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1 Letter In the format provided by the authors and unedited. SUPPLEMENTARY INFORMATION Sensitivity of atmospheric CO 2 growth rate to observed changes in terrestrial water storage Vincent Humphrey 1 *, Jakob Zscheischler 1, Philippe Ciais 2, Lukas Gudmundsson 1, Stephen Sitch 3 & Sonia I. Seneviratne 1 * 1 Institute for Atmospheric and Climate Science, ETH Zurich, Zurich, Switzerland. 2 Laboratoire des Sciences du Climat et de l Environnement, CEA CNRS UVSQ, Gif-sur-Yvette, France. 3 College of Life and Environmental Sciences, University of Exeter, Exeter, UK. * vincent.humphrey@env.ethz.ch; sonia.seneviratne@ethz.ch 2018 Springer Nature Limited. All rights reserved. NATURE

2 Supplementary Information Table 1. Dataset references and access information. Dataset name Short description Refs Data access GRACE monthly global water mass grids NETCDF RELEASE 5.0. Ver. 5.0 Trends in atmospheric carbon dioxide, National Oceanic & Atmospheric Administration, Earth System Research Laboratory (NOAA/ESRL) GRACE_REC WGHM version 2.2a IRR70_S GLDAS Noah Land Surface Model L4 monthly 0.25 x 0.25 degree V2.0 TRENDY Experiment, version 3, simulation S2 (no land use) FluxCom Initiative Multi-Source Weighted-Ensemble Precipitation (MSWEP) Global Precipitation Climatology Project (GPCP) - Monthly, Version 2.3 Climatic Research Unit (CRU) Time-Series (TS) Version 4.0 Berkeley Earth Multivariate ENSO Index (MEI) MODIS MCD12C1 land cover classification Water storage anomalies from satellite gravimetry Mean global carbon dioxide growth rates based on a global air measurement network Water storage anomalies from a statistical model trained with GRACE observations Terrestrial water storage anomalies from a global hydrological model Soil moisture and snow storage from a land surface model Soil moisture content and carbon fluxes from 10 DGVMs Water availability index and up-scaled carbon fluxes from 3 machine learners Precipitation product used in GRACE_REC Precipitation product based on gauge stations and satellite data Precipitation and temperature product based on weather stations Temperature dataset based on weather stations ENSO Index Land cover classes 38,39 41,42 15, , , dx.doi.org/ / TEMSC-OCL05 gmd/ccgg/trends/ dx.doi.org/ /ethz-b de/ / 7_GWdepletion disc.sci.gsfc.nasa.gov/ datacollection/ GLDAS_NOAH025_M_2.0.html The TRENDY v3 data are available from S.S. (s.a.sitch@exeter.ac.uk) upon reasonable request geodb/projects/home.php data/gridded/data.gpcp.html cru/data/hrg/ psd/enso/mei/ data/dataprod/mod12.php 1

3 Supplementary Information Table 2. List of some regularly updated monthly gridded GRACE datasets potentially suitable for carbon cycle applications (not intended to be comprehensive). Dataset name Method Spatial URL sampling GRCTellus Land (solutions from GFZ, CSR and JPL) Spherical harmonics 1 (grid) JPL Mascons Mascons 3 (equalarea) CSR Mascons Mascons 1 (equalarea) RL05_mascons.html GSFC Mascons Mascons 1 (equalarea) products.html Supplementary Information Table 3. Complete overview of considered time intervals (with number of available data points used in Figures 2, 4, Supplementary Information Figure 8 and 9, for yearly (y) and monthly (m) scales). Note that some months are occasionally not available for GRACE observations. If the overlap with CGR is less than 10 years, correlations are not reported. Dataset name All available years, excluding (main paper) Homogeneous time interval (Suppl. Information Fig. 8 & 9) CO 2 Growth Rate GRACE (y=15, m=158) (y=12, m=131) GRACE-REC (y=34, m=408) (y=12, m=144) WaterGAP (y=27, m=324) Less than 10 years overlap GLDAS2-Noah (y=28, m=336) Less than 10 years overlap TRENDY v (y=31, m=372) (y=12, m=144) FluxCom (y=31, m=372) (y=12, m=144) GPCP (y=34, m=408) (y=12, m=144) CRU (y=33, m=396) (y=12, m=144) Berkeley (y=34, m=408) (y=12, m=144) MEI (y=33, m=396) (y=12, m=144) 2

4 r(nee Water,W) r(nee Temp,T) r(nee Water,T) r(nee Temp,W) Correlation Supplementary Information Figure 1. Expanded version of Figure 4d. The water-driven NEE (NEE Water ) of a given model is correlated to its global mean soil moisture signal (blue bars), while the temperature-driven NEE (NEE Temp ) is correlated to global mean temperature (orange bars). This indicates an internal consistency between the global mean of a climatic driver and its associated NEE response. Full bars correspond to the different TRENDY models (CABLE, ISAM, LPJ, LPJ-GUESS, ORCHIDEE, VEGAS, VISIT) and empty bars to the different FluxCom machine learning algorithms (ANN, MARS and RF). 3

5 Supplementary Information Figure 2. Land cover classes. Derived from MODIS MCD12C1 land cover classification (Supplementary Information Table 1). 4

6 Supplementary Information Figure 3. Global water availability signal in TRENDY models, GRACE-REC and GRACE observations. Values in a) are standardized because models have very different amplitudes in terms of absolute values. b) R 2 between models and GRACE observations, evaluated over the period (with trends removed over that period). For a comparison between GRACE (blue) and GRACE-REC (light blue) time series, refer to Extended Data Figure

7 Supplementary Information Figure 4. Correlations between yearly regional mean TWS and global CGR by land cover type. Significant correlations (see Methods) are indicated by an asterisk. Land cover type from MODIS data (Supplementary Information Figure 2). 6

8 Supplementary Information Figure 5. Comparison between several GRACE products. Products can be accessed through the links listed in Supplementary Information Table

9 Supplementary Information Figure 6. Comparison between CGR IAV (as used in this paper) and IAV of the residual land sink (RLS) from the Global Carbon Project

10 Supplementary Information Figure 7. Same as Figure 2, but using yearly estimates of the residual land sink (RLS) from the Global Carbon Project Left panels are empty because there is no monthly CGR data available from the Global Carbon Project. 9

11 Supplementary Information Figure 8. Same as Figure 2 but restricting the analysis on the period (see Supplementary Information Table 3). Black crosses indicate that the correlation is not significant (see Methods). When the overlap with CGR is less than 10 years, correlations are not reported (here, this concerns WaterGAP and GLDAS2-Noah). 10

12 Correlation with temperature 1 a Observed CGR DGVM NEE FluxCom NEE Correlation with modeled water storage (for models) Correlation with observed water storage (for CGR) NEE Water NEE Temp b c Individual models Ensemble mean r(nee Temp,T) r(nee Water,W) Correlation Supplementary Information Figure 9. Same as Figure 4, restricting the analysis on the period (see Supplementary Information Table 3). The uncertainty intervals for the correlations with CGR (gray shading) are based on Supplementary Information Fig. 8. d 11

13 Supplementary Information Figure 10. Same as Figure 2 but including the years affected by the eruption of Mt. Pinatubo ( ). 12