCF/dTs scattered against the change of the tropical ascending area fraction per unit surface warming, dFω/dTs. The tropical ascending area is defined by ω250 < 0 Pa s−1. (b) The tropical-mean dOLR/dTs scattered against the tropicalmean dCF/dTs. The sensitivities are derived from the abrupt4×CO2 experiments using the linear regression method. Each model is represented by a lowercase letter. Multi-model-means are marked in solid colored circles. The least-squares linear regression lines and correlation coefficients between the x-axis and y-axis variables are shown.

8

(a) Interannual

(b) Centernnial

2

1.0 g

l q h ur

-2

o

m p

j

dFω /dTs (% K−1)

dFω /dTs (% K−1)

0

0.5

c o sf a

t

w n

ev b

-4

-6 -4 -2 dHw /dTs(oK−1)

0

2

j

p

-0.5 -1.0 -1.5

correlation = 0.49

-8

0.0

-2.0 -2.0

h me lrw a vf n b

u

g s

c

q

t

correlation = 0.62

-1.5 -1.0 -0.5 dHw /dTs (oK−1)

0.0


Supplementary Figure 7. Relationship between the change of the width of the ascending branch of the Hadley Circulation and the change of tropical ascending area per unit surface warming. (a) interannual and (b) centennial. The width of the ascending branch of the Hadley Circulation (Hw) is defined by the latitudinal width in degrees of the annual-mean zonalmean upward vertical velocity at 250 hPa. The change of tropical ascending area per unit surface warming is based on monthly upward vertical velocity at 250 hPa. Each model is represented by a lowercase letter. Multi-model-means are marked in solid colored circles. The least-squares linear regression lines and correlation coefficients between the x-axis and y-axis variables are shown.

9

Centennial

LvdP/dTs (W m−2K−1)

3.5

t b v

s

3.0 2.5

q t

l m r n

s

c

p

u

2.0

f g bf v n q g

1.5 1.0

Wet-area LvdPwet /dTs correlation = − 0.52

Global LvdP/dTs correlation = − 0.65

a lw m ure ap w e

o

d hk h

k

j j

o i i d c

-1.0

-0.8

-0.6 -0.4 -0.2 0.0 Tropical dFω/dTs (% K−1)

0.2

0.4


Supplementary Figure 8. Relationships between the tightening of Hadley ascent and precipitation changes. The tightening of the tropical ascending areas based on the upward velocity at 250 hPa (dFω/dTs) scattered against the global-mean precipitation change normalized by global-mean surface temperature increase (red) and the tropical wet-area mean precipitation change normalized by tropical-mean surface temperature increase (cyan) for 23 models on the centennial time scale. Each model is represented by a lowercase letter. Multi-model-means are marked in solid colored circles. The least-squares linear regression lines and correlation coefficients between the x-axis and y-axis variables are shown.

10

2

Interannual Centennial

Multi-Model Mean: 6 4 2

0

0

W m−2K−1

% K−1

1

-1 -2 -2 dCF/dTs

−0.61−0.55

−0.77−0.71

dLWC/dTs

dOLR/dTs

−0.65−0.49

−0.62−0.62

-4

dOLRclr/dTs dCRElw/dTs

Supplementary Figure 9. Relationships between the inter-model spreads in tropical high cloud fraction sensitivity and longwave radiative sensitivities. Colored circles mark the individual models’ interannual (blue) and centennial (red) sensitivities to surface temperature for tropical-mean high cloud fraction (CF), longwave radiative cooling (LWC), all-sky OLR, clearsky OLR (OLRclr), and longwave cloud radiative effect (CRElw). Multi-model-means are shown in black “+”. The left y-axis is for high cloud fraction sensitivity and the right y-axis is for longwave radiative sensitivities. The across-model correlations between dCF/dTs and the radiative sensitivities are shown above the x-axis for interannual (blue) and centennial (red) rates.

11

5

oo t g

ECS (K)

4

w e d

3 2 1 -2.0


h

f b

a

u

t l gmm h ew cc qf r

s sv p n n

q r

u b a v p j

k

j

correlation = 0.19 correlation = −0.13

-1.5

-1.0 -0.5 0.0 −1 dCF/dTs (% K )

0.5

1.0

Supplementary Figure 10. Relationship between tropical-mean high cloud fraction sensitivity and equilibrium climate sensitivity. ECS scattered against tropical-mean dCF/dTs (interannual in blue, centennial in red) across the models. Each model is represented by a lowercase letter. Multi-model-means are marked in solid colored circles. The least-squares linear regression lines and correlation coefficients between the x-axis and y-axis variables are shown.

12

Terra MODIS

0.0 -0.5 -1.0 -1.5 -2.0

Slope = −1.48 +/− 0.37 %/K Correlation = −0.63

-0.4

-0.2

0.0 0.2 dTs (K)

0.5 0.0 -0.5 -1.0 -1.5 -2.0

0.4

(b)

1.0

dCFAqua_MODIS (%)

0.5

0.6


-0.4

ISCCP 1.5

-1.0 Slope = −2.39 +/− 0.29 %/K Correlation = −0.82

-0.2

0.0 0.2 dTs (K)

0.4

0.5 0.0 -0.5 -1.0 -1.5 -2.0

0.6

0.4

0.6

0.0

-1.0 Slope = −0.68 +/− 0.24 %/K Correlation = −0.41

-0.2

0.0 0.2 dTs (K)

0.0 0.2 dTs (K)

0.4

0.6

2 0 -2 -4

0.4

(f)

4

-0.5

-0.4

-0.2

CloudSat+CALIPSO

0.5

-1.5 -2.0


-0.4

(e)

1.0

dCFAIRS (%)

dCFISCCP (%)

0.0 -0.5

-0.4

0.0 0.2 dTs (K)

(c)

1.0

Aqua AIRS

0.5

-1.5 -2.0

-0.2

1.5

(d)

1.0

Terra+Aqua MODIS 1.5

dCFAqua+Terra_MODIS (%)

(a)

1.0

dCFTerra_MODIS (%)

Aqua MODIS 1.5

dCFCloudSat-CALIPSO (%)

1.5

0.6

Correlation = −0.08 Slope = −0.88 +/− 2.41 %/K

-0.4

-0.2

0.0 0.2 dTs (K)

0.4

0.6

Supplementary Figure 11. Observed tropical-mean high cloud fraction sensitivity to surface temperature. (a) Terra MODIS (7/2002-6/2010), (b) Aqua MODIS (7/2002-6/2015), (c) Terra-Aqua MOSIS (7/2002-6/2010), (d) ISCCP (1/1995-12/2005), (e) Aqua AIRS (9/200212/2013), and (f) CloudSat/CALIPSO joint retrieval (6/2006-6/2015). The least-squares linear regression lines are drawn, with correlations and regressions slopes marked.

13

CNRM_cm5

5 0 Correlation = 0.86 Slope = 9.73 +/-0.99 %/K

0.5

0 -5 -10

1.0

Correlation = 0.77 Slope = 9.19 +/-1.34 %/K

-0.5

10

(d)

5 0 -5 -10


-0.5

0.0

0.5

10


0.5


10


0.5

10 0


-0.5

dUTWVP (%)

dUTWVP (%)

0 Correlation = 0.86 Slope = 14.23 +/-1.45 %/K

0.0 0.5 dTs (K)

0.0

0.5

1.0

10

1.0

(f)

0 -5 -10


-0.5

0.0

0.5

1.0

10

(i)

5 0 -5 -10


-0.5

0.0

0.5

1.0

NCC_noresm1-m

(k)

-5 -10

0.5

5

1.0

1.0

Observations

(m)

-0.5

0.5

5

1.0

5 -5 -10

0.0

0.0

MPI_esm-lr


UKMO_hadgem2-a 10

10

1.0

0

-0.5

dUTWVP (%)

dUTWVP (%)

0

0.0

-0.5

NCAR_cam5

(j)

-0.5

0.5

(h)

-5 -10

1.0

5 -5 -10

0.0

5

MRI_cgcm3 10


INM_cm4

0

-0.5

dUTWVP (%)

dUTWVP (%)

0

0.0

0 -5 -10

MIROC_miroc5

(g)

-0.5

(c)

5

1.0

(e)

-5 -10

1.0

5 -5 -10

0.5

5

IPSL_cm5a-lr 10

0.0

10

GISS_e2-r dUTWVP (%)

dUTWVP (%)

GFDL_cm3

dUTWVP (%)

0.0

5

dUTWVP (%)

-0.5

CSIRO_mk3.6

(b)

dUTWVP (%)

-5 -10

10

dUTWVP (%)

(a)

dUTWVP (%)

dUTWVP (%)

CCCMA_canam4 10

10

(l)

5 0 -5 -10


-0.5

0.0 0.5 dTs (K)

1.0

(n)

5 0 -5 -10


-0.5

0.0 0.5 dTs (K)

1.0

Supplementary Figure 12. Upper tropospheric (440 hPa to 100 hPa) water vapor path sensitivity to surface temperature in models and observations. Aqua AIRS and Aura MLS combined water vapor profiles are used for the observed sensitivity. The least-squares linear regression lines are drawn, with correlations and regressions slopes marked.

14

Centennial global LvdP/dTs (W m−2K−1)

2.2 correlation = 0.55

s

2.0

l f

1.8

o

1.6

1.4

q p

h

c e

m

b

r ta n d u v w k OBS.

1.2 0

1 2 3 −2 −1 Interannual global LvdP/dTs (W m K )


Supplementary Figure 13. Relationship between interannual and centennial global-mean precipitation sensitivity to surface temperature. Centennial LvdP/dTs scattered against interannual LvdP/dTs. Each model is represented by a lowercase letter. The observation-based interannual LvdP/dTs with the 95% confidence level is marked in gray shading. The ensemble model means for the 20 models and the five better-performing models are shown in solid circles and black cross, respectively. The least-squares linear regression line and correlation coefficient between the x-axis and y-axis variables are shown.

15

GPCP

CMAP

3

3

(b) 2

1

1

LvdP (W m−2)

LvdP (W m−2)

(a) 2

0 -1 -2

0.2

-1 -2

Correlation = 0.46 Slope = 2.71 +/-0.90

-3 -0.3 -0.2 -0.1 -0.0 0.1 dTs (K)

0

0.3

Correlation = 0.09 Slope = -0.55 +/-1.04

-3 -0.3 -0.2 -0.1 -0.0 0.1 dTs (K)

0.2

0.3

Supplementary Figure 14. Observed global-mean precipitation sensitivity to surface temperature. (a) GPCP and (b) CMAP global-mean precipitation anomalies scattered against surface temperature anomalies for the period of 1995-2005. The least-squares linear regression lines are drawn, with correlations and regressions slopes marked. The CMAP precipitation sensitivity is not used due to large uncertainty.

16

(b) 4

s 3

g 2

ht f op r q n w jl e m c

ba

1

correlation = 0.50 0

Centennial dOLR/dTs (W m−2K−1)

Temperature Mediated dOLR/dTs (W m−2K−1)

(a) 4

t 3

correlation = 0.59

s 2

p f n ob w e r hg m q c a l

1

0 0

2 4 6 Interannual dOLR/dTs (W m−2K−1)

0 1 2 3 4 Temperature Mediated dOLR/dTs (W m−2K−1)


Supplementary Figure 15. Relationships between interannual, temperature-mediated and centennial tropical-mean dOLR/dTs. (a) The temperature-mediated dOLR/dTs scattered against the interannual dOLR/dTs. (b) The centennial dOLR/dTs scattered against the temperaturemediated dOLR/dTs. Multi-model-means are marked in solid circles. The least-squares linear regression lines and correlation coefficient between the x-axis and y-axis variables are shown.

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Supplementary Discussion The dominance of longwave radiative control on precipitation sensitivity. The dominance of longwave radiation in controlling the global-mean precipitation change is remarkable. We find that the inter-model spread in global-mean dP/dTs is highly correlated with the model differences in global-mean dLWC/dTs (R = 0.94 for interannual and 0.84 for centennial rates, Supplementary Figure 1) and the latter is mainly driven by the outgoing longwave radiation (OLR) sensitivity (dOLR/dTs) at the top-of-atmosphere (TOA) (Supplementary Figure 1). Although the atmospheric column LWC is strongly enhanced through increased net downward surface longwave radiation (SLR = surface downward – upward longwave flux) when the surface warms, the model diversity in dLWC/dTs is not dominated by the differences in dSLR/dTs (Supplementary Figure 1). Treating OLR as the sum of clear-sky OLR (OLRclr) and longwave cloud radiative effect (CRElw), we find that the model spreads in dOLRclr/dTs and dCRElw/dTs are both correlated with that in dP/dTs with larger correlations between dCRElw/dTs and dP/dTs (R=0.74 for interannual and 0.77 for centennial rates, Supplementary Figure 1). Thus, it is reasonable to hypothesize that clouds play an important role in causing the model differences in dOLR/dTs and therefore dLWC/dTs, which governs the inter-model spread in dP/dTs. Model spreads in tropical-mean high cloud fraction sensitivity and longwave radiative sensitivities. Supplementary Figure 9 shows the simulated high cloud fraction sensitivity (dCF/dTs) in relation to various components of the longwave radiative sensitivities on interannual (blue) and centennial (red) time scales. The rates of dCF/dTs vary from −1.9% K−1 to 0.5% K−1 on the interannual time scale for the 22 AMIP models and from −0.87% K−1 to 0.62% K−1 for the 21 coupled models on the centennial time scale (CNRM_cm5 and INM_cm4 models are missing cloud fraction outputs). The multi-model-means are −0.7% K−1 for interannual and

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−0.2% K−1 for centennial time scales. The inter-model spread in dCF/dTs is highly correlated with that of dLWC/dTs on both time scales (correlation R = −0.61 and −0.55, respectively), but not with dSWA/dTs (R = −0.1 and 0.05 respectively, figure not shown). The correlations between dCF/dTs and dLWC/dTs largely result from the role of high cloud fraction in regulating dOLR/dTs. In comparison, the correlations between dCF/dTs and dSLR/dTs are less than 0.3 at both time scales (figure not shown). The inter-model spread in dCF/dTs is correlated with both model spreads in dOLRclr/dTs (R = −0.65 for interannual and R = −0.49 for centennial) and longwave component of cloud radiative effect (dCRElw/dTs) (R = −0.62 for both time scales), suggesting that the amount of high clouds governs not only longwave CRE, but also modulates the capacity of clear-sky LWC by changing the upper tropospheric dry and clear areas. High cloud fraction sensitivity in relation to ECS. We find that the correlations between dCF/dTs and equilibrium climate sensitivity (ECS) are not statistically significant, R = 0.19 for the 22 models on the interannual and R = −0.13 for the 20 available models on the centennial time scales (Supplementary Figure 10). This indicates that high cloud fraction sensitivity is not a dominant factor in driving the model discrepancy in ECS. Contribution of upper tropospheric water vapor to the longwave radiative feedback biases. We have analyzed the simulated upper tropospheric water vapor sensitivity to surface warming in the models and find all models capture the increase of upper tropospheric water vapor path (UTWVP) with surface temperature, at the rates between 9.2% K−1 and 15.6% K−1, approximately consistent with the Clausius-Clapeyron relation. The multi-model-mean is 11.9% K−1, higher than that derived from the combined AIRS and MLS water vapor observations, 9.6% ± 1.5% K−1 (Supplementary Figure 12), although within the AIRS and MLS data uncertainty of ~25%. All models (except CNRM_cm5) produce greater upper tropospheric moistening with

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surface warming than the observations. The CNRM_cm5 model has the largest decrease of high cloud fraction with surface warming (Figure 2a) and also the weakest upper tropospheric moistening (Supplementary Figure 12b). The moist biases in the rest of the models, consistent with relatively weak decreases of high cloud fraction (the correlation between the spreads in dUTWVP/dTs and dCF/dTs for the 13 models is 0.57), would contribute to the low biases in the magnitudes of dOLR/dTs. However, based on the calculations using the radiative kernelsError! Reference source not found.,Error! Reference source not found.

, we find that the ensemble-mean moist bias of 2%

K−1 in the upper troposphere would only contribute to a small fraction of the low bias in dOLR/dTs, on the order of 0.05 W/m2 K−1. In addition, the inter-model spread in dUTWVP/dTs has rather weak correlations with the spreads in dOLR/dTs, dOLRclr/dTs and dCRElw/dTs (R = −0.31, −0.23, −0.26, respectively) on the interannual time scale. Therefore, we conclude that the misrepresentation of dCF/dTs is a dominant source for the model spread in dOLR/dTs across the CMIP5 models and the moist bias in the upper troposphere associated with the muted high cloud shrinkage contributes only slightly to the low bias in the magnitude of dOLR/dTs. Determination of the observation-based interannual precipitation sensitivity. Two sets of observations are used to determine the best estimate of the interannual precipitation sensitivity. First, we obtain an OLR-constrained LvdP/dTs based on the approximately linear relationship between the model simulated interannual tropical-mean dOLR/dTs and global-mean LvdP/dTs and the CERES observed tropical-mean dOLR/dTs, i.e., the OLR-constrained LvdP/dTs = A⋅ (dOLR/dTs)CERES + B + ε, where A and B are the slope and intercept for the least squares regression across the models, respectively, and ε is the linear fitting residual. The statistical distributions of the slope and intercept for the regression between the modeled dOLR/dTs and

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LvdP/dTs are determined by 10000 bootstrap iterations with replacement. The resulting mean slope and intercept are 0.33 and 0.56, respectively. With the CERES dOLR/dTs at 3.8±0.4 W m−2 K−1, the mean value of the OLR-constrained LvdP/dTs = 0.33 × 3.8 + 0.56 = 1.8 W m−2 K−1 with the standard deviation of 0.1 W m−2 K−1. Assuming that LvdP/dTs contains random variations not captured by the linear relation with dOLR/dTs, the statistics of the fitting residual ε is characterized by all the models’ fitting residuals, which yield a standard deviation of 0.39. Thus, the OLR-constrained LvdP/dTs has a mean of 1.8 W m−2 K−1 and a standard deviation of 0.4 =

0.39 2 + 0.12 W m−2 K−1. Hence, the value of the OLR-constrained LvdP/dTs at the 95% confidence level (within two times of the standard deviation) is 1.8 ± 0.8 W m−2 K−1. Second, we compute the interannual precipitation sensitivity directly from the least squares regression of the GPCP precipitation onto the HadCRUT4 surface temperature for the period of 1995 to 2005. The 5-month running averaging is applied onto the de-seasonalized anomalies. This gives the GPCP LvdP/dTs at 2.7±0.9 W m−2 K−1. Third, we choose the overlapped range of the two observational measures of the interannual LvdP/dTs, 1.8-2.6 W m−2 K−1 as the best estimate of the observation-based short-term precipitation sensitivity at the 95% confidence level (Figure 4). Significance tests for the correlations in the study. For correlation coefficients involving 21 models, the 2-sided student-t test requires R ≥ 0.433 for the 95% significance level and R ≥ 0.558 for the 99% significance level. Hence, all the correlations relevant to our conclusions are statistically significant at the 95% level and in many cases at 99% significance level.

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