## 3 Results  
### How Did Each Climate Component Control Simulated Trends in Global GPP? The effect of each climate component on the interannual variations of global GPP is shown in Figure 1. Under _S_control_, GPP kept increasing until around 2000 and then declined modestly until 2007. This trend is consistent with the results of shorter-term studies using the MODIS 17 algorithm [6,32]. For each climate variable analysis, only _S_vpd_ showed a consistent decreasing trend, while the other simulations all produced increasing trends in global GPP (Figure 1). These results suggest that land models solely relying on VPD may overestimate the reduction in GPP caused by water stress in 2000s. The cross-correlation coefficient matrix among the GPP time series produced by the different simulations is shown in Table 2. The GPP derived from the four climate variable simulations (_S_temp_, _S_vpd_, _S_precip_, and _S_srad_) did not correlate well with each other. The highest correlation was found between _S_temp_ and _S_precip_, but the Pearson coefficient is still low (r = 0.43). Thus, the high correlation between _S_clim_ and _S_precip_ can be simply explained with precipitation having the strongest influence on climate-driven GPP. \begin{table}
\begin{tabular}{l c c c c c c} \hline  & **LAI/FPAR** & **Temperature** & **VPD** & **Precipitation** & **Radiation** & **Model** \\ \hline _S\_control_ & x & x & x & x & x & \\ _S\_veg_ & x & & & & & \\ _S\_clim_ & x & x & x & x & & \\ _S\_temp_ & x & & & & & \\ _S\_vpd_ & & & x & & & \\ _S\_precip_ & & & & x & & \\ _S\_srad_ & & & & & x & \\ _S\_wo\_vpd_ & x & x & x & x & \(\Psi_{\rm VPD}=1\) \\ _S\_wo\_sm_ & x & x & x & x & \(\Psi_{\rm SM}=1\) \\ \hline \end{tabular}
\end{table} 
Table 1: Terrestrial Observation and Prediction System (TOPS) simulations naming convention. For each simulation, X indicates the variables allowed to vary while the climatology was used for the remaining variables. For the simulations with either \(\Psi_{VPD}=1\) or \(\Psi_{SM}=1\), the down regulation function of either Vapor Pressure Deficit (VPD) or soil moisture was set to 1 so to have no control on Gross Primary Production (GPP). _S_control_ was the GPP simulation with changing all the input variables. _S_veg_ was the simulation driven by only Leaf Area Index (LAI)/FPAR, and the trend of _S_veg_ was made from GIMMS 3g trend. _S_clim_ was the simulation driven by climate variables, and represented the GPP trend explained by climate variability. _S_temp_, _S_vpd_, _S_precip_, and _S_srad_ were driven by temperature, VPD, precipitation, and shortwave radiation, respectively. _S_wo_vpd_ and _S_wo_sm_ were simulation without VPD and soil moisture regulation, and thus represented models whose drought down-regulation were functions of soil moisture and VPD, respectively. Figure 1: Sensitivity tests of global Gross Primary Production (GPP) to the individual climate variables for the period 1982 to 2009. Each anomaly in global GPP was simulated with (**a**) control run (_S_control_) and changing, (**b**) temperature (_S_temp_), (**c**) Vapor Pressure Deficit (VPD) (_S_vpd_), (**d**) precipitation (_S_precip_), or (**e**) shortwave radiation (_S_srad_). The vertical grey stripes indicate the timing of the Multivariate ENSO (El Ni \(\tilde{\text{n}}\)–Southern Oscillation) Index (MEI) phases, with darker shades representing stronger El Ni \(\tilde{\text{n}}\) phases. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & _S\_elim_ & _S\_temp_ & _S\_vpd_ & _S\_precip_ & _S\_srad_ & **CO\({}_{2}\)** & **MEI** & **GISS** \\ \hline _S\_clim_ & - & 0.25 & 0.48 & 0.70 & 0.15 & –0.49 & –0.73 & –0.25 \\ _S\_temp_ & 0.25 & – & –0.39 & 0.43 & 0.37 & 0.29 & –0.35 & 0.55 \\ _S\_vpd_ & 0.48 & –0.39 & – & –0.21 & –0.35 & –0.69 & –0.04 & –0.87 \\ _S\_precip_ & 0.70 & 0.43 & –0.21 & – & 0.37 & 0.01 & –0.79 & 0.37 \\ _S\_srad_ & 0.15 & 0.37 & –0.35 & 0.37 & – & 0.18 & –0.19 & 0.41 \\ \hline \end{tabular}
\end{table}