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1 doi: /nature12434 A statistical blind test The real data of T max, T min, precipitation, solar radiation time series were extracted from 100 pixels in CRU TS3.1 datasets from 1982 to 2009; and a pseudo NDVI time series was constructed based on Equation (1) with pre-made slopes similar we analyzed from the real NDVI data. NDVI = a*t max + b*t min + c*p + d*rs + random error (Eq. 1) In Equation (1), a, b, c, d are the pre-made slope parameters, and T max, T min, P (precipitation) and Rs (solar radiation) are CRU TS3.1 observations (all variables detrended). Also the magnitude of the random error was similar as that in the real NDVI data. We then applied the full regression to the pseudo NDVI data with real T max, T min, P and Rs data to extract the regressed slope for each variable. Among the 100 test pixels, using the full regression method for pseudo-ndvi vs. T max, T min, P and Rs, the sign of the retrieved slope for T max from the pseudo NDVI data was found to be different from the pre-made slopes in only 6% pixels (7% of the pixels in the case of T min ). In contrast, using the reduced regression of pseudo-ndvi vs. T max, P and Rs, and T min, P and Rs, the sign of the retrieved slope for T max from the pseudo NDVI data was found to be different from the pre-made slopes in 20% of the pixels (48% of the pixels in the case of T min ). This blind test shows that the full regression or partial correlation method used in our study correctly captures a relationship between NDVI and T max, T min if there is one. 1

2 Table S1. The percentage of area with significant partial correlations between growing season NDVI and each climate variable (maximum temperature (T max ), minimum temperature (T min ), precipitation, and solar radiation) over different regions of Northern Hemisphere (NH) vegetated area (mean annual NDVI>0.1), while all other climate variables are controlled for. The numbers in parentheses indicate percentage of area with significant positive partial correlations between growing season NDVI and each climate variable. Percentage of area with significant partial correlation between growing season Significance NDVI and climate variables Level Solar T max T min Precipitation radiation Boreal P< % (22%) 8% (3%) 8% (5%) 10% (5%) (>50 o N) P<0.1 32% (30%) 14% (5%) 14% (8%) 17% (9%) Temperate P< % (6%) 8% (3%) 17% (16%) 10% (6%) (25-50 o N) P<0.1 20% (10%) 15% (5%) 25% (23%) 16% (10%) NH P< % (15%) 8% (3%) 12% (9%) 10% (5%) (>25 o N) P<0.1 27% (22%) 15% (5%) 19% (14%) 16% (9%) 2

3 Table S2. Warming experiments results versus NDVI analysis in this study. Warming experiments sites information includes country, site name, latitude (Lat, o N), longitude (Lon, o E), elevation (Elev, m), vegetation type, mean annual temperature (MAT, o C), mean annual precipitation (MAP, mm), experiment study period (Period). The effects of Tmax and Tmin on vegetation growth in warming experiments are indicated by - (negative and insignificant), -- (negative and significant), + (positive and insignificant), ++ (positive and significant). The partial correlation coefficients between growing season NDVI and maximum temperature (Tmax) after controlling for growing season minimum temperature (Tmin), precipitation and solar radiation (R Tmax) and the partial correlation coefficients between growing season NDVI and Tmin after controlling for Tmax, precipitation and solar radiation (R Tmin) for each warming experiment location are shown in the last two columns. Country Site name Lat Lon Elev Vegetation type MAT MAP Period Diurnal temperature effects on vegetation growth Warming experiment NDVI analysis Tmax Tmin R Tmax R Tmin Denmark 1 Mols Shrubland N/A UK 1 Clocaenog Shrubland N/A Netherlands 1 Oldebroek Shrubland N/A Spain 1 Garraf Shrubland N/A China 2 Duolun Grassland Data from Beier, C. et al. Carbon and nitrogen cycles in European ecosystems respond differently to global warming. Sci. Total Environ. 407, (2008). 2. Data from Wan, S., Xia, J., Liu, W. & Niu, S. Photosynthetic overcompensation under nocturnal warming enhances grassland carbon sequestration. Ecology 90, (2009). 3

4 Table S3. Sensitivity of annual atmospheric CO 2 amplitude (AMP) at Point Barrow (BRW) and Mauna Loa (MLO) to changes in corresponding (from May to September for BRW station and from May to October for MLO station) T max and T min over a broad region surrounding each station by ±20 degrees of latitude. The same analysis as Fig. 2, but with ISCCP and NASA/GEWEX SRB solar radiation substituting CRU-NCEP solar radiation, with precipitation datasets from GPCP, GPCC, ref. S1 (WM09) and VPD substituting CRU TS3.1 precipitation (see Methods). The value in the parenthesis is the sensitivity of AMP to temperature as percentage. * indicates statistically significance at the 90% (P<0.1) level, and ** indicates statistically significance at the 95% (P<0.05) level. Period Sensitivity of AMP at BRW to temperature (ppm C -1 ) Period T max T min Sensitivity of AMP at MLO to temperature (ppm C -1 ) T max T min ISCCP ** (33%) -6.8** (-40%) (-1%) -0.1 (-1%) SRB ** (32%) -6.3** (-37%) (3%) -0.2 (-3%) GPCP ** (21%) -4.3** (-25%) (-15%) 1.0 (15%) GPCC ** (21%) -4.3** (-25%) (1%) 0.0 (-1%) WM * (17%) -3.6** (-21%) (-7%) 0.3 (5%) VPD * (22%) -3.3* (-19%) (10%) -0.8 (-12%) 4

5 Table S4. Sensitivity of corresponding season NCE in boreal (50-90 o N) and temperate (25-50 o N) regions (from May to September for boreal regions and from May to October for temperate regions) to changes in corresponding T max and T min. The same analysis as Fig. 3, but with ISCCP and NASA/GEWEX SRB solar radiation substituting CRU-NCEP solar radiation, with precipitation datasets from GPCP, GPCC, ref. S1 (WM09) and VPD substituting CRU TS3.1 precipitation (see Methods). * indicates statistically significance at the 90% (P<0.1) level, and ** indicates statistically significance at the 95% (P<0.05) level. Period Sensitivity of NCE in boreal regions to temperature (Pg C C -1 Period ) T max T min Sensitivity of NCE in temperate reigons to temperature (Pg C C -1 ) T max T min ISCCP * -2.1** * -1.7* SRB * -2.0** GPCP ** -1.8** GPCC ** -1.9** WM ** VPD * -1.2**

6 Figure S1. Spatial distribution of Pearson correlation coefficient (R) between growing season maximum temperature (T max ) and minimum temperature (T min ) (both T max and T max detrended). The tick label values of the color bars, R=±0.48, R=±0.37, R=±0.32 and R=±0.25 correspond to 1%, 5%, 10% and 20% significance levels, respectively. 6

7 Figure S2. Spatial distributions of the response of growing season (from April to October) NDVI to T max and T min in the Northern Hemisphere. Sensitivity of growing season NDVI to (a) T max and (b) T min by multiple linear regression ; Sensitivity of growing season NDVI to (c) T max and (d) T min by ridge regression. The sensitivity of growing season NDVI to changes in T max and T min was expressed as the slope from the multiple linear regression or ridge regression analysis using detrended growing season NDVI as dependent variable and the detrended growing season precipitation, solar radiation, T max, and T min as independent variables. a Sensitivity of growing season NDVI to T max by multiple linear regression c Sensitivity of growing season NDVI to T max by ridge regression b Sensitivity of growing season NDVI to T min by multiple linear regression d Sensitivity of growing season NDVI to T min by ridge regression 7

8 Figure S3. Same as Fig. 1, but the growing season is defined as May to October. 8

9 Figure S4. Same as Fig. 1, but the growing season is defined as May to September. 9

10 Figure S5. Same as Fig. 1, but the solar radiation was substituted by ISCCP solar radiation during the period

11 Figure S6. Same as Fig. 1, but the solar radiation was substituted by NASA/GEWEX SRB solar radiation during the period

12 Figure S7. Same as Fig. 1, but the precipitation was substituted by GPCP precipitation. 12

13 Figure S8. Same as Fig. 1, but the precipitation was substituted by GPCC precipitation. 13

14 Figure S9. Same as Fig. 1, but the precipitation was substituted by precipitation from ref. S

15 Figure S10. Same as Fig. 1, but the precipitation was substituted by VPD calculated from CRU TS

16 Figure S11. The response of interannual growing season (from April to October) NDVI to interannual changes in growing season maximum temperature (T max ) and minimum temperature (T min ) in the Northern Hemisphere for individual meteorological station. Daily T max / T min, precipitation data during the period were obtained from Global Surface Summary of Day (GSOD) datasets stored in National Climatic Data Center (NCDC) (ref. S2). In order to reduce uncertainties caused by short time period of observation, we considered only 1736 meteorological stations for which at least 20 years of data are available during the period Because there are few meteorological stations with measurement of shortwave radiation, the corresponding growing season shortwave radiation for each meteorological station was obtained from CRU-NCEP shortwave radiation. The corresponding NDVI for each meteorological station was extracted as the average of 3 by 3 pixels (8 8 km 2 resolution pixel) around each meteorological station location. 16

17 Figure S

18 Figure S12. Same as Fig. S11, but the corresponding growing season NDVI for each meteorological station was extracted as the average of 5 by 5 pixels around each meteorological station location. 18

19 Figure S13. (a) Spatial distribution of the partial correlation coefficients (R) between growing season (from April to October) NDVI and maximum temperature (T max ) after controlling for precipitation and solar radiation (all variables detrended); (b) Spatial distribution of partial correlation coefficients between growing season NDVI and minimum temperature (T min ) after controlling for precipitation and solar radiation (all variables detrended); (c) Spatial distribution of difference in partial correlation coefficients shown in a and b. The tick label values of color bars in a and b, R=±0.50, R=±0.39, R=±0.33 and R=±0.26 correspond to 1%, 5%, 10% and 20% significance levels, respectively. 19

20 Figure S14. The response of growing season NDVI to changes in growing season (from April to October) average (T mean ) of and difference (DTR) between maximum temperature (T max ) and minimum temperature (T min ) (T mean = (T max +T min )/2 and DTR = T max -T min ) in the Northern Hemisphere. (a) Spatial distribution of the partial correlation coefficients (R) between growing season NDVI and T mean after controlling for DTR, precipitation and solar radiation (all variables detrended); (b) Spatial distribution of the partial correlation coefficients between growing season NDVI and DTR after controlling for T mean, precipitation and solar radiation (all variables detrended). The tick label values of color bars in a and b, R=±0.51, R=±0.40, R=±0.34 and R=±0.27 correspond to 1%, 5%, 10% and 20% significance levels, respectively. 20

21 Figure S15. Same as Fig. 3, but the inversion-based NCE was substituted by an inversion of NCE ( ) with a climatology of model simulations of NCE (without any interannual variations) as prior information. Sensitivity of NCE to temperature (Pg C C -1 ) * ** Boreal T max Temperate T min 21

22 Figure S16. The response of atmospheric inversion model estimated growing season (May to October) net terrestrial CO 2 exchange (NCE) to changes in maximum temperature (T max ) and minimum temperature (T min ) in the Northern Hemisphere. Spatial distribution of sensitivity of growing season NCE to (a) T max and (b) T min; (c) Percentage of pixels with domain (positive pixels > 50% or negative pixels > 50%) partial correlation (all variables detrended) between growing season NCE and T max after controlling for T min, precipitation and solar radiation in each 5 C interval of mean annual temperature and 100 mm interval of mean annual precipitation climate space; (d) Percentage of pixels with domain partial correlation (all variables detrended) between growing season NCE and T min after controlling for T max, precipitation and solar radiation in each 5 C interval of mean annual temperature and 100 mm interval of mean annual precipitation climate space. The right color bars and the numbers in each interval climate space of c and d indicate the same as in Fig. 1c and d. The sensitivity of atmospheric inversion model estimated growing season NCE to changes in T max and T min was calculated using the same approach for estimating sensitivity of growing season NDVI in Fig. S2a and b. Positive value indicates increase in terrestrial carbon sink. 22

23 Figure S16. a Sensitivity of growing season NCE to T max c Statistics for partial correlation between growing season NCE and T max b Sensitivity of growing season NCE to T min d Statistics for partial correlation between growing season NCE and T min 23

24 Figure S17. Same as Fig. S16, but the growing season is defined as May to September. a Sensitivity of growing season NCE to T max c Statistics for partial correlation between growing season NCE and T max b Sensitivity of growing season NCE to T min d Statistics for partial correlation between growing season NCE and T min 24

25 Figure S18. Same as Fig. 1c and d, but for statistics of partial correlation between growing season top-soil water content (SWC) and maximum temperature (T max ) and minimum temperature (T min ). a Statistics for partial correlation between growing season SWC and T max b Statistics for partial correlation between growing season SWC and T min 25

26 Figure S19. Same as Fig. 4, but the growing season is defined as May to October. 26

27 Figure S20. Same as Fig. 4, but the growing season is defined as May to September. 27

28 Figure S21. Same as Fig. S2, but for growing season top-soil water content (SWC) during the period The sensitivity of growing season SWC to T max and T min is found in opposite direction in 79% and 58% of the pixels by multiple linear regressions, and by ridge regression, respectively. Furthermore, the areas with positive correlation between soil water content and T min is 59% by partial correlation (significant over 6% of the areas) and 50% by ridge regression, respectively. The observed positive correlation between T min and SWC, particularly over the boreal and wet temperate regions, could be partly attributed to a decrease in evapotranspiration driven by a decrease in vegetation photosynthetic activity (or leaf area index), since higher T min is generally accompanied by lower growing season NDVI over these regions (Fig. 1). a Sensitivity of growing season SWC to T max by multiple linear regression c Sensitivity of growing season SWC to T max by ridge regression b Sensitivity of growing season SWC to T min by multiple linear regression d Sensitivity of growing season SWC to T min by ridge regression 28

29 Figure S22. Spatial distribution of average number of days with available daily top-soil water content data per month during the growing season from 1988 to 2007 in the Northern Hemisphere. References S1. ts_2009.html (accessed January 20 th, 2013). S2. ftp://ftp.ncdc.noaa.gov/pub/data/gsod/ (accessed January 31 th, 2013). 29